The solution of the shortest path problem on a surface is not only a theoretical problem to be solved in the field of mathematics, but also problems that need to be solved in very different fields such as medicine, defense and construction technologies. When it comes to the land specific, solution algorithms for these problems are also of great importance in terms of determination of the shortest path in an open area where the road will pass in the field of civil engineering, or route determination of manned or unmanned vehicles for various logistic needs, especially in raw terrains.
In addition, path finding problems in the raw terrains are also important for manned and unmanned ground vehicles (UGV) used in the defense industry. Within the scope of this study, a method that can be used for instant route determinations within sight range or for route determinations covering wider areas is proposed. Although the examples presented within the scope of the study are land-based, the method can be applied to almost all problem types of similar nature. The approach used in the study can be briefly described as the mechanical analysis of a surface transformed into a structural load bearing system based on mechanical analogies.
In this approach, the determination of the shortest path connecting two points can be realized by following the stress-strain values that will occur by moving the points away from each other or by following a linear line that will be formed between two points during the mechanical analysis. If the proposed approach is to be carried out with multiple rigid body dynamics approaches instead of flexible bodies mechanics, it can be carried out easily and very quickly by determining the shortest path between two points or by tracking the forces. However, the proposed approach in this study is presented by simulating examples of flexible bodies using the finite element method. The approach used in this study is based on the approaches presented in Altintas [144].
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Finite element analysis of underground metro tunnelsIAEME Publication
This document summarizes a study that performed finite element analysis of underground metro tunnels in Bangalore, India. It analyzed the tunnels' response to gravity, hydrostatic pressure, and blast-induced pressures from a hypothetical terror attack. The analysis used ANSYS to model the twin-tunnel system and surrounding soil, validating the results against theoretical solutions. It studied stresses, deformations, and effects on neighboring tunnels over time from a simulated pressure wave. The analysis also compared responses of different tunnel shapes and support systems under these loads.
This document summarizes a computational fluid dynamics (CFD) simulation of airflow around a simplified pickup van model. The study used a commercial CFD software to perform a 3D, steady-state simulation using the Reynolds-averaged Navier-Stokes equations and a k-ε turbulence model. The simulation was run at Reynolds numbers of 3x105 and results were validated against experimental wind tunnel data. Key findings included pressure and velocity distributions that matched experimental data well, indicating CFD can be an effective alternative to wind tunnel testing for pickup van aerodynamic analysis.
Simulation and Experiment Study of Flow Field of Flow channel for Rectangular...IJRESJOURNAL
ABSTRACT: Electrochemical Machining (ECM) is an effective method for machining the parts with the whole structure or special structure. Because the conventional machining methods are not suitable for processing these kinds of structures. In this work, taking electrochemical machining rectangular holes as the research objective, and analyzing the flow field characteristics of machined surface with three kinds of cathode channel structures. First discussing the working state of the ECM process and some equations to be complied with, then numerically simulating the models which have the same characteristics with design and simulation parameters, obtained the pressure contour and velocity contour on the machined surface. The simulation results indicated that the machining effect of long slot structure was not as good as that of arc slot and tilted slot structure, and few differences in machining effects were observed between the arc slot and tilted slot structure. A case study was presented to illustrate the effectiveness of the application of Computational Fluid Dynamics (CFD) in designing the flow field of cathode for ECM.
Comparison of MOC and Lax FDE for simulating transients in Pipe FlowsIRJET Journal
This document compares the method of characteristics (MOC) and Lax finite difference explicit (Lax FDE) methods for simulating transients in pipe flows. It develops numerical models using both MOC and Lax FDE to discretize the governing equations of fluid flow through a pipe. The models are implemented using data from a previous study to simulate pressure and discharge changes after rapid valve closure. The results show that Lax FDE provides more damping of pressure and discharge fluctuations compared to MOC. Therefore, the document concludes that Lax FDE is a better numerical method for calculating hydraulic transients in pipes.
This document describes a study that uses finite element analysis to calculate harmonic Green's functions of a homogeneous soil. Green's functions describe the dynamic response of a medium to concentrated forces and are important for modeling ground-borne vibrations from traffic and other sources. The study presents an axisymmetric finite element model of a 100m x 100m homogeneous soil domain with a concentrated force applied at the origin. An explicit time integration scheme is used to solve the elastodynamic equations over 0.24 seconds, capturing multiple periods of vibration from the 50Hz force. The model mesh size is optimized to balance accuracy near the force versus computational cost. This represents the first use of finite element analysis to directly compute soil Green's functions.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Finite element analysis of underground metro tunnelsIAEME Publication
This document summarizes a study that performed finite element analysis of underground metro tunnels in Bangalore, India. It analyzed the tunnels' response to gravity, hydrostatic pressure, and blast-induced pressures from a hypothetical terror attack. The analysis used ANSYS to model the twin-tunnel system and surrounding soil, validating the results against theoretical solutions. It studied stresses, deformations, and effects on neighboring tunnels over time from a simulated pressure wave. The analysis also compared responses of different tunnel shapes and support systems under these loads.
This document summarizes a computational fluid dynamics (CFD) simulation of airflow around a simplified pickup van model. The study used a commercial CFD software to perform a 3D, steady-state simulation using the Reynolds-averaged Navier-Stokes equations and a k-ε turbulence model. The simulation was run at Reynolds numbers of 3x105 and results were validated against experimental wind tunnel data. Key findings included pressure and velocity distributions that matched experimental data well, indicating CFD can be an effective alternative to wind tunnel testing for pickup van aerodynamic analysis.
Simulation and Experiment Study of Flow Field of Flow channel for Rectangular...IJRESJOURNAL
ABSTRACT: Electrochemical Machining (ECM) is an effective method for machining the parts with the whole structure or special structure. Because the conventional machining methods are not suitable for processing these kinds of structures. In this work, taking electrochemical machining rectangular holes as the research objective, and analyzing the flow field characteristics of machined surface with three kinds of cathode channel structures. First discussing the working state of the ECM process and some equations to be complied with, then numerically simulating the models which have the same characteristics with design and simulation parameters, obtained the pressure contour and velocity contour on the machined surface. The simulation results indicated that the machining effect of long slot structure was not as good as that of arc slot and tilted slot structure, and few differences in machining effects were observed between the arc slot and tilted slot structure. A case study was presented to illustrate the effectiveness of the application of Computational Fluid Dynamics (CFD) in designing the flow field of cathode for ECM.
Comparison of MOC and Lax FDE for simulating transients in Pipe FlowsIRJET Journal
This document compares the method of characteristics (MOC) and Lax finite difference explicit (Lax FDE) methods for simulating transients in pipe flows. It develops numerical models using both MOC and Lax FDE to discretize the governing equations of fluid flow through a pipe. The models are implemented using data from a previous study to simulate pressure and discharge changes after rapid valve closure. The results show that Lax FDE provides more damping of pressure and discharge fluctuations compared to MOC. Therefore, the document concludes that Lax FDE is a better numerical method for calculating hydraulic transients in pipes.
This document describes a study that uses finite element analysis to calculate harmonic Green's functions of a homogeneous soil. Green's functions describe the dynamic response of a medium to concentrated forces and are important for modeling ground-borne vibrations from traffic and other sources. The study presents an axisymmetric finite element model of a 100m x 100m homogeneous soil domain with a concentrated force applied at the origin. An explicit time integration scheme is used to solve the elastodynamic equations over 0.24 seconds, capturing multiple periods of vibration from the 50Hz force. The model mesh size is optimized to balance accuracy near the force versus computational cost. This represents the first use of finite element analysis to directly compute soil Green's functions.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Analysis of green’s function and surface current density for rectangular micr...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Analysis of green’s function and surface current density for rectangular micr...eSAT Journals
Abstract In this paper, Green’s function and surface current density for planar structure has been calculated. The approach makes use of the popular and rigorously used spectral domain full wave analysis method in conjunction with method of moment as numerical analysis tool. In present approach, boundary conditions are applied at patch metallization, which leads to integral equation with the involvement of green’s function in spectral domain, which includes the effect of dielectric, conductor loss, surface wave modes and space wave radiation. By applying Galerkin’s moment method integral equation are transformed to linear set of equations. Entire domain basis function is used to improve the efficiency of the solution. Keywords: Spectral domain full wave analysis, Green function, Galerkin’s moment method, Entire domain basis function, Surface current density.
This document summarizes research on MHD flow and heat transfer for an upper-convected Maxwell fluid over a stretching sheet with viscous dissipation. The researchers investigated the governing boundary layer equations of motion and heat transfer using similarity variables and solved them numerically. They found that a thinning of the boundary layer and drop in skin friction occurs for higher elastic numbers, agreeing with prior work. The objective was to examine the effects of elastic parameter β, magnetic parameter Mn, Prandtl number Pr, and Eckert number Ec on the temperature field above the sheet.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Comparative analysis of singularities of 3 prs and 3-prs parallel manipulator...eSAT Journals
Abstract
Grassmann-Cayley Algebra (GCA) is a symbolic approach to Plücker coordinates lines. It is used to write expressions for
geometric incidences in projective geometry.GCA gives a useful way to analyze mechanism singularity without algebraic
coordinate expression. Since it has great powerful tools for coordinate’s free representation, geometric interpretation and
singularity analyzing in real time computing, this method is implemented in the present research. The goal of this study is finding
the singularities conditions of 3-PRS Parallel Manipulators (PMs) based on GCA when the position of the actuators is firstly on
prismatic joints and secondly on revolute joints. Geometric method of reciprocal screw is used to formulate the Global Wrench
System (GWS) of the PMs. GWS represents the determinant of Jacobian matrix which rows are Plücker coordinate lines. The
degeneracy analysis of determinant of this matrix based on the dependency notion of Plücker coordinate lines is performed in
coordinate free expressions and provides double and single singularities conditions, respectively for3-PRS and 3-PRS PMs,
which contains all generals and specials cases. The keys elements of transition between the rows of Jacobian matrix and
singularity condition are the introduction of Plücker lines, superbrackets, join and meet operators. The vanishing points of these
superbrackets decomposition are analyzed to describe the singularity conditions associated with different motions. The results
indicate that for the 3-PRS and 3-PRS PMs, a common singularity occurs when the three constraints forces of the mobile platform
lie on the common plane and intersect at a unique point. It is suggested that both position and orientation of the actuator have to
be integrated in the conceptual design stage in order to optimize the rigidity frame of the mechanism.
Key Words: Singularity, 3-PRS Parallel Manipulators, Grassmann-Cayley Algebra, Projective space, Wrench graph.
A review of advanced linear repetitive scheduling methods and techniquesAsadullah Malik
ABSTRACT
Over the past two decades, significant attention has been focused on the development of advanced scheduling methods for repetitive/linear construction projects. Several approaches have been proposed by various research groups in order to solve specific problems in the scheduling of repetitive/linear construction projects such as high-rise buildings, bridges, pipelines, and highways. Some of these approaches represent milestones in the authors’ researches, and others provide a thorough solution implemented in computer software. This paper is a review of several articles related to this topic, which have been published in specialized journals since 1998. The solution methods for repetitive/linear scheduling problems are various, extending from simple graphical techniques to complex computational and optimization methods, such as genetic algorithms. The methods underlying the different solutions can be divided into three groups: exact, heuristic and metaheuristic. This paper presents an introduction into the different repetitive/linear scheduling problems, outlines the optimization methods proposed, classifies the different approach methods utilized and, finally, areas for future research are suggested.
Keywords: linear scheduling, construction management, repetitive units, optimization, genetic algorithms.
This document presents a study that uses gene expression programming (GEP) to develop a model for predicting sediment transport in sewers under no-deposition conditions. The study first reviews existing sediment transport equations developed using dimensional analysis and semi-experimental methods. It then describes using GEP to present six different models considering effective parameters on sediment transport. The best model is selected by comparing their performance on validation data not used in model development. The results show the GEP model achieves a root mean squared error of 0.12 and mean average percentage error of 2.56 on the training data, and 0.14 and 2.82 respectively on the validation data. This performance is compared to existing sediment transport equations.
This document discusses using MATLAB for optimizing the cost of bridge superstructures. It describes formulating the design of reinforced concrete T-beam girders as an optimization problem by defining design variables like slab depth and girder width, constraints like stress limits, and an objective function to minimize total cost. The Sequential Unconstrained Minimization Technique (SUMT) is used to solve the optimization problem, treating it as a series of unconstrained problems with penalty terms added. An example application optimizes girder costs for different spans and material grades, with results compared graphically showing optimized cost points.
Today, retrofitting of the old structures is important. For this purpose, determination of capacities for these buildings, which mostly are non-ductile, is a very useful tool. In this context, non-ductile RC joint in concrete structures, as one of the most important elements in these buildings are considered, and the shear capacity, especially for retrofitting goals can be very beneficial. In this paper, three famous soft computing methods including artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) and also group method of data handling (GMDH) were used to estimating the shear capacity for this type of RC joints. A set of experimental data which were a failure in joint are collected, and first, the effective parameters were identified. Based on these parameters, predictive models are presented in detail and compare with each other. The results showed that the considered soft computing techniques are very good capabilities to determine the shear capacity.
The document discusses using a machine learning algorithm called Multi Expression Programming (MEP) to develop a computational model for predicting the compressive strength of carbon fiber-reinforced polymer (CFRP) confined concrete. The model will be based on an extensive database of 828 experimental specimens, incorporating parameters like specimen diameter, height, unconfined concrete strength, CFRP layer thickness, and elastic modulus. MEP is described as an advanced evolutionary algorithm that can accurately model problems with unspecified complexities better than other techniques. The validation and performance of the proposed MEP model will be assessed by comparing predictions to experimental data and other existing strength models.
Changes in dam break hydrodynamic modelling practice - Suter et alStephen Flood
Abstract: Today, many organisations rely on hydrodynamic modelling to assess the consequences of dam break failure on downstream populations and infrastructure. The availability of finite volume shock-capturing schemes and flexible mesh schematisations in widely used software platforms imply that dam break modelling projects will be carried out differently in the future: Finite volume based platforms allow widespread application of shock-capturing methods and flexible mesh platforms can represent features in the study area more realistically and are more flexible thanks to varying mesh resolutions. Furthermore, the recent adoption of Graphics Processing Unit (GPU) technology in mainstream scientific and engineering computing will also significantly decrease computation times at relatively low cost.
This paper examines the application of finite volume, flexible mesh and GPU technologies to dam break modelling. One-dimensional (1D) modelling results are compared to those from two-dimensional (2D) finite difference and finite volume approaches. The results demonstrate that there are differences between modelling approaches and that the computational speeds of 2D simulations can be significantly reduced by the use of GPU processors.
Cost Optimization of Elevated Circular Water Storage Tanktheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Fault diagnosis using genetic algorithms and principal curveseSAT Journals
Abstract Several applications of nonlinear principal component analysis (NPCA) have appeared recently in process monitoring and fault diagnosis. In this paper a new approach is proposed for fault detection based on principal curves and genetic algorithms. The principal curve is a generation of linear principal component (PCA) introduced by Hastie as a parametric curve passes satisfactorily through the middle of data. The existing principal curves algorithms employ the first component of the data as an initial estimation of principal curve. However the dependence on initial line leads to a lack of flexibility and the final curve is only satisfactory for specific problems. In this paper we extend this work in two ways. First, we propose a new method based on genetic algorithms to find the principal curve. Here, lines are fitted and connected to form polygonal lines (PL). Second, potential application of principal curves is discussed. An example is used to illustrate fault diagnosis of nonlinear process using the proposed approach. Index Terms: Principal curve, Genetic Algorithm, Nonlinear principal component analysis, Fault detection.
This document analyzes the optimal sizing of elements in hinged portal frames under different static loads through an elastic analysis. It determines the minimum depth of each frame element based on the bending moment and axial force. The cost of the frame is proportional to its volume, while the benefit is proportional to the ratio of cross-sectional area to perimeter. Graphs of cost/benefit ratio against height-to-span ratio show minimum points for different load-to-material strength ratios. Tables present the optimal height-to-span ratios that correspond to minimum cost/benefit for different load cases. The analysis finds that the optimal ratio depends on the load characteristics and load-to-strength ratio.
Effect of Residual Modes on Dynamically Condensed Spacecraft StructureIRJET Journal
This document discusses the effect of residual modes on the fundamental frequencies of a condensed spacecraft structure. It presents the modeling and dynamic analysis of a spacecraft bus structure using finite element analysis. The structure is condensed using the Craig-Bampton method to reduce the degrees of freedom. Residual modes are then computed and included to recover data lost during condensation. The results show that including residual modes provides frequencies for the condensed structure that closely match those of the original full structure model, demonstrating the effectiveness of using residual modes for data recovery after structural condensation.
Numerical simulation of wind flow over complex terrain (yangon city)Zin Soul
This document describes a numerical simulation of wind flow over the complex terrain of Yangon City, Myanmar. The study uses the OpenFOAM computational fluid dynamics (CFD) toolbox to model wind flow for different directions using the k-epsilon turbulence model. Vertical wind speed profiles are simulated for various locations in Yangon and compared to measured field data. The results show the influence of Yangon's topography on wind directions. Accounting for more wind direction sectors could improve the vertical wind profile predictions. This research aims to help engineers better understand wind conditions for building design in Yangon.
This document provides an overview of isogeometric analysis (IGA), which uses Non-Uniform Rational B-Splines (NURBS) as basis functions for both geometry representation and numerical analysis. The key benefits of IGA are a tighter integration between CAD and analysis models, reducing the time from design to analysis. Recent developments and applications of IGA in various fields are discussed, as well as some computational aspects and challenges. Alternative geometry representations such as T-splines are also introduced to address some limitations of NURBS.
Flow Modeling Based Wall Element TechniqueCSCJournals
Two types of flow where examined, pressure and combination of pressure and Coquette flow of confined turbulent flow with a one equation model used to depict the turbulent viscosity of confined flow in a smooth straight channel when a finite element technique based on a zone close to a solid wall has been adopted for predicting the distribution of the pertinent variables in this zone and examined even with case when the near wall zone was extended away from the wall. The validation of imposed technique has been tested and well compared with other techniques.
This document summarizes a study that performed finite element analysis on an arch dam to determine stress concentrations and deflections. It provides background on arch dam types and traditional analysis methods. It then describes the finite element method and process, including discretization, element formulation, assembly, applying boundary conditions, and solving for deformations and stresses. The analysis used ANSYS software to model the dam and resolve the complex stress distributions in a more realistic way than other methods.
An Algebraic Multigrid Solver For Transonic Flow ProblemsLisa Muthukumar
This document summarizes an article about developing an algebraic multigrid solver for transonic flow problems. The key points are:
- The solver is based on the full potential equation, which can model subsonic, transonic, and supersonic flows.
- Algebraic multigrid methods are used instead of geometric multigrid to avoid dependencies on grid geometry.
- The discretization approach handles the mixed elliptic-hyperbolic nature of the governing equations across flow regimes.
- Applications to complex geometries on structured grids are demonstrated, achieving an order of magnitude reduction in residual per cycle.
This document summarizes a research article that proposes a new technique for more accurately identifying vehicle axle loads using data from an instrumented bridge. The technique modifies an existing iterative calculation method (updated static component technique) to include the measured bridge influence line, which contains information about the actual road surface conditions and measurement noise. Both numerical simulations and experimental tests using scaled bridge models were performed. The results showed the proposed technique more accurately identified moving axle loads compared to other conventional methods, especially in cases with rough road surfaces and high measurement noise levels. It was able to decrease identification errors and produce accurate results over a broader range of regularization parameter values.
This document describes a study that uses finite element analysis to develop an alternative method for analyzing rigid pavements. The study uses the commercial FEM software LUSAS to model a two-layer pavement system under single-wheel loading conditions. Results for flexural stresses are compared between plane strain and axisymmetric models, as well as with results from the Portland Cement Association design method. An example problem is presented to illustrate how FEM can be used for rigid pavement analysis and design.
Analysis of green’s function and surface current density for rectangular micr...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Analysis of green’s function and surface current density for rectangular micr...eSAT Journals
Abstract In this paper, Green’s function and surface current density for planar structure has been calculated. The approach makes use of the popular and rigorously used spectral domain full wave analysis method in conjunction with method of moment as numerical analysis tool. In present approach, boundary conditions are applied at patch metallization, which leads to integral equation with the involvement of green’s function in spectral domain, which includes the effect of dielectric, conductor loss, surface wave modes and space wave radiation. By applying Galerkin’s moment method integral equation are transformed to linear set of equations. Entire domain basis function is used to improve the efficiency of the solution. Keywords: Spectral domain full wave analysis, Green function, Galerkin’s moment method, Entire domain basis function, Surface current density.
This document summarizes research on MHD flow and heat transfer for an upper-convected Maxwell fluid over a stretching sheet with viscous dissipation. The researchers investigated the governing boundary layer equations of motion and heat transfer using similarity variables and solved them numerically. They found that a thinning of the boundary layer and drop in skin friction occurs for higher elastic numbers, agreeing with prior work. The objective was to examine the effects of elastic parameter β, magnetic parameter Mn, Prandtl number Pr, and Eckert number Ec on the temperature field above the sheet.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Comparative analysis of singularities of 3 prs and 3-prs parallel manipulator...eSAT Journals
Abstract
Grassmann-Cayley Algebra (GCA) is a symbolic approach to Plücker coordinates lines. It is used to write expressions for
geometric incidences in projective geometry.GCA gives a useful way to analyze mechanism singularity without algebraic
coordinate expression. Since it has great powerful tools for coordinate’s free representation, geometric interpretation and
singularity analyzing in real time computing, this method is implemented in the present research. The goal of this study is finding
the singularities conditions of 3-PRS Parallel Manipulators (PMs) based on GCA when the position of the actuators is firstly on
prismatic joints and secondly on revolute joints. Geometric method of reciprocal screw is used to formulate the Global Wrench
System (GWS) of the PMs. GWS represents the determinant of Jacobian matrix which rows are Plücker coordinate lines. The
degeneracy analysis of determinant of this matrix based on the dependency notion of Plücker coordinate lines is performed in
coordinate free expressions and provides double and single singularities conditions, respectively for3-PRS and 3-PRS PMs,
which contains all generals and specials cases. The keys elements of transition between the rows of Jacobian matrix and
singularity condition are the introduction of Plücker lines, superbrackets, join and meet operators. The vanishing points of these
superbrackets decomposition are analyzed to describe the singularity conditions associated with different motions. The results
indicate that for the 3-PRS and 3-PRS PMs, a common singularity occurs when the three constraints forces of the mobile platform
lie on the common plane and intersect at a unique point. It is suggested that both position and orientation of the actuator have to
be integrated in the conceptual design stage in order to optimize the rigidity frame of the mechanism.
Key Words: Singularity, 3-PRS Parallel Manipulators, Grassmann-Cayley Algebra, Projective space, Wrench graph.
A review of advanced linear repetitive scheduling methods and techniquesAsadullah Malik
ABSTRACT
Over the past two decades, significant attention has been focused on the development of advanced scheduling methods for repetitive/linear construction projects. Several approaches have been proposed by various research groups in order to solve specific problems in the scheduling of repetitive/linear construction projects such as high-rise buildings, bridges, pipelines, and highways. Some of these approaches represent milestones in the authors’ researches, and others provide a thorough solution implemented in computer software. This paper is a review of several articles related to this topic, which have been published in specialized journals since 1998. The solution methods for repetitive/linear scheduling problems are various, extending from simple graphical techniques to complex computational and optimization methods, such as genetic algorithms. The methods underlying the different solutions can be divided into three groups: exact, heuristic and metaheuristic. This paper presents an introduction into the different repetitive/linear scheduling problems, outlines the optimization methods proposed, classifies the different approach methods utilized and, finally, areas for future research are suggested.
Keywords: linear scheduling, construction management, repetitive units, optimization, genetic algorithms.
This document presents a study that uses gene expression programming (GEP) to develop a model for predicting sediment transport in sewers under no-deposition conditions. The study first reviews existing sediment transport equations developed using dimensional analysis and semi-experimental methods. It then describes using GEP to present six different models considering effective parameters on sediment transport. The best model is selected by comparing their performance on validation data not used in model development. The results show the GEP model achieves a root mean squared error of 0.12 and mean average percentage error of 2.56 on the training data, and 0.14 and 2.82 respectively on the validation data. This performance is compared to existing sediment transport equations.
This document discusses using MATLAB for optimizing the cost of bridge superstructures. It describes formulating the design of reinforced concrete T-beam girders as an optimization problem by defining design variables like slab depth and girder width, constraints like stress limits, and an objective function to minimize total cost. The Sequential Unconstrained Minimization Technique (SUMT) is used to solve the optimization problem, treating it as a series of unconstrained problems with penalty terms added. An example application optimizes girder costs for different spans and material grades, with results compared graphically showing optimized cost points.
Today, retrofitting of the old structures is important. For this purpose, determination of capacities for these buildings, which mostly are non-ductile, is a very useful tool. In this context, non-ductile RC joint in concrete structures, as one of the most important elements in these buildings are considered, and the shear capacity, especially for retrofitting goals can be very beneficial. In this paper, three famous soft computing methods including artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS) and also group method of data handling (GMDH) were used to estimating the shear capacity for this type of RC joints. A set of experimental data which were a failure in joint are collected, and first, the effective parameters were identified. Based on these parameters, predictive models are presented in detail and compare with each other. The results showed that the considered soft computing techniques are very good capabilities to determine the shear capacity.
The document discusses using a machine learning algorithm called Multi Expression Programming (MEP) to develop a computational model for predicting the compressive strength of carbon fiber-reinforced polymer (CFRP) confined concrete. The model will be based on an extensive database of 828 experimental specimens, incorporating parameters like specimen diameter, height, unconfined concrete strength, CFRP layer thickness, and elastic modulus. MEP is described as an advanced evolutionary algorithm that can accurately model problems with unspecified complexities better than other techniques. The validation and performance of the proposed MEP model will be assessed by comparing predictions to experimental data and other existing strength models.
Changes in dam break hydrodynamic modelling practice - Suter et alStephen Flood
Abstract: Today, many organisations rely on hydrodynamic modelling to assess the consequences of dam break failure on downstream populations and infrastructure. The availability of finite volume shock-capturing schemes and flexible mesh schematisations in widely used software platforms imply that dam break modelling projects will be carried out differently in the future: Finite volume based platforms allow widespread application of shock-capturing methods and flexible mesh platforms can represent features in the study area more realistically and are more flexible thanks to varying mesh resolutions. Furthermore, the recent adoption of Graphics Processing Unit (GPU) technology in mainstream scientific and engineering computing will also significantly decrease computation times at relatively low cost.
This paper examines the application of finite volume, flexible mesh and GPU technologies to dam break modelling. One-dimensional (1D) modelling results are compared to those from two-dimensional (2D) finite difference and finite volume approaches. The results demonstrate that there are differences between modelling approaches and that the computational speeds of 2D simulations can be significantly reduced by the use of GPU processors.
Cost Optimization of Elevated Circular Water Storage Tanktheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Fault diagnosis using genetic algorithms and principal curveseSAT Journals
Abstract Several applications of nonlinear principal component analysis (NPCA) have appeared recently in process monitoring and fault diagnosis. In this paper a new approach is proposed for fault detection based on principal curves and genetic algorithms. The principal curve is a generation of linear principal component (PCA) introduced by Hastie as a parametric curve passes satisfactorily through the middle of data. The existing principal curves algorithms employ the first component of the data as an initial estimation of principal curve. However the dependence on initial line leads to a lack of flexibility and the final curve is only satisfactory for specific problems. In this paper we extend this work in two ways. First, we propose a new method based on genetic algorithms to find the principal curve. Here, lines are fitted and connected to form polygonal lines (PL). Second, potential application of principal curves is discussed. An example is used to illustrate fault diagnosis of nonlinear process using the proposed approach. Index Terms: Principal curve, Genetic Algorithm, Nonlinear principal component analysis, Fault detection.
This document analyzes the optimal sizing of elements in hinged portal frames under different static loads through an elastic analysis. It determines the minimum depth of each frame element based on the bending moment and axial force. The cost of the frame is proportional to its volume, while the benefit is proportional to the ratio of cross-sectional area to perimeter. Graphs of cost/benefit ratio against height-to-span ratio show minimum points for different load-to-material strength ratios. Tables present the optimal height-to-span ratios that correspond to minimum cost/benefit for different load cases. The analysis finds that the optimal ratio depends on the load characteristics and load-to-strength ratio.
Effect of Residual Modes on Dynamically Condensed Spacecraft StructureIRJET Journal
This document discusses the effect of residual modes on the fundamental frequencies of a condensed spacecraft structure. It presents the modeling and dynamic analysis of a spacecraft bus structure using finite element analysis. The structure is condensed using the Craig-Bampton method to reduce the degrees of freedom. Residual modes are then computed and included to recover data lost during condensation. The results show that including residual modes provides frequencies for the condensed structure that closely match those of the original full structure model, demonstrating the effectiveness of using residual modes for data recovery after structural condensation.
Numerical simulation of wind flow over complex terrain (yangon city)Zin Soul
This document describes a numerical simulation of wind flow over the complex terrain of Yangon City, Myanmar. The study uses the OpenFOAM computational fluid dynamics (CFD) toolbox to model wind flow for different directions using the k-epsilon turbulence model. Vertical wind speed profiles are simulated for various locations in Yangon and compared to measured field data. The results show the influence of Yangon's topography on wind directions. Accounting for more wind direction sectors could improve the vertical wind profile predictions. This research aims to help engineers better understand wind conditions for building design in Yangon.
This document provides an overview of isogeometric analysis (IGA), which uses Non-Uniform Rational B-Splines (NURBS) as basis functions for both geometry representation and numerical analysis. The key benefits of IGA are a tighter integration between CAD and analysis models, reducing the time from design to analysis. Recent developments and applications of IGA in various fields are discussed, as well as some computational aspects and challenges. Alternative geometry representations such as T-splines are also introduced to address some limitations of NURBS.
Flow Modeling Based Wall Element TechniqueCSCJournals
Two types of flow where examined, pressure and combination of pressure and Coquette flow of confined turbulent flow with a one equation model used to depict the turbulent viscosity of confined flow in a smooth straight channel when a finite element technique based on a zone close to a solid wall has been adopted for predicting the distribution of the pertinent variables in this zone and examined even with case when the near wall zone was extended away from the wall. The validation of imposed technique has been tested and well compared with other techniques.
This document summarizes a study that performed finite element analysis on an arch dam to determine stress concentrations and deflections. It provides background on arch dam types and traditional analysis methods. It then describes the finite element method and process, including discretization, element formulation, assembly, applying boundary conditions, and solving for deformations and stresses. The analysis used ANSYS software to model the dam and resolve the complex stress distributions in a more realistic way than other methods.
An Algebraic Multigrid Solver For Transonic Flow ProblemsLisa Muthukumar
This document summarizes an article about developing an algebraic multigrid solver for transonic flow problems. The key points are:
- The solver is based on the full potential equation, which can model subsonic, transonic, and supersonic flows.
- Algebraic multigrid methods are used instead of geometric multigrid to avoid dependencies on grid geometry.
- The discretization approach handles the mixed elliptic-hyperbolic nature of the governing equations across flow regimes.
- Applications to complex geometries on structured grids are demonstrated, achieving an order of magnitude reduction in residual per cycle.
This document summarizes a research article that proposes a new technique for more accurately identifying vehicle axle loads using data from an instrumented bridge. The technique modifies an existing iterative calculation method (updated static component technique) to include the measured bridge influence line, which contains information about the actual road surface conditions and measurement noise. Both numerical simulations and experimental tests using scaled bridge models were performed. The results showed the proposed technique more accurately identified moving axle loads compared to other conventional methods, especially in cases with rough road surfaces and high measurement noise levels. It was able to decrease identification errors and produce accurate results over a broader range of regularization parameter values.
This document describes a study that uses finite element analysis to develop an alternative method for analyzing rigid pavements. The study uses the commercial FEM software LUSAS to model a two-layer pavement system under single-wheel loading conditions. Results for flexural stresses are compared between plane strain and axisymmetric models, as well as with results from the Portland Cement Association design method. An example problem is presented to illustrate how FEM can be used for rigid pavement analysis and design.
The document presents a study on using the NURBS-based isogeometric finite element method for free vibration and buckling analysis of laminated composite plates. Key points:
- An isogeometric finite element method is developed using NURBS basis functions for the approximation of deflection fields and geometry parameterization.
- The Lagrange multiplier method is used to enforce essential boundary conditions and an orthogonal transformation technique is applied to the discrete eigenvalue equation.
- Numerical examples are presented to demonstrate the accuracy of the proposed method for laminated composite plates with different boundary conditions, fiber orientations, and modes of vibration/buckling. Results are verified against analytical and other numerical solutions.
Optimal design of storm sewer networksBhanu Pratap
This document provides a review of past, present and future approaches to optimal design of storm sewer networks. It discusses how optimization techniques have been used since the 1960s to minimize construction costs while ensuring system performance, moving from linear programming and non-linear programming to more advanced techniques like dynamic programming and discrete differential dynamic programming. The document also outlines key advantages of optimal design over traditional design methods.
This document describes the implementation of a pressure-based incompressible flow solver in the open-source CFD code SU2 for wind turbine applications. The solver uses a second-order finite volume method on unstructured grids with implicit and explicit time integration schemes. Two turbulence models (SST k-ω and Spalart-Allmaras) are available. The pressure-velocity coupling is handled using a SIMPLE-like algorithm with Rhie-Chow momentum interpolation to avoid checkerboarding of pressure. Standard test cases are used to verify the solver, which is then applied to study the effect of a vortex generator on a turbulent boundary layer.
IRJET- Optimization of Fink and Howe TrussesIRJET Journal
This document describes research on optimizing the weight of different truss configurations, including double fink, triple fink, modified fink, double Howe, and triple Howe trusses. The optimization problem aims to minimize weight by treating cross-sectional areas as design variables, while satisfying stress, buckling, and deflection constraints. An improved sequential linear programming technique is used to solve the optimization problem. The process involves developing a C program for load calculation, using MATLAB for truss analysis, and applying an optimizer based on improved SLP to determine optimized cross-sectional areas. A parametric study is then carried out by varying span, height, and spacing to identify the most economical truss configuration under the given conditions.
This document provides details of a three-day Plaxis Advanced Course held in New Delhi, India from October 29-31, 2014. The course consisted of six sessions covering topics such as geotechnical finite element analysis, soil behavior modeling, deep excavation modeling, groundwater modeling, initial stresses/slope stability, and tunneling in rock. It lists the lecturers and course contents for each of the sessions.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document describes a methodology for modeling S-curves to forecast cost distribution over time for construction projects. It discusses three approaches to S-curve modeling: 1) Analyzing cost-time curves from literature, 2) Examining data from completed projects, and 3) Creating standard critical path models. The results from each approach are presented through mathematical expressions and diagrams. Finally, the results of the three approaches are integrated to develop final S-curves showing standard cost dynamics over time for different project types (buildings, tunnels, motorways). The proposed methodology can be used to forecast cost schedules during early project phases when detailed information is limited.
This document describes a methodology for modeling S-curves to forecast cost distribution over time for construction projects in early phases when detailed information is limited. Three approaches are used - analyzing literature, completed project data, and standardized critical path models - and their results are integrated into final S-curves for different project types (buildings, tunnels, motorways). The methodology allows cash flow forecasting for all project phases, especially early phases with limited information. The results provide cost scheduling principles under standard project organization conditions.
Integrated Methodology for the Seismic Design of Reinforced Embankments with ...IRJET Journal
This document presents an integrated methodology for the seismic design of reinforced soil embankments with berms (slopes with stepped terraces). The methodology is based on limit analysis and the quasi-static approach. It accounts for seismic loading conditions and considers cohesionless soils that deform plastically according to the Coulomb failure criterion. A software application was designed to implement this methodology for seismic design. It allows the user to define seismic hazard and design reinforced slopes based on potential failure planes. The results are compared to conventional methods and finite element analysis. Continuous slopes are also compared to slopes with berms, highlighting the advantages of composite geometries for high embankments.
The shortest not necessarily the best. other path on the basis of the optimal...eSAT Journals
The document presents an analysis of using the Dijkstra algorithm to find alternative shortest paths between nodes in a maritime traffic network. It begins by introducing the traditional method of using Dijkstra's algorithm to find the single shortest path and proposes removing edges from this path to find additional suboptimal paths. A numerical example with 29 edges between 8 islands is provided. The algorithm finds the shortest path between nodes 0 and 3, then this path is modified by removing edges to produce two additional paths. The document concludes that finding alternative paths can be done quickly using modern computers and is worth further research considering multiple criteria.
The shortest not necessarily the best other path on the basis of the optimal ...eSAT Publishing House
The document presents an analysis of using the Dijkstra algorithm to find alternative shortest paths between nodes in a maritime traffic network. It begins by introducing the traditional use of the Dijkstra algorithm to find the single shortest path. It then proposes removing edges from the optimal path one by one and recalculating the shortest path on the new graph to find alternative suboptimal paths. A numerical example with 29 edges between 8 islands is used to demonstrate the approach, finding 2 additional paths beyond the true shortest. The analysis suggests this could be a starting point for developing decision support systems for ship captains.
An Adaptive Moving Mesh Method For Two-Dimensional Relativistic Magnetohydrod...Scott Faria
This document describes an adaptive moving mesh method for solving two-dimensional thin film flow equations that include surface tension. The method uses moving mesh partial differential equations (MMPDEs) and mesh density functions to adaptively move the computational mesh based on solution characteristics like curvature. Numerical results show this r-adaptive moving mesh technique accurately captures the moving contact line and associated fingering instability with reduced computational effort compared to a fixed uniform mesh.
This document proposes algorithms using geometric functions like spirals and Lissajous curves to generate smoother trajectories for UAVs performing area coverage compared to the traditional lawnmower approach. The smoother trajectories are expected to reduce the time and energy required for area coverage by 22% and 30% respectively while still achieving at least 98% coverage. The algorithms will be implemented using ROS and experiments conducted in Gazebo simulation to evaluate the performance of the proposed methods versus the lawnmower approach.
Finite element method in solving civil engineering problemSaniul Mahi
The applications of Finite Element Method in solving Civil Engineering problem and the merits of using a finite element procedure over the other methods.
Similar to Finding shortest path on a terrain surface by using finite element method ( report no mcbucivileng.r 2022.1 ) (20)
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
Mechatronics is a multidisciplinary field that refers to the skill sets needed in the contemporary, advanced automated manufacturing industry. At the intersection of mechanics, electronics, and computing, mechatronics specialists create simpler, smarter systems. Mechatronics is an essential foundation for the expected growth in automation and manufacturing.
Mechatronics deals with robotics, control systems, and electro-mechanical systems.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELijaia
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Generative AI Use cases applications solutions and implementation.pdfmahaffeycheryld
Generative AI solutions encompass a range of capabilities from content creation to complex problem-solving across industries. Implementing generative AI involves identifying specific business needs, developing tailored AI models using techniques like GANs and VAEs, and integrating these models into existing workflows. Data quality and continuous model refinement are crucial for effective implementation. Businesses must also consider ethical implications and ensure transparency in AI decision-making. Generative AI's implementation aims to enhance efficiency, creativity, and innovation by leveraging autonomous generation and sophisticated learning algorithms to meet diverse business challenges.
https://www.leewayhertz.com/generative-ai-use-cases-and-applications/
Generative AI Use cases applications solutions and implementation.pdf
Finding shortest path on a terrain surface by using finite element method ( report no mcbucivileng.r 2022.1 )
1. MCBUCIVILENG.R-2022.1 MCBU CIVIL ENGINEERING REPORTS
Gökhan Altıntaş
Finding Shortest Path on a Terrain Surface by
Using Finite Element Method
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
Finding Shortest Path on a Terrain Surface
by Using Finite Element Method
Gökhan Altıntaş
MCBU CIVIL ENGINEERING REPORTS
MCBUCIVILENG.R-2022.1
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
Author(s)
Gökhan Altıntaş
Report Identification Code
MCBUCIVILENG.R-2022.1
Abstract
The solution of the shortest path problem on a surface is not only a theoretical problem to be solved in the
field of mathematics, but also problems that need to be solved in very different fields such as medicine,
defense and construction technologies. When it comes to the land specific, solution algorithms for these
problems are also of great importance in terms of determination of the shortest path in an open area where
the road will pass in the field of civil engineering, or route determination of manned or unmanned vehicles
for various logistic needs, especially in raw terrains.
In addition, path finding problems in the raw terrains are also important for manned and unmanned ground
vehicles (UGV) used in the defense industry. Within the scope of this study, a method that can be used for
instant route determinations within sight range or for route determinations covering wider areas is
proposed. Although the examples presented within the scope of the study are land-based, the method can
be applied to almost all problem types of similar nature. The approach used in the study can be briefly
described as the mechanical analysis of a surface transformed into a structural load bearing system based
on mechanical analogies.
In this approach, the determination of the shortest path connecting two points can be realized by following
the stress-strain values that will occur by moving the points away from each other or by following a linear
line that will be formed between two points during the mechanical analysis. If the proposed approach is to
be carried out with multiple rigid body dynamics approaches instead of flexible bodies mechanics, it can
be carried out easily and very quickly by determining the shortest path between two points or by tracking
the forces. However, the proposed approach in this study is presented by simulating examples of flexible
bodies using the finite element method. The approach used in this study is based on the approaches
presented in Altintas [144].
Keywords
Shortest Path, Path Finding, FEM, Analogy, Mechanical Analogy, Geodesic, Mesh
Generation
Pages
27
Report Information
Independent Research Project
Sponsor(s) / Funds / Support(s) -
Acceptance Date 10.01.2022
Acceptance & Review Committee (5)
Prof. Dr. A. Uğur Öztürk Prof. Dr. Ali Demir Prof. Dr. Erkan Doğan
Assoc. Prof. Dr.MehmetB. Bozkurt Dr. Abdülkerim Ergüt
Contact Addresses & Affiliations
Prof. Dr. Gökhan Altıntaş
Email(s): gokhanaltintas@gmail.com gokhan.altintas@cbu.edu.tr
Address: Manisa Celal Bayar University, Civil engineering Department., Engineering
Faculty
B Blok, Şehit Prof. Dr. İlhan Varank Kampüsü 45140, Yunusemre Manisa Turkey
Report Title
Finding Shortest Path on a Terrain Surface by Using Finite Element Method
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
Abstract
The solution of the shortest path problem on a surface is not only a theoretical problem to be solved in the
field of mathematics, but also problems that need to be solved in very different fields such as medicine,
defense and construction technologies. When it comes to the land specific, solution algorithms for these
problems are also of great importance in terms of determination of the shortest path in an open area where
the road will pass in the field of civil engineering, or route determination of manned or unmanned vehicles
for various logistic needs, especially in raw terrains.
In addition, path finding problems in the raw terrains are also important for manned and unmanned ground
vehicles (UGV) used in the defense industry. Within the scope of this study, a method that can be used for
instant route determinations within sight range or for route determinations covering wider areas is proposed.
Although the examples presented within the scope of the study are land-based, the method can be applied
to almost all problem types of similar nature. The approach used in the study can be briefly described as the
mechanical analysis of a surface transformed into a structural load bearing system based on mechanical
analogies.
In this approach, the determination of the shortest path connecting two points can be realized by following
the stress-strain values that will occur by moving the points away from each other or by following a linear
line that will be formed between two points during the mechanical analysis. If the proposed approach is to
be carried out with multiple rigid body dynamics approaches instead of flexible bodies mechanics, it can be
carried out easily and very quickly by determining the shortest path between two points or by tracking the
forces. However, the proposed approach in this study is presented by simulating examples of flexible bodies
using the finite element method. The approach used in this study is based on the approaches presented in
Altintas [144].
Keywords: Shortest Path, Path Finding, FEM, Analogy, Mechanical Analogy, Geodesic, Mesh Generation
5. P a g e | 4
Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
TABLE OF CONTENTS
TABLE OF CONTENTS 4
LIST OF FIGURES 55
INTRODUCTION 6
PROBLEM DEFINITION AND SOLUTION APPROACHING 7
ELEMENT SELECTION AND MESHES 9
Mesh Conversion Procedure 12
Comparison of meshes consisting of truss elements 14
GEOGRAPHICAL APPLICATION EXAMPLES 16
RESULTS 20
REFERENCES 21
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
LIST OF FIGURES
Figure 1: (a) Original terrain surface with nodes, (b) Stretched terrain surface and shortest path
region (based on stresses), (c) Shortest path region on undeformed terrain surface
9
Figure 2: (a) Real surface, (b) Discrete surface mesh with triangular elements, (c) Transformed
surface consisting of truss elements
11
Figure 3: (a) Surface with triangular elements, (b) Surface demonstrated by truss elements, (c)
Surface demonstrated by divided truss elements
12
Figure 4: Stress results of analogical models (undeformed presentations), (a) Model with
discretized truss elements, (b) Model with membrane elements (model has same number of nodes
of model (a))
13
Figure 5: Visual algorithm for mesh conversion in Grasshopper 3D 14
Figure 6: Element conversion, (a) Surface mesh generation fields for various strategies, (b)
Generated surface meshes, (c) Mesh of discrete truss elements converted from surface meshes
15
Figure 7: Shortest path solutions obtained from models with different mesh types 16
Figure 8: Shortest Path Solution on terrain by using surface elements 18
Figure 9: Shortest Path Solution on terrain by various elements and mesh structures 20
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
Introduction
Determination of the shortest path on a surface is not only a mathematical problem, but also one of the
important problems that need to be solved in areas different from each other. It is often used in determining
the shortest path between two points in the field [1-41], which is one of the typical application areas for the
solution of the shortest path problem on a surface. In addition, solving many problems with appropriate
geometry in different fields such as electrical engineering [40, 41, 42-47] and medicine [41-52] are also
among the problem types in this scope. However, in the literature, it is possible to say that the majority of
the publications in the context of the application areas are the publications on the applications [29-32, 40,
41, 45, 52-57] and algorithm developments [34-39, 43-46, 58-81] of navigation problems.
It is possible to divide the surfaces of interest into two, mainly discretized and analytical surfaces, within
the scope of the subject, where current studies continue without slowing down. Although the studies in the
scope of analytical surfaces, which is one of the pioneering studies of the subject in mathematical context
[82-93], still maintain their importance and actuality, studies dealing with discrete surfaces are increasingly
taking place in the literature due to the support of developments in the fields of computational mathematics
and engineering and their wide use in practice [94, 95]. In this context, it is possible to come across many
studies in the current literature on the solutions of polyhedral surfaces [12-14, 96-107] and some of the
studies within this scope have also focused on the exact solutions [108-112]. One of the biggest reasons
why current studies are carried out with polyhedral surface definitions is that it is much more applicable to
represent terrain and brain surface-like surface geometries, which are needed intensely for shortest path
problem solutions, with polyhedral definitions, despite the difficulty of converting them as a whole to an
analytically represented surface.
The issue is particularly important for navigation situations on unstructured, raw terrains. First of all, even
if the surface itself is handled as a discrete surface instead of analytical definitions, a much more difficult
problem has to be solved compared to the problem types on which road-dependent navigations are made.
The importance of solving such problems, in which there are much more possible routes between two points
in terms of mathematics, emerges as an increasing need. The reason for this situation is closely related to
the navigation needs of unmanned autonomous vehicles and robots as well as manned vehicles that move
dependent on grounds [2-11, 15-25, 27, 28, 47, 60-81, 113-115, 116-118]. All logistics needs for
commercial, agricultural or military purposes [116-118] can be considered in this context. Innovative
methods, some of which are quite different from each other, constitute an important part of the current
literature in the field of path planning [2-11, 47, 60-81, 115, 118-140]. The results obtained from these
studies and the algorithms created are not only important for medical problems where CT and MRI data are
used, and for path planning problems created by considering large areas where data such as GIS etc. are
used, but also important for path planning problems where environmental conditions can change
dynamically within the sight range. In addition, these studies are also necessary for the navigation needs of
piloted or autonomous Rovers that are sent not only on Earth but also locations out of Earth [20-28].
In this study, approaches that can be easily applied with the already widely used FEA programs or the built-
in physics engines of game engines are proposed. The approaches used can be compared to combinatorial
approaches from various angles or surface flattening approaches [141-143]. However, mechanical analogies
are based on different foundations from these approaches and thus offer a range of solutions in which new
and different approaches are included. In the case of using the mechanics of flexible bodies, it is possible to
reach the results quickly by using values such as strain, deformation, position and form, or by using criteria
such as position, form or the values of forces with the approaches of connected rigid body dynamics or
connected particle dynamics. It should be noted that mechanical analogies are not limited to those presented
in this study, but can easily be further diversified.
The approaches presented in this study can be implemented with many mechanical analysis and simulation
programs currently used in engineering and simulation fields. In this study, the results were obtained by
using the analyzes made with the finite element method in the examples presented.
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Report No: MCBUCIVILENG.R-2022.1
Release Year: 2022
Problem definition and solution approaching
The approach proposed in this study for the determination of the shortest path between two points on a
surface is an adapted version of the approach proposed by Altintas [144,145] for the solution of optimization
problems to be applied to surfaces. Before presenting visually supported applications about the presented
approach, briefing about the preferred approach in the study will make the reasons for making some choices
more understandable. Since mechanical analogies are essentially independent of mathematical techniques,
the presented approach can be applied to surfaces that are defined as analytical or discrete. However, in the
case of real-world problems, it is often not possible to express surfaces analytically. Expressing geometries
with discrete elements and polyhedral surfaces, as in frequently encountered path finding problems in
terrain, is a useful and adaptable approach to different problems. Although mechanical approaches are
independent of numerical methods, special care should be taken not to include conditions arising from
numerical methods as boundary conditions in the problem in some cases.
In order to apply the approach presented in this study appropriately to the problems, discrete surfaces were
studied and the finite element method was used as a numerical method in the realization of mechanical
simulations. Finite element method is a very suitable method for use in the mechanical modeling of discrete
surfaces, as in this study. However, by transforming the surfaces into models of rigid body dynamics and
connected particles dynamics with appropriate transformations, the models obtained can be simulated even
by game engines. Since the subject can also be discussed from a topological point of view, in order to use a
correct terminology, although the definition of "geodesic distance" is the same as the shortest path in most
geometries, the term shortest path was used in the study due to the existence of exceptional cases [108].
The types of problems to be dealt with in this study are the determination of the shortest distance between
two points on the same side of a surface geometry. The examples presented in the study are mainly about
finding the distance between two points, which isolates a certain part of the land from the terrain. The two
points in question can be two distant points on the terrain or two very close points within close region of
sight, in both cases the suggested approach can be used. The proposed mechanical analogy is based on the
principle of transforming the surface into a structure that can act like a fabric and obtaining the shortest path
between them by moving the two points apart (Figure 1), depending on various mechanical criteria.
Although the above recipe is simple, there are many points to be considered in practice. Before addressing
these issues, it may be useful to make a brief comment on Figure 1, which includes a simple example whose
result can be easily predicted even without analysis, in order to understand the introductory example. In
order to determine the shortest path between points A and B in Figure 1, a finite element model created in
such a way that the surface can behave like a fabric is used to simulate the situation where the points can be
moved apart from each other appropriately.
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Report No: MCBUCIVILENG.R-2022.1
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Figure 1: (a) Original terrain surface with nodes, (b) Stretched terrain surface and shortest path region
(based on stresses), (c) Shortest path region on undeformed terrain surface
(a)
(b)
(c)
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The result was obtained by following the changes in the stress, deformation and structural form that occurred
during the simulation. In fact, it is possible to reach a result if only one of these evaluation criteria is used
appropriately. The example, which was prepared for the visual intelligibility of the subject in a natural way,
was used in the simulation, with properties such as gravity and interaction, which would normally be more
appropriate not to be used. In the example in Figure 1, where gravity and interaction properties are used in
terms of visual intelligibility, they do not have considerable effects on the solution set, but using these two
properties in mechanical analogies may change the solution set and lead to erroneous results [146].
Due to the use of the finite element method as a numerical method, the results that can be obtained such as
stress and deformation can be affected by properties such as materials and geometry. Although these outputs
such as stress, deformation and displacement are evaluation criteria on the way to a solution, keeping them
within certain limits prevents the emergence of erroneous solutions. The finite element method, which is
the numerical method used in this study, was used in order to follow and comprehend the results of the
mechanical analogy in the easiest way. Whether it is the best and feasible method of investigation may be a
subject of separate criticism. However, it can be said that it is both possible and often faster and more
effective to obtain solutions with rigid body dynamics-based approaches without the need for the use and
management of outputs such as stress and deformation. The operations to be done in order to obtain the
solution set as precisely as possible are not only related to getting rid of unnecessary properties such as
interaction and gravity in analogy, but also closely related to other optional features of the approach to be
used in the numerical method.
The element types used in this study and the selections related to the meshes are also examined in sample
solutions because they have an effect on the results. It should be considered that an important part of the
information to be given about the configurations of finite element meshes in this section are the
arrangements that can be used in simulations based on rigid body dynamics.
Element selection and meshes
Speaking of using FEM as a numerical method, it can be thought that the most accurate element type that
can be used to represent a surface is the surface element types (shell, membrane, etc.). However, in the
problem of interest, the geometric form that should be considered in the first plan for a path expression
between two points is a line rather than a region to be presented by surface type elements. While using
surface elements in finite element analysis, it is also possible to obtain a solution set that will form a set of
linear lines, albeit indirectly, with post-processing operations. However, starting with the idea of finding a
region from the beginning as a solution set carries the risk of getting away from certainty, but this method
has its own advantages. For this reason, analyzes were made with different element types in the study in
order for the practitioners to choose the most suitable approach for them.
The source of the surface presented in Figure 2(a) can be a point cloud and data from another source and in
any case can be subjected to the triangularization process used in the calculations as seen in Figure 2(b). At
this stage, the result of the problem of interest can be obtained with surface elements using the stretching
process in mechanical analogy. In solutions obtained by using surface elements, it is possible to obtain
regional solution sets as seen in Figure 1 based on parameters such as stress or deformation. With this
approach, it can be possible to reduce the regions that make up the solution sets based on the numerical
values of the parameters to be used in the evaluation, or to construct the solution set with linear lines with
post-processing operations.
However, instead of dealing with post processing to reach solution sets consisting of linear lines, it is
possible to reach the solution with different element and mesh types. On the other hand, in order to make
an accurate analysis, constructing a model from surface elements, as used in the simulation in Figure 1, may
require many additional measures such as excluding some unnecessary stiffnesses and other unnecessary
properties from the simulation that are not needed at the core of the problem. In addition, it is certain that
the process of increasing the mesh density to increase the precision of the calculation will increase the
computational cost. But mesh density incrementation with element types low computational cost may offer
a more efficient approach. However, it may not be possible to realize this approach by remaining in the
option pool of the surface elements.
An approach in which the shortest path on a surface can be obtained as linear lines using element types with
low computational cost is presented below. This approach is implemented by using truss elements that can
rotate freely around the connection points instead of shell or membrane elements (Figure 2(b)) in modeling
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the surface of interest (Figure 2(c)).
Figure 2: (a) Real surface, (b) Discrete surface mesh with triangular elements, (c) Transformed surface
consisting of truss elements
With this approach, problems not only enable different element types of mechanical analogies to be solved,
but also turn into a problem type that can be expressed and solved with discrete mathematics and graph
theory. However, to speak again within the scope of mechanical analogies, there is an additional
improvement that needs to be made in order for the system to give appropriate results in the case of
converting the surface (Figure 3(a)) into a truss system (Figure 3(b)).
The exclusion of rigid triangular structures, which are likely to be found in truss systems obtained from
surface triangles, by adding additional hinges is important in terms of making a suitable mechanical
simulation [146]. In this context, joints should be added to the systems in order to eliminate rigid triangular
structures. For this purpose, as can be seen in Figure 3(c), each truss is divided into two with a joint at the
middle of the element [145].
(a)
(b)
(c)
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Figure 3: (a) Surface with triangular elements, (b) Surface demonstrated by truss elements, (c) Surface
demonstrated by divided truss elements
No matter what type of different element types (triangular, quadrilateral, honeycomb etc.) the surfaces are
represented, the surface meshes can be transformed into truss meshes by preserving the edges of surface
elements . Each of the aforementioned approaches has advantages in different aspects, these advantages and
disadvantages may also vary depending on problem types.
(a)
(b)
(c)
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Figure 4: Stress results of analogical models (undeformed presentations), (a) Model with discretized truss
elements, (b) Model with membrane elements (model has same number of nodes of model (a))
Looking at the solutions in Figure 4, the differences between truss elements (each divided) (Figure 4(a))
and solutions modeled with membrane elements (Figure 4(b)) can be easily seen. While the lines are
obtained as the solution set in the system composed of truss elements, a certain region emerges as the
solution set in the analysis made using the surface elements. Sharp turns seen in solution sets consisting of
linear lines and large area coverages seen in solution sets obtained by using surface elements are features
that can be arranged with post-processing if necessary in both approaches. Even increasing the number of
elements used in truss systems and changing the color scale of the solution set revealed by the surface
elements can also provide a distinctive observation of the solutions on the land.
Mesh Conversion Procedure
Any surface or volume meshes with point and edge definitions can be converted to a meshes with truss
elements. However, it is not always possible to make this conversion, which also brings about a change in
the mesh topology, directly with standard drawing programs or mesh editors. An algorithm (Figure 5)
created in Grasshopper 3D visual programming language [147] was used to obtain the transformed meshes
mentioned in this study. With this algorithm, the surface meshes were deconstructed based on their points
and edges, and they were reconstructed in the desired format and brought together.
(a)
(b)
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Figure 5: Visual algorithm for mesh conversion in Grasshopper 3D
The Visual Algorithm created in Grasshopper 3D, which is used for converting surface meshes (in file
formats as STL (Standard Tessellation Language), OBJ (Wavefront), VRML (Wavefront) formats) to
meshes consisting of divided truss elements and neutral file formats (such as IGES (Initial Graphics
Exchange Specification)) is presented in Figure 5. Of course, the file types that can be processed and the
approaches that can be used in conversions are not limited to those used in the study. Surface meshes (Figure
6 (b)) formed in various forms (Figure 6(a)) can be easily converted into meshes made of divided truss
elements (Figure 6(c)) with the algorithm developed for this study. Although the possibility of forming rigid
structures in the process of converting forms other than triangular surfaces into truss elements is not very
likely, truss elements are presented by being discretized again in the images in Figure 6. In other words,
regardless of whether the surface elements are quadrilaterals or triangulars, they are transformed into meshes
(Figure 6(c)) consisting of discretized truss elements with the Grasshopper 3D algorithm presented in Figure
5.
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Figure 6: Element conversion, (a) Surface mesh generation fields for various strategies, (b) Generated
surface meshes, (c) Mesh of discrete truss elements converted from surface meshes
Comparison of meshes consisting of truss elements
In the case of surface elements, it can be said that the increase in mesh intensity in shortest path analyzes is
important in terms of obtaining more sensitive results. However, when it comes to truss element meshes
derived from surface element meshes, increasing the number of truss elements by dividing has no effect on
the solution of the shortest path problem, except for the elimination of rigid triangular structures, due to the
preservation of the nodal points from the surface meshes. Unlike the evaluation of a pure mechanical
problem, analyzes using models of truss element meshes require increasing the intensity of the surface
meshes from which the existing truss elements are created, rather than dividing them within themselves, to
produce more accurate results.
Truss elements can offer solutions with lower computational costs than other element types, but as seen in
Figure 4(a), the path they offer as solutions are directly dependent on the mesh, and the path in the resulting
solution set may contain sharp direction changes. Increasing mesh intensity or using higher number of truss
elements to define the original surface with various methods can reduce the direction changes in the solution
sets, or by using post-processing techniques on original geometry paths can contain more realistic lines.
In this context, it will be useful to compare the solutions offered by meshes consisting of truss elements
created with several different approaches. In the sample prepared for this aim, there is a small hill on the
surface where the shortest path between the points at its two opposite corners is desired to be determined,
and the solutions obtained for the different meshes of the surface are presented in Figure 7. Structured
meshes with full and partial orthogonal properties were used in the first two solutions, and unstructured
meshes with different intensities were used in the others. In Figure 7(a), the lengths of the elements in the
mesh consisting of truss elements derived from surface with quadrilateral elements formed entirely of
orthogonal grids in the plan differ only in the hill region. Theoretically, the lengths of the paths consisting
of orthogonal lines between two points in the plane are the same, but the lengths of the paths are slightly
longer due to the slope only in the region around the hill and its immediate vicinity. For this reason, it is not
possible to obtain a single shortest path in the analysis made by stretching the numerical model between two
(a) (b)
(c)
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points.
In Figure 7(b), a surface mesh with a similar orthogonal grid formation in plan and consisting of isosceles
right triangle elements was transformed into a mesh of truss elements. Since the orientation of the diagonal
truss elements, which were not available in the previous system, is parallel to the direction connecting the
two points, it was quite easy to determine the shortest path. However, if the additional diagonal elements
were in the direction opposite to the current orientation, it would not have been possible to obtain the results
so well.
Deformed shape
Top view of undeformed
shape presentation with
stress conturs
Perpective view of undeformed shape
presentation with stress conturs
(a)
(b)
(c)
(d)
(e)
Figure 7: Shortest path solutions obtained from models with different mesh types
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In Figure 7(c), (d) and (e), the naturalness of the solution paths presented by the models with different
densities of unstructured meshes and their suitability to the original terrain increased depending on the
increase in mesh intensity. Regardless of mesh intensity in the limitations of above meshes, it can be said
that the performance of unstructured meshes is generally better in this problem. It should not be forgotten
that there are mesh formations produced with very different techniques, apart from the meshes presented in
Figure 7.
Geographical application examples
The applications that were presented as an example problem and that wanted to determine the shortest
distance between two points in a certain geographical region were also presented within the scope of the
study. In the first example below, in the determination of the shortest path, a solution was obtained as if
dealing with a geometry problem without considering obstacles, slopes, etc. that cannot be crossed for any
vehicle.
In the first example, the points where the shortest path between them is desired are located on both sides of
a valley, as seen in Figure 8 (a). The finite element model of the terrain, based on geographical data, consists
of triangular surface elements (Figure 8(b)). The solution region was determined based on the stress,
deformation and position values that occur by moving the points of interest of the finite element mesh away
from each other (Figure 8 (c)). Any of these evaluation criteria can be used alone as evaluation criteria in
flexible systems. The obtained shortest path solution set is presented in Figure 8(d) on the undeformed finite
element mesh. Since surface elements are used in the analysis, a region was found as the solution set, and if
desired, the region can be narrowed by refinement of the stress scale until it turns into a thin line or by a
more direct post-processing approach.
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Figure 8: shortest path solution on terrain by using surface elements
In Figure 9, although the terrain and points of interest in Figure 8 are the same, in the analysis to be made
in this part, some restrictions were created for the route that the shortest path between two points will pass
through. Unlike the situation in Figure 8, where the shortest path region can be found predictably easily
over a direct geographic connection, as in Figure 8, this example is set to show the constraints of the regions
where the route can pass during the determination of the shortest path and to present the solution that the
(a)
(b)
(c) (d)
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proposed approach can reveal. In this context, the terrain was flooded up to a certain height and the area
created by the regions that could be used in the solution was reduced. Similar to the explanation above, an
additional example of the practical applications of reducing the area that the route can pass through is the
situation where an unmanned land vehicle will encounter, such as certain slopes, swampy and bush areas,
which impede the progress of the vehicle.
With the proposed approach, the method to be used to solve such a problem is to remove the regions that
cannot be used as a route from the finite element mesh and use the remaining part in the analysis. The two
points in question are marked in Figure 9(a) and the solution is based on the finite element model created
by using membrane elements. For this purpose, as in the previous examples, the terrain was modeled with
membrane elements, allowing it to behave like a fabric, and the points were separated from each other until
a tense and linear line was formed between the two points, as seen in Figure 9(b). In Figure 9(b) the final
stress state of the simulation is superimposed on the original geometry of the terrain (Figure 9(c)) to see the
placement of the line on the ordinary state of the terrain, which may not be clearly distinguishable on the
deformed shape (Figure 9(c)). Due to the element type used, a region with a certain area connecting the two
points is determined as the region through which the shortrest path will pass, and if desired, the said region
can be further narrowed as mentioned before.
In Figure 9(d), it is determined by using a finite element model created with truss elements, as in Figure
4(a) and Figure 7, in order to determine the desired route with lower computational cost and linear lines
instead a region. As it can be seen more clearly from Figure 9(e), which is the close view image, since the
finite element mesh is created with the structured mesh technique, the solution line found, as in the previous
examples, is highly affected by the finite element mesh and is somewhat incompatible with the natural
surface of the land. This situation is clearly seen in Figure 7 in the study in which different meshes are
compared. In this context, additional analyzes were made using a model with a finite element mesh created
with the unstructured mesh technique in the region of interest. As can be clearly seen from Figure 9(d) and
Figure 9(e), the regions that cannot be used as route region were removed from the images in order to focus
on the results of the analyzes made using unstructured mesh (Figure 9(f), Figure 9(g)). When looking at the
results for the region, the close view of which is presented in Figure 9(f) and the close view in Figure 9(g),
although fewer elements are used, more suitable routes to the land surface were obtained compared to the
analyzes made using structured mesh.
As a striking point in the results, in Figure 9(d) and Figure 9(e), three alternative routes stand out in the
region on the left side of the land, and the middle one of these three routes offers the shortest path among
them, due to the fact that it has the biggest stress and deformation (not shown numerically). However, since
there is a very small distance difference between the other two alternative routes, they have not been
removed from the images in order to be seen as options that can be used on alternative routes for different
reasons.
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Figure 9: Shortest path solution on terrain by various elements and mesh structures
(c)
(d)
(a)
(b)
(f) (g)
(e)
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Results
In this study, various solutions based on mechanical analogies were proposed to find the shortest path
between two points on a surface. The finite element method was used in realizing the mechanical analogies
of flexible systems, and the results obtained by using various element types and meshes in the creation of
the finite element models used in the solutions were compared.
In analyzes using surface elements, there is a solution region through which the shortest path must pass,
depending on the surface properties, the mesh intensity, and the threshold values of the discriminating
parameters used to determine the solution set. Regional solution sets can be easily reduced to a linear lines
with post processing operations, but this study focuses directly on the results of primary analysis.
Another element type used in the analysis is truss elements, and it can be thought that the computational
cost of truss elements is lower than the surface elements. Meshes of truss elements can be converted from
various surface mesh types or constructed from data from various sources.
The results obtained show that the results obtained from the models in which truss elements are used in the
analyzes related to the determination of the shortest paths are highly affected by forms of the meshes. In the
comparative analyzes made in this context, it can be said that unstructured meshes generally perform better
than structured meshes, based on the samples within the scope of the study.
Although primary analyzes are included in this study, it is clear that solution sets consisting of linear lines
obtained by using truss elements can be made more suitable for the land by post-processing. It is obvious
that the sensitivity will increase with the increase of mesh intensity, valid for both the meshes consisting of
truss elements and surface elements. It should be noted that the increase in the intensity of mesh consisting
of truss elements depends on the increase in the mesh intensity of the surfaces from which they are derived.
Both models, in which surface elements and truss elements are used, have their own advantages and it is
possible to choose the most suitable one according to the application area. As suggested in Altintas [144],
the interaction property should not be used in the mechanical analogical model unless it is part of the original
problem. In this way, constraints that are not contained in the original problem are not included in the
problem. In the analyzes made with models created using truss elements, they were subjected to additional
discretization process in order to avoid the emergence of rigid triangular structures that could hinder the
appropriate results from being obtained [146].
The presented models, and especially the models consisting of truss elements, can be solved very quickly
not only with the finite element method, but also with simulations based on rigid body dynamics (connected
multiple rigid bodies etc.). In fact, such a procedure can theoretically be much faster and more effective than
the analysis used with the finite element method, but in this study, the finite element method was used in
order to include more mechanical parameters in the use of mechanical analogies and to understand the
subject on a mechanical basis. On the other hand, it is clear that the meshes consisting of truss elements
formed by the finite element method can also be solved by the methods of Graph theory. Considering the
issue as an optimization problem, the problem can be solved with a similar approach based on mechanical
analogy [146].
Finally, since the approaches presented in this report can be used with almost all current finite element based
engineering software, it is thought to be valuable not only theoretically but also for practitioners.
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