This document summarizes a thesis on using genetic algorithms to optimize space trusses. It begins with background information on the thesis author and supervisors. It then discusses the importance of structural optimization to reduce weight while maintaining safety. The research objectives are outlined as developing a new approach to overcome drawbacks of classical optimization methods by using different design variables. The document provides details on the genetic algorithm approach and compares the proposed method to traditional techniques. Several case studies are presented to demonstrate applying the proposed approach to optimize benchmark space truss problems. Results are compared to other studies to validate the effectiveness of the method.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
Truss Analysis using Finite Element method pptanujajape
This document discusses the finite element analysis of trusses. It explains that truss elements can be determinate or indeterminate, and that joint displacements are unknown variables. It presents the formulation of the stiffness matrix for a truss element, including the nodal displacement vector and elemental stiffness matrix. It also discusses the transformation matrix used to relate local and global coordinate systems for truss elements, and how to assemble the global stiffness matrix for a truss from the elemental stiffness matrices.
Finite element method vs classical method 1manoj kumar
The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include:
- Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems.
- Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these.
- Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries.
- Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.
we select cantilever beam having I,C,T section and we select material cast iron, stainless steel, steel and analyze base upon modal and static analysis.we see here deformation,stress ,strain and based upon it we conclude.
Green composites are sustainable composite materials made from bio-polymers or polymers reinforced with bio-fibers to create strong, lightweight materials with natural resources. The main advantages of green composites are that they are recyclable and biodegradable. Polymer matrix composites consist of thermoset, thermoplastic, or elastomer matrices mixed with fibrous reinforcements. Fiber-reinforced polymer composites are used because they have low cost, are biodegradable, have good mechanical and thermal insulating properties. Wood plastic composites are an important green composite that provides durability without toxic elements by combining plant fibers with polymers.
The document describes 7 examples of designing steel frames using SAP2000. Example 1 analyzes a column using both frame and shell finite element models in SAP2000, finding the shell models more accurately consider shear flexibility. Example 2 analyzes a beam, with shell models again more accurate by including shear and local/distortional effects. Example 3 analyzes a beam-column, showing shell models provide more accurate buckling loads than formulas alone by including shear and joint geometry. Overall, the examples illustrate how SAP2000 tools can be used to both check and optimize steel frame designs according to Eurocode 3, and that shell models tend to provide more accurate analyses and results compared to frame models or formulas alone.
This document discusses the finite element method (FEM) for numerical analysis of engineering problems. It describes the general steps of FEM which include discretizing the domain into simple geometric elements, choosing interpolation functions, deriving the element stiffness matrices, assembling the matrices into a global system, applying boundary conditions, and solving for displacements/stresses. FEM allows for approximate solutions of complex problems involving various material properties, geometries, and loading conditions.
The document discusses design loads for structural elements. It introduces limit state design philosophy and different types of loads structures must withstand, including dead loads, live loads, snow loads and lateral loads. Load factors are applied to loads for ultimate and serviceability limit state design. Load paths and examples of load cases for different structural components are presented.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
Truss Analysis using Finite Element method pptanujajape
This document discusses the finite element analysis of trusses. It explains that truss elements can be determinate or indeterminate, and that joint displacements are unknown variables. It presents the formulation of the stiffness matrix for a truss element, including the nodal displacement vector and elemental stiffness matrix. It also discusses the transformation matrix used to relate local and global coordinate systems for truss elements, and how to assemble the global stiffness matrix for a truss from the elemental stiffness matrices.
Finite element method vs classical method 1manoj kumar
The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include:
- Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems.
- Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these.
- Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries.
- Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.
we select cantilever beam having I,C,T section and we select material cast iron, stainless steel, steel and analyze base upon modal and static analysis.we see here deformation,stress ,strain and based upon it we conclude.
Green composites are sustainable composite materials made from bio-polymers or polymers reinforced with bio-fibers to create strong, lightweight materials with natural resources. The main advantages of green composites are that they are recyclable and biodegradable. Polymer matrix composites consist of thermoset, thermoplastic, or elastomer matrices mixed with fibrous reinforcements. Fiber-reinforced polymer composites are used because they have low cost, are biodegradable, have good mechanical and thermal insulating properties. Wood plastic composites are an important green composite that provides durability without toxic elements by combining plant fibers with polymers.
The document describes 7 examples of designing steel frames using SAP2000. Example 1 analyzes a column using both frame and shell finite element models in SAP2000, finding the shell models more accurately consider shear flexibility. Example 2 analyzes a beam, with shell models again more accurate by including shear and local/distortional effects. Example 3 analyzes a beam-column, showing shell models provide more accurate buckling loads than formulas alone by including shear and joint geometry. Overall, the examples illustrate how SAP2000 tools can be used to both check and optimize steel frame designs according to Eurocode 3, and that shell models tend to provide more accurate analyses and results compared to frame models or formulas alone.
This document discusses the finite element method (FEM) for numerical analysis of engineering problems. It describes the general steps of FEM which include discretizing the domain into simple geometric elements, choosing interpolation functions, deriving the element stiffness matrices, assembling the matrices into a global system, applying boundary conditions, and solving for displacements/stresses. FEM allows for approximate solutions of complex problems involving various material properties, geometries, and loading conditions.
The document discusses design loads for structural elements. It introduces limit state design philosophy and different types of loads structures must withstand, including dead loads, live loads, snow loads and lateral loads. Load factors are applied to loads for ultimate and serviceability limit state design. Load paths and examples of load cases for different structural components are presented.
1. The stiffness method is used to analyze the beam by determining its degree of kinematic indeterminacy, selecting unknown displacements, restraining the structure, and generating a stiffness matrix.
2. A 4m beam with supports at 1.5m and 3m is analyzed using a stiffness matrix approach. The displacements selected are the rotations at joints B and C.
3. The stiffness matrix is generated by applying unit rotations at each joint and calculating the actions. This matrix is then used along with the applied loads in a superposition equation to solve for the unknown displacements.
Isoparametric formulation allows for more accurate modeling of curved boundaries by mapping regular element shapes from a natural coordinate system to the actual curved geometric shapes in the global coordinate system. This mapping technique revolutionized finite element analysis by reducing unnecessary stress concentrations compared to using only straight-edged elements. The document goes on to define isoparametric, superparametric, and subparametric elements, and explains the basic theorems and uniqueness conditions for valid mappings between coordinate systems. It also describes Gaussian numerical integration for assembling stiffness matrices in isoparametric finite element analysis and provides some illustrative numerical examples.
The document provides an overview of the history and basics of finite element analysis (FEA). It discusses how FEA was first developed in 1943 and expanded in the following decades. The basics section describes common FEA applications, basic steps which include converting differential equations to algebraic equations, element types, boundary conditions including loads and constraints, and pre-processing, solving, and post-processing steps. Key element types are also summarized.
A Picture Album of the Finite Element MethodRahul Leslie
FEM is still taught in some parts of the world as a dry subject: the faculty, after dealing with the Riley-Ritz, Galerkin’s and other numerical approaches, draws a small rectangle on the board, introduces it to the students as ‘this is an element’ and then quickly rushes into the derivations: polynomial representation, shape functions, strain energy equations, Gaussian quadrature, etc.
In those universities/colleges, the students might given a hands of experience in ANSYS or the like, for name sake, demonstrating the ‘plate with a hole’ sample (or the like, and may be a cantilever beam too), leaving the students unaware of the greater wider world of FEM (of course, unless the student is a web-miner, digging up and reading all those extra stuff, downloading some FE software himself, installing, and trying it out)
Here an effort is being made to present a “A Picture Album of the Finite Element Method”, so to say, which any FEM tutor can present to his class and introduce the range of applications that makes FEM such a wonderful tool, explaining each at his own capacity (which I’m confident of), before going into the dull ordeal of the underlying derivations. Such an introduction is sure to make the dull latter phase interesting to the students.
I’m also of the belief that hands of experience with an FEM package dealing with a range of problems, intending to give the student a deeper view into the versatility of FEM and the nearly unlimited things one can do with it makes it of interest enough, that I’m sure many of them will proclaim FEM to be ‘My hobby’ – at least some of the students.
Rahul Leslie
Jan ‘17
Pre-engineered steel buildings are designed and fabricated off-site using standardized structural components. They are lighter and more economical than conventional construction. The key components include tapered steel columns, rafters, purlins, girts, and sheet metal panels. Structural analysis and design are performed to calculate loads and optimize the frame based on factors like wind speed and seismic zone. Components are then erected on-site by connecting prefabricated pieces together using bolted joints.
1) The document discusses the basics of the finite element method (FEM), which involves dividing a structure into simple subdomains called finite elements connected at nodes.
2) FEM allows for the analysis of complex problems by replacing differential equations with algebraic equations at nodes. This is done using shape functions to interpolate values within an element.
3) The document compares FEM to other numerical methods like the finite difference method, noting advantages of FEM include better accuracy with fewer elements and the ability to model curved boundaries and nonlinear problems.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is determined based on the loads applied, including axial load only, symmetrical beam loading, or loading in one or two bending directions. Links are included to prevent bar buckling. Examples show how to design column longitudinal reinforcement and links for different load cases.
This document provides an introduction and overview of a course on the theory of elasticity and plasticity. It discusses key topics that will be covered, including stress, strain, material behavior, elasticity problem formulation, energy principles, finite element methods, and plasticity. It outlines the organization of the course, including lecture materials made available online, instructors, office hours, grading based on homework, exams, and participation. Mathematical preliminaries are also introduced, including definitions and properties of scalars, vectors, tensors, and transformations between coordinate systems.
Tall Structures
Usually structure or building having height more than 80m is considered as a tall structure.
Generally tall structure may be defined as one that because of its height it is affected by lateral.
Classification: 1. Multi storeyedresidential building.
2. Multi storeyedcommercial building.
3. Tall chimneys.
4. Transmission Towers
5. Cooling towers
Prestressed Concrete
•Prestressis defined as a method of applying pre-compression to control the stresses resulting due to external loads below the neutral axis of the beam tension developed due to external load which is more than the permissible limits of the plain concrete.
Demolition
•The action or process of destroying(demolishing)the building or other structures.
•In congested area, in particular, the quality of demolition technique becomes an essential element which determines the success of revitalization of city.
•In addition to efficiency in demolition, strategies must be adopted to avoid noise, vibration and dust which affect the surrounding environment and there must be efficient disposal of waste products
This document provides information on masonry arch bridges, including their load transfer mechanisms, failure modes, inspection and maintenance, and strengthening. Key points discussed include:
1. Masonry arch bridges make up a significant portion of bridge infrastructure globally and in India. Their structural behavior depends on load flow and material properties.
2. Failure can occur due to the formation of hinges or sliding. Dismantling requires a systematic approach to avoid unbalanced forces.
3. Inspection focuses on defects in the arch barrel, spandrel walls, and other elements. Maintenance includes drainage improvements, crack repair, and monitoring.
4. Assessment of load capacity considers the contributions of the arch ring as
This document summarizes a seminar on top down construction presented at Ajay Kumar Garg Engineering College. The seminar introduced top down construction as an alternative to conventional bottom-up construction for large projects with time or space constraints. It described the methodology of top down construction including installing diaphragm walls and piles, excavating below roof slabs with structural supports, and progressively excavating and constructing underground levels while building above-ground levels simultaneously. Advantages of top down construction are shortened timelines from simultaneous work, more early operational space, and suitability for tall urban buildings. Disadvantages include higher costs and requiring skilled supervision.
Composite materials are engineered materials made from two or more constituent materials with different physical or chemical properties. The materials remain separate within the finished structure. One material, called the reinforcing phase, is embedded in the other material called the matrix phase. Common examples include concrete, where aggregates are embedded in cement, and fiberglass, where glass fibers are embedded in a polymer matrix. Composites are used because their overall properties are superior to their individual components. Some of the oldest composites include wattle and daub and concrete, and composites now make up common materials like asphalt, fiberglass, cement, and plywood.
Finite Element Analysis of Truss StructuresMahdi Damghani
The document discusses the finite element method (FEM) for analyzing truss structures. It begins with objectives of becoming familiar with FEM concepts for truss elements like stiffness matrices and assembling the global stiffness matrix. It then covers derivation of the element stiffness matrix in local coordinates, transforming it to global coordinates, and assembling the global stiffness matrix of the overall structure from the element matrices. Strain and stress calculations are also briefly discussed. Finally, an example problem is presented to demonstrate the FEM process for a simple truss structure.
Mivan shuttering is an aluminum formwork system originally developed in Europe that allows for fast and economical construction of buildings through cast-in-place concrete. It involves erecting large room-sized aluminum forms for walls and slabs that are poured with concrete in a single continuous pour. This results in monolithic structures that require no plastering and can be constructed at a rate of one floor per week. While it has been widely used internationally and offers benefits like reduced costs and timelines, Mivan technology has not been extensively utilized in India but has potential to help achieve goals around affordable housing construction.
This document provides a question bank for the Finite Element Analysis course ME6603 taught at R.M.K College of Engineering and Technology. It contains 180 questions divided into two parts - Part A (short questions) and Part B (long questions). The questions cover the main topics of the course including the basic concepts and procedure of finite element analysis, discretization, element types, weighted residual methods, potential energy approach, and boundary conditions. Commercial FEA software packages and steps to use them are also discussed. The document aims to help students prepare for exams by providing a variety of questions related to the finite element method and its applications in engineering problems.
The document provides an introduction to the finite element method (FEM) through lecture notes. It discusses the basic concepts of dividing a complex problem into smaller, simpler pieces called finite elements. The history and applications of FEM in engineering are described, including using FEM for structural analysis which involves dividing a structure into finite elements connected at nodes. The table of contents outlines the topics that will be covered in the subsequent chapters, such as bar, beam, plate, shell and solid elements, as well as structural dynamics, vibration and thermal analysis using FEM.
we select cantilever beam having I,C,T section and we select material cast iron, stainless steel, steel and analyze base upon modal and static analysis.we see here deformation,stress ,strain and based upon it we conclude.
This document provides an overview of the contents of the book "Advanced Structural Analysis with Finite Element Method" by Ashok K. Jain. The book covers various structural analysis methods including flexibility methods, stiffness methods, and the finite element method. It contains 15 chapters that discuss topics such as beams, frames, trusses, arches, plastic analysis, geometric and material nonlinearity, and the use of MATLAB for structural analysis. The book contains over 600 pages and provides 170 solved examples to illustrate the application of the covered structural analysis techniques.
2015, wbc, archila, h., measurement of the in plane shear moduli of bamboo-gu...Hector Archila
Iosipescu shear test method was applied to engineered bamboo strips that were previously thermo-hydro-mechanically modified.
The bamboo species used for this novel testing procedure was Guadua angustifolia Kunth.
The research was undertaken at the University of Bath with financial support from Amphibia Group.
This document describes the optimization of a hollow torsion rod design to meet requirements for shear stress, twist, and buckling. The design variables are the inner and outer diameters of the rod. The objective is to minimize mass. Genetic algorithm is used to solve this combinatorial problem involving rod type, material selection, and continuous diameters. The optimal design found has an inner diameter of 0.4833m, outer diameter of 0.4845m, rod type 1 made of beryllium material. All constraints are satisfied.
1. The stiffness method is used to analyze the beam by determining its degree of kinematic indeterminacy, selecting unknown displacements, restraining the structure, and generating a stiffness matrix.
2. A 4m beam with supports at 1.5m and 3m is analyzed using a stiffness matrix approach. The displacements selected are the rotations at joints B and C.
3. The stiffness matrix is generated by applying unit rotations at each joint and calculating the actions. This matrix is then used along with the applied loads in a superposition equation to solve for the unknown displacements.
Isoparametric formulation allows for more accurate modeling of curved boundaries by mapping regular element shapes from a natural coordinate system to the actual curved geometric shapes in the global coordinate system. This mapping technique revolutionized finite element analysis by reducing unnecessary stress concentrations compared to using only straight-edged elements. The document goes on to define isoparametric, superparametric, and subparametric elements, and explains the basic theorems and uniqueness conditions for valid mappings between coordinate systems. It also describes Gaussian numerical integration for assembling stiffness matrices in isoparametric finite element analysis and provides some illustrative numerical examples.
The document provides an overview of the history and basics of finite element analysis (FEA). It discusses how FEA was first developed in 1943 and expanded in the following decades. The basics section describes common FEA applications, basic steps which include converting differential equations to algebraic equations, element types, boundary conditions including loads and constraints, and pre-processing, solving, and post-processing steps. Key element types are also summarized.
A Picture Album of the Finite Element MethodRahul Leslie
FEM is still taught in some parts of the world as a dry subject: the faculty, after dealing with the Riley-Ritz, Galerkin’s and other numerical approaches, draws a small rectangle on the board, introduces it to the students as ‘this is an element’ and then quickly rushes into the derivations: polynomial representation, shape functions, strain energy equations, Gaussian quadrature, etc.
In those universities/colleges, the students might given a hands of experience in ANSYS or the like, for name sake, demonstrating the ‘plate with a hole’ sample (or the like, and may be a cantilever beam too), leaving the students unaware of the greater wider world of FEM (of course, unless the student is a web-miner, digging up and reading all those extra stuff, downloading some FE software himself, installing, and trying it out)
Here an effort is being made to present a “A Picture Album of the Finite Element Method”, so to say, which any FEM tutor can present to his class and introduce the range of applications that makes FEM such a wonderful tool, explaining each at his own capacity (which I’m confident of), before going into the dull ordeal of the underlying derivations. Such an introduction is sure to make the dull latter phase interesting to the students.
I’m also of the belief that hands of experience with an FEM package dealing with a range of problems, intending to give the student a deeper view into the versatility of FEM and the nearly unlimited things one can do with it makes it of interest enough, that I’m sure many of them will proclaim FEM to be ‘My hobby’ – at least some of the students.
Rahul Leslie
Jan ‘17
Pre-engineered steel buildings are designed and fabricated off-site using standardized structural components. They are lighter and more economical than conventional construction. The key components include tapered steel columns, rafters, purlins, girts, and sheet metal panels. Structural analysis and design are performed to calculate loads and optimize the frame based on factors like wind speed and seismic zone. Components are then erected on-site by connecting prefabricated pieces together using bolted joints.
1) The document discusses the basics of the finite element method (FEM), which involves dividing a structure into simple subdomains called finite elements connected at nodes.
2) FEM allows for the analysis of complex problems by replacing differential equations with algebraic equations at nodes. This is done using shape functions to interpolate values within an element.
3) The document compares FEM to other numerical methods like the finite difference method, noting advantages of FEM include better accuracy with fewer elements and the ability to model curved boundaries and nonlinear problems.
The document discusses reinforced concrete columns, including their functions, failure modes, classifications, and design considerations. Columns primarily resist axial compression but may also experience bending moments. They can fail due to compression, buckling, or a combination. Design depends on whether the column is short or slender, braced or unbraced. Reinforcement is determined based on the loads applied, including axial load only, symmetrical beam loading, or loading in one or two bending directions. Links are included to prevent bar buckling. Examples show how to design column longitudinal reinforcement and links for different load cases.
This document provides an introduction and overview of a course on the theory of elasticity and plasticity. It discusses key topics that will be covered, including stress, strain, material behavior, elasticity problem formulation, energy principles, finite element methods, and plasticity. It outlines the organization of the course, including lecture materials made available online, instructors, office hours, grading based on homework, exams, and participation. Mathematical preliminaries are also introduced, including definitions and properties of scalars, vectors, tensors, and transformations between coordinate systems.
Tall Structures
Usually structure or building having height more than 80m is considered as a tall structure.
Generally tall structure may be defined as one that because of its height it is affected by lateral.
Classification: 1. Multi storeyedresidential building.
2. Multi storeyedcommercial building.
3. Tall chimneys.
4. Transmission Towers
5. Cooling towers
Prestressed Concrete
•Prestressis defined as a method of applying pre-compression to control the stresses resulting due to external loads below the neutral axis of the beam tension developed due to external load which is more than the permissible limits of the plain concrete.
Demolition
•The action or process of destroying(demolishing)the building or other structures.
•In congested area, in particular, the quality of demolition technique becomes an essential element which determines the success of revitalization of city.
•In addition to efficiency in demolition, strategies must be adopted to avoid noise, vibration and dust which affect the surrounding environment and there must be efficient disposal of waste products
This document provides information on masonry arch bridges, including their load transfer mechanisms, failure modes, inspection and maintenance, and strengthening. Key points discussed include:
1. Masonry arch bridges make up a significant portion of bridge infrastructure globally and in India. Their structural behavior depends on load flow and material properties.
2. Failure can occur due to the formation of hinges or sliding. Dismantling requires a systematic approach to avoid unbalanced forces.
3. Inspection focuses on defects in the arch barrel, spandrel walls, and other elements. Maintenance includes drainage improvements, crack repair, and monitoring.
4. Assessment of load capacity considers the contributions of the arch ring as
This document summarizes a seminar on top down construction presented at Ajay Kumar Garg Engineering College. The seminar introduced top down construction as an alternative to conventional bottom-up construction for large projects with time or space constraints. It described the methodology of top down construction including installing diaphragm walls and piles, excavating below roof slabs with structural supports, and progressively excavating and constructing underground levels while building above-ground levels simultaneously. Advantages of top down construction are shortened timelines from simultaneous work, more early operational space, and suitability for tall urban buildings. Disadvantages include higher costs and requiring skilled supervision.
Composite materials are engineered materials made from two or more constituent materials with different physical or chemical properties. The materials remain separate within the finished structure. One material, called the reinforcing phase, is embedded in the other material called the matrix phase. Common examples include concrete, where aggregates are embedded in cement, and fiberglass, where glass fibers are embedded in a polymer matrix. Composites are used because their overall properties are superior to their individual components. Some of the oldest composites include wattle and daub and concrete, and composites now make up common materials like asphalt, fiberglass, cement, and plywood.
Finite Element Analysis of Truss StructuresMahdi Damghani
The document discusses the finite element method (FEM) for analyzing truss structures. It begins with objectives of becoming familiar with FEM concepts for truss elements like stiffness matrices and assembling the global stiffness matrix. It then covers derivation of the element stiffness matrix in local coordinates, transforming it to global coordinates, and assembling the global stiffness matrix of the overall structure from the element matrices. Strain and stress calculations are also briefly discussed. Finally, an example problem is presented to demonstrate the FEM process for a simple truss structure.
Mivan shuttering is an aluminum formwork system originally developed in Europe that allows for fast and economical construction of buildings through cast-in-place concrete. It involves erecting large room-sized aluminum forms for walls and slabs that are poured with concrete in a single continuous pour. This results in monolithic structures that require no plastering and can be constructed at a rate of one floor per week. While it has been widely used internationally and offers benefits like reduced costs and timelines, Mivan technology has not been extensively utilized in India but has potential to help achieve goals around affordable housing construction.
This document provides a question bank for the Finite Element Analysis course ME6603 taught at R.M.K College of Engineering and Technology. It contains 180 questions divided into two parts - Part A (short questions) and Part B (long questions). The questions cover the main topics of the course including the basic concepts and procedure of finite element analysis, discretization, element types, weighted residual methods, potential energy approach, and boundary conditions. Commercial FEA software packages and steps to use them are also discussed. The document aims to help students prepare for exams by providing a variety of questions related to the finite element method and its applications in engineering problems.
The document provides an introduction to the finite element method (FEM) through lecture notes. It discusses the basic concepts of dividing a complex problem into smaller, simpler pieces called finite elements. The history and applications of FEM in engineering are described, including using FEM for structural analysis which involves dividing a structure into finite elements connected at nodes. The table of contents outlines the topics that will be covered in the subsequent chapters, such as bar, beam, plate, shell and solid elements, as well as structural dynamics, vibration and thermal analysis using FEM.
we select cantilever beam having I,C,T section and we select material cast iron, stainless steel, steel and analyze base upon modal and static analysis.we see here deformation,stress ,strain and based upon it we conclude.
This document provides an overview of the contents of the book "Advanced Structural Analysis with Finite Element Method" by Ashok K. Jain. The book covers various structural analysis methods including flexibility methods, stiffness methods, and the finite element method. It contains 15 chapters that discuss topics such as beams, frames, trusses, arches, plastic analysis, geometric and material nonlinearity, and the use of MATLAB for structural analysis. The book contains over 600 pages and provides 170 solved examples to illustrate the application of the covered structural analysis techniques.
2015, wbc, archila, h., measurement of the in plane shear moduli of bamboo-gu...Hector Archila
Iosipescu shear test method was applied to engineered bamboo strips that were previously thermo-hydro-mechanically modified.
The bamboo species used for this novel testing procedure was Guadua angustifolia Kunth.
The research was undertaken at the University of Bath with financial support from Amphibia Group.
This document describes the optimization of a hollow torsion rod design to meet requirements for shear stress, twist, and buckling. The design variables are the inner and outer diameters of the rod. The objective is to minimize mass. Genetic algorithm is used to solve this combinatorial problem involving rod type, material selection, and continuous diameters. The optimal design found has an inner diameter of 0.4833m, outer diameter of 0.4845m, rod type 1 made of beryllium material. All constraints are satisfied.
This document summarizes a thesis that studied the seismic performance of perforated steel plate shear walls (P-SPSWs) designed according to Canadian seismic provisions. Finite element models were developed and analyzed using nonlinear time history analysis to evaluate response parameters of 4-, 8-, and 12-story P-SPSWs. Results showed that dynamic base shear was significantly higher than static design values. Dynamic storey shear in the perforated infill plates agreed reasonably well with code equations. Infill plates yielded fully at peak accelerations for some earthquakes, while boundary members remained elastic.
Adaptive Aperture Commissioning Presentation at 57th PTCOG Minglei Kang
This document summarizes the commissioning of an adaptive aperture (AA) on a HYPERSCAN particle therapy system. The AA aims to reduce penumbra size. Commissioning tests showed leaf leakage was reduced to ≤1.5% with AA upgrades. Leaf position accuracy was within 1mm. Penumbra size was reduced by 2mm for 227MeV beams, 7-8mm for 110MeV beams, and 10-13mm for 64MeV beams compared to without AA. The appropriate air gap between the patient and AA was critical for determining penumbra size. The AA was concluded to successfully reduce penumbra sizes compared to the previous system without adaptive collimation.
The International Journal of Mechanical Engineering Research and Technology is an international online journal published Quarterly offers fast publication schedule whilst maintaining rigorous peer review. The use of recommended electronic formats for article delivery expedites the process of All submitted research articles are subjected to immediate rapid screening by the editors consultation with the Editorial Board or others working in the field of appropriate to ensure that they are likely to be the level of interest and importance of appropriate for the journal.
The International Journal of Mechanical Engineering Research and Technology is an international online journal published by Quarterly offers fast publication schedule with whilst maintaining rigorous peer review. The use of recommended electronic formats for article delivery expedites and the process of All submitted research articles are subjected to immediate rapid screening by the editors consultation with the Editorial Board or others working in the field of appropriate to ensure that they are likely to be the level of interest and importance of appropriate for the journal.
This document compares the robustness of metaheuristic algorithms for steel frame optimization. It defines algorithmic robustness as the ability to consistently converge to low-cost designs regardless of variable space or initial starting point. The performance of these algorithms depends on balancing diversification, which searches new regions, and intensification, which draws from favorable regions. Several metaheuristic algorithms are tested on steel frame design problems of varying size and complexity. The results show that design driven harmony search is most robust, obtaining the lowest average weight and feasible solutions in all tests. Tabu search, harmony search and adaptive harmony search perform well as variable space increases. Further study with seismic loads is recommended.
The document discusses the design and analysis of injector nozzles for minimizing thrust loss. The objectives are to fabricate a thrust measurement system and measure thrust loss with different injector nozzle designs including ramped nozzles. Analytical calculations were performed using isentropic equations to estimate thrust ranges from 30.06N to 72.52N for various stagnation pressures and nozzle designs. Computational fluid dynamics analysis was also conducted using a shear stress transport turbulence model to simulate different nozzle designs and obtain thrust values for validation. Experimental thrust measurements will also be taken and compared to the analytical and computational results.
The document proposes a new hybrid conjugate gradient method called SW-A that combines the WYL and AMRI conjugate gradient methods. It presents the algorithm for SW-A and evaluates its performance on 18 standard unconstrained optimization test functions compared to WYL and AMRI in terms of number of iterations and CPU time. The results show that SW-A is able to solve all test problems while WYL solves 97% and AMRI solves 95%, demonstrating the effectiveness of the new hybrid method.
The document summarizes the dynamic analysis of the XYZ wellhead platform based on API RP2A WSD. It includes redesign details, main data used in the analysis such as soil properties, wave and earthquake information. It then covers the steps of the seismic, fatigue and load out analyses including determination of critical members. The maximum member and joint utilisation checks are reported. Load out analysis is also presented for the BOA BARGE 21/22 carrying containers. Final ballasting steps to achieve the desired draft are provided.
This document provides an overview of the design of beams and one-way slabs for flexure, shear, and torsion according to IS 456. It discusses key concepts like requirements for flexural reinforcement, minimum and maximum reinforcement limits, clear cover, deflection control, and selection of member sizes. The document also includes a worked example showing the step-by-step design of a rectangular reinforced concrete beam for flexure. Design checks are performed to check for strength and deflection requirements. Modules for the course will cover analysis and design of beams, one-way slabs, and reinforcement detailing in accordance with limit state design principles and code specifications.
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1. ZAGAZIG UNIVERSITY
FACULTY OF ENGINEERING
STRUCTURAL ENGINEERING DEPARTMENT
Optimization of Space Trusses Using Genetic
Algorithm
By
Osman Hamdy Osman Mohammed
B.Sc. in Civil Engineering, Faculty of Engineering, Zagazig University
Supervised by
Prof. Dr. Osman Shallan
Prof. of Structural Engineering - Head of Structural Engineering Department - Zagazig University
Prof. Dr. Atef Eraky
Prof. of Structural Engineering - Zagazig University
2015
Asst. Prof. Dr. Tharwat Sakr
Asst. Prof. of Structural Engineering - Zagazig University
2. 2
Optimization is a design process aims to save the
most valuable factors used where in structure
case it is the weight and that leads to safe :
STRUCTURAL OPTIMIZATION IMPORTANCE
4. The objective of this research is to develop a new approach to overcome drawbacks
of classical method by using untraditional variables
Study
objectives
Reduce No
of variables
and
chromosome
Length
Overcome
drawbacks
of using X-
section as a
variable
Over come
complexity of
making
Topology Opt.
simultaneousl
y With other
Opts.
THE OBJECTIVE OF THIS RESEARCH
5. GENETIC ALGORITHM
Genetic algorithm (GA) is an optimization tool that mimics the processes
of evolution theory through selection , crossover and mutation processes.
.
For instance, the following string consists of five genes, g1-g5, representing five design variables:
𝑁𝑜. 𝑜𝑓 𝐵𝑖𝑡𝑒𝑠 = 𝑙𝑜𝑔2
ximax
− ximin
∈ i
Where:
Xi
min is the lower bound of variable i;
Xi
max is the upper bound of variable i;
∈i is the desired precision in variable i;
In GA decimal values represented in binary coded string
The number of string (chromosome ) bites is dependent on
The number
of variables
need opt.
Min. and Max
limits for the
variable.
The required
precision.
No of object
subjected To
opt.
7. 7
Design Variables in Traditional
Technique
Members
cross sections
A1,A2,A3 …etc.
Shape
optimization
Free nodes
coordinates
x1,y1,z1,x2,y2,z2
…etc.
Topology
optimization
Members
distribution
1 for presence
0 for absence
TRADITIONAL VARIABLE
8. Design Variables in proposed approach
Nodal coordinates x, y and z
coordinates of variable nodes of the
truss
Nodal Deflection Dx, Dy and Dz
of non-support nodes of the truss
Chromosome sample for 10-bar plane truss
PROPOSED APPROACH VARIABLES
9. COMPARISONS BETWEEN NO. OF BITES FOR TRADITIONALAND
PROPOSED APPROACH
10-bar plane benchmark truss.
Optimization Variable Traditional Method Proposed Method
Shape 30 30
Size 80 ــــــــــــــــــــــــــ
Topology 10 ــــــــــــــــــــــــــ
Deflection ــــــــــــــــــــــــــ 48
Total 120 Bites 78 Bites
No. of possible solutions 1.32923E+36 3.02231E+23
As it is shown the number of possible solution has been reduced from
1.32923E+36 to 2.8823E+17 which represents approximately 100 % reduction.
10. 10
Proposed Versus
Traditional Approaches
X-sec. Random
Selection
X-sec. Long
Chromosome
Topology
complex.
Shorter
Chromosome
Reduction In No. of Variables
Defl. Limit is Lower than X-sec. limits
Defl. Related to nodes not members
Defl. Limits could be reduced 50%
Better
Solution
TRADITIONAL VARIABLE
11. Proposed Steps
Calculate each member length in the truss according to
proposed coordinates Li = ∆x2 + ∆y2 + ∆z 2
Calculate each member elongation according to proposed
deflections and coordinates
ΔL = ∆x Cosθx + ∆y Cosθy + ∆z Cosθz
Combining topology matrix by comparing the strain of each
member to the allowable strain of used material (all)
excluding members violate this condition
0.0 <
𝛥𝐿
L0
≤ εall
Making analysis for the proposed truss (topology and node
coordinate) considering A/L=constant to check the stability
and to get the local forces Fi in the truss members
Calculate the proposed cross section for each member Ai
= Max(
Fi
σall
,
FiLi
E∆Li
)
Finally making full analysis for the proposed truss (topology,
node coordinates and member cross sections ) to check stress
and deflection constrains
12. constraints
Stability
The proposed
truss must be
statically
stable
Constructability
No nodes
come over
other one
Member
stresses
All members
stresses not
exceed
allowable
stress
Nodal
displacements
All nodes
deflections
not exceed
allowable
deflection
13. Proposed approach is used to optimize the most
three famous benchmark problems through the
literature
25-bar space
truss
72-bar space
truss
STUDY CASES
14. A- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 10-BAR PLANE TRUSS .
F=445.374 KN (100 kips) & a=9.144 m (360 inches) , E = 68.95 Gpa (104 ksi) & ρ = 2
,768 kg/m3 (0.1 lb/in3) allowable stress=172.37 MPa (25 KSI) & allowable deflection =
50.8 mm (in2).
Structure of the10-bar truss
15. Optimized structure of the 10-bar
The optimized truss consist of 6-bars and 5-nodes where 4 bars are
removed. Coordinates of free Node P3 is (11.73 ; 6.4).
A- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 10-BAR PLANE TRUSS .
Max. actual deflection absolute value is 50.79 in Z- direction at node P2
which represent 99.98% of allowable deflection
Max. actual stress absolute value is 23.424 KSI at member M1 which
represents 93.70% of allowable stress
Element No.
Area
in2
m2
M1 6.045 0.004
M2 24.18 0.016
M3 19.18 0.012
M4 12.5 0.008
M5 21.08 0.014
M6 28.87 0.019
Cross Sections Area
16. Results of 10-bar plane truss compared with literature results.
Search Method
Optimization category
Weight (lbs.) Note
Size Shape Topology
Rajeev (1992) LINRM √
6249.00
Rajeev (1992) SUMT √
5932.00
Rajeev (1992) GRP-UI √
5727.00
Rajeev (1992) M-5 √
5725.00
Rajeev (1992) M-3 √
5719.00
Rajeev (1992) Genetic algorithm √
5613.84
Coello Coello (1994) Genetic algorithm √
5586.59
Rajeev (1992) CONMIN √
5563.00
Rajeev (1992) OPTDYN √
5472.00
Galante (1996) Genetic algorithm √ √ 5119.3
Kripakaran, Gupta and Baugh Jr. (2007) Hybrid search method. √ 5073.03
Li, Huang and Liu (2006) Particle swarm √ 5060.9
Su Ruiyi, Gui Liangjin, Fan Zijie (2009) Genetic algorithm √ √ 4962.07
Schmid (1997) Genetic algorithm √ √ 4962.10
Rajan (1995) Genetic algorithm √ √ 4962.1
Hajela and Lee (1995) Genetic algorithm √ √ 4942.7
Rajeev (1997) Genetic algorithm √ √ √ 4925.80 Two stages
Wenyan (2005) Genetic algorithm √ √ 4921.25
Deb and Gulati (2001) Genetic algorithm √ √ 4899.15
H. Rahami, A. Kaveh (2008) Force method √ √ 4855.2
Deb and Gulati (2001)
Genetic algorithm √ √ 4731.65
Const. constrain
not considered
Genetic algorithm √ √ 4899.15
Const. constrain
considered
This study Genetic algorithm √ √ √ 4762.1
A- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 10-BAR PLANE TRUSS .
17. B- SIZE OPTIMIZATION FOR 25-BAR SPACE TRUSS.
E =68.95 GPa (104 ksi) & ρ = 2,768 kg/m3 (0.1 lb/in3) allowable stress= 275.8 MPa (40
KSI) & allowable deflection = 8.9 mm (0.35 in).
Structure of 25-bar truss
Node Fx (lbs.) Fy (lbs.) Fz (lbs.)
1 1000 -10000 -10000
2 0 -10000 -10000
3 500 0 0
6 600 0 0
Loading case
18. Member Area (in2) Length (in) Weight (lb.)
1,2 0.1 75.00 0.75
2,6 0.3 130.50 3.92
1,5 0.3 130.50 3.92
2,3 0.3 130.50 3.92
1,4 0.3 130.50 3.92
1,6 3.6 106.80 38.45
1,3 3.6 106.80 38.45
2,5 3.6 106.80 38.45
2,4 3.6 106.80 38.45
6,5 1.7 75.00 12.75
3,4 1.7 75.00 12.75
5,4 0.1 75.00 0.75
6,3 0.1 75.00 0.75
4,9 0.8 181.14 14.49
5,8 0.8 181.14 14.49
6,7 0.8 181.14 14.49
3,10 0.8 181.14 14.49
6,9 0.4 181.14 7.25
5,10 0.4 181.14 7.25
4,7 0.4 181.14 7.25
3,8 0.4 181.14 7.25
5,9 3.6 133.46 48.05
6,10 3.6 133.46 48.05
4,8 3.6 133.46 48.05
3,7 3.6 133.46 48.05
Weight (lb.) 476.337
Max. actual deflection absolute value is 8.8002
mm at node 1 in Y direction which represents
98.87% of allowable deflection.
Max. actual stress absolute value is 124.17
MPA (18.01 KSI) in member 6,3 which
represents 45.02% of allowable stress.
B- SIZE OPTIMIZATION FOR 25-BAR SPACE TRUSS.
Resulted Cross section for 25-bar space truss
19. Results of sizing optimized 25-bar space truss compared with literature results.
Search Year Weight (lbs.)
Zhu 1986 562.93
Rajeev and Krishnamoor-thy 1992 546.01
Coello et al. 1994 493.94
Cao 1996 485.05
Erbatur et al. 2000 493.8
Lee et al. 2005 484.85
Camp 2007 484.85
Kaveh and Shojaee 2007 484.85
To˘gan and Dalo˘glu 2008 483.35
Talaslioglu 2009 485.9
Li et al. 2009 484.85
Tayfun Dede 2011 484.85
This study 476.337
B- SIZE OPTIMIZATION FOR 25-BAR SPACE TRUSS.
20. Shape, Sizing and Topology optimized 25-bar space truss
structure Model in Matlab .
Size, shape and topology optimized 25-bar space
truss literature results
Members and its groups
Wu [48] Wenyan [22] H. Rahami [23]
This study
1995 2005 2008
Cross section area (in2)
1,2 Group 1 0.1 Removed Removed Removed
2,6
Group 2
0.2 0.10 0.10 0.10
1,5 0.2 0.10 0.10 0.10
2,3 0.2 0.10 0.10 0.10
1,4 0.2 0.10 0.10 Removed
1,6
Group 3
1.1 0.90 0.90 0.90
1,3 1.1 0.90 0.90 0.90
2,5 1.1 0.90 0.90 0.90
2,4 1.1 0.90 0.90 0.90
6,5
Group 4
0.2 Removed Removed Removed
3,4 0.2 Removed Removed Removed
5,4
Group 5
0.3 Removed Removed Removed
6,3 0.3 Removed Removed Removed
4,9
Group 6
0.10 0.10 0.10 0.10
5,8 0.10 0.10 0.10 0.10
6,7 0.10 0.10 0.10 0.10
3,10 0.10 0.10 0.10 0.10
6,9
Group 7
0.2 0.10 0.10 0.10
5,10 0.2 0.10 0.10 0.10
4,7 0.2 0.10 0.10 0.10
3,8 0.2 0.10 0.10 0.10
5,9
Group 8
0.90 1.00 1.00 1.00
6,10 0.90 1.00 1.00 1.00
4,8 0.90 1.00 1.00 1.00
3,7 0.90 1.00 1.00 1.00
X4 41.07 39.91 38.7913 40.60
Y4 53.47 61.99 66.111 58.40
Z4 124.6 118.23 112.9787 123.80
X8 50.8 53.13 48.7924 56.20
Y8 131.48 138.49 138.891 139.20
Weight (lb.) 136.2 114.74 114.3701 114.171
C- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 25-BAR SPACE TRUSS.
Max. actual deflection absolute value is 8.8889 mm at node
1 in Y direction which represents 99.87% of allowable
deflection.
Max. actual stress absolute value is 119.62 MPA (17.35 KSI)
in member 2,5 which represents 43.73% of allowable stress .
Node 3,4,5& 6 are free in X,Y & Z Dir.
Node 7,8,9&10 are free in X& Y Dir.
21. C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
E = 68.95 Gpa (104 ksi) & ρ = 2 ,768 kg/m3 (0.1 lb/in3) & allowable stress=172.37
MPa (25 KSI) & allowable deflection = 6.35 mm (0.25 in). in x and y directions for
nodes = 17,18,19 and 20.
Structure of the 72-bar truss
23. Load Case 1 Max. actual deflection absolute value is 6.3 mm for node 17
in X and Y direction which represents 99.21 % of allowable
deflection.
Max. Stress absolute value is 111.6 MPA (16.186 KSI) for
member 55 which represent 64.74% of allowable stress.
C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
24. Load case 2 Max. Stress absolute value is 4.206/0.1733 = 24.27 KSI for
members 55, 56, 57 and 58 which represent 97.08% of
allowable stress.
Max. Stress absolute value is 0.99949 mm for nodes 17, 18, 19
and 20 in X and Y directions which represents 15.74 % of
allowable deflection.
C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
25. 25
Size optimization results for 72-bar space truss.
Search Year W (lb)
Venkayya 1971 381.2
Gellatly and Berke 1971 395.97
Schmit and Farshi 1974 388.63
Khan et al. 1979 387.67
Adeli and Kamal 1986 379.31
Cao 1996 380.32
Erbatur et al. 2000 383.12
Barbaso and Lemonge 2003 384.1341
Camp 2007 379.85
Perez and Behdinan 2007 381.91
Talaslioglu 2009 380.783
Tayfun Dede 2011 382.35
This study 375.77
C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
26. 26
Conclusion
Genetic algorithm
is considered as
suitable tool for
truss optimization.
The proposed
approach
succeeded to
reduce the
chromosome
length lead to
reduction in
calculation time
and effort.
Proposed
approach
succeeded to
overcome
traditional
drawbacks of x-
section variables
and topology
optimization
The results
obtained by using
the proposed
approach are
more optimized
when compared
with previous
research.
27.
28. Max. actual deflection absolute value is 50.79 in Z- direction at node P2 which
represent 99.98% of allowable deflection
Element No. Dimensions (mm)
Area Stress
% Stress of allowable
in2 m2 KSI Mpa
M1 200x200x5 6.045 0.004 23.424 161.5 93.70%
M2 400x400x10 24.18 0.016 -8.398 -57.9 33.60%
M3 260x260x12.5 19.18 0.012 -5.782 -39.9 23.10%
M4 180x180x12 12.5 0.008 -8.236 -56.8 32.90%
M5 350x350x10 21.08 0.014 6.8122 46.97 27.20%
M6 400x400x12 28.87 0.019 7.1245 49.12 28.50%
Max. actual stress absolute value is 23.424 KSI at member M1 which represents
93.70% of allowable stress
A- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 10-BAR PLANE TRUSS .
29. A- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 10-BAR PLANE TRUSS .
30. Member Area (in2) Length (in) Weight (lb.) Axial Force (lb.) Stress Abs. value (KSI)
1,2 0.1 75.00 0.75 -7.00 0.07
2,6 0.3 130.50 3.92 3,815.00 12.72
1,5 0.3 130.50 3.92 3,120.00 10.40
2,3 0.3 130.50 3.92 709.00 2.36
1,4 0.3 130.50 3.92 1,014.00 3.38
1,6 3.6 106.80 38.45 55,766.00 15.49
1,3 3.6 106.80 38.45 10,236.00 2.84
2,5 3.6 106.80 38.45 45,923.00 12.76
2,4 3.6 106.80 38.45 15,032.00 4.18
6,5 1.7 75.00 12.75 -6,731.00 3.96
3,4 1.7 75.00 12.75 3,113.00 1.83
5,4 0.1 75.00 0.75 -1,222.00 12.22
6,3 0.1 75.00 0.75 -1,801.00 18.01
4,9 0.8 181.14 14.49 743.00 0.93
5,8 0.8 181.14 14.49 -3,304.00 4.13
6,7 0.8 181.14 14.49 -4,616.00 5.77
3,10 0.8 181.14 14.49 1,350.00 1.69
6,9 0.4 181.14 7.25 -2,308.00 5.77
5,10 0.4 181.14 7.25 -1,652.00 4.13
4,7 0.4 181.14 7.25 372.00 0.93
3,8 0.4 181.14 7.25 675.00 1.69
5,9 3.6 133.46 48.05 -20,181.00 5.61
6,10 3.6 133.46 48.05 -28,191.00 7.83
4,8 3.6 133.46 48.05 4,539.00 1.26
3,7 3.6 133.46 48.05 8,243.00 2.29
Weight (lb.) 476.337 Max Stress 18.01
Max. actual deflection absolute value is 8.8002
mm at node 1 in Y direction which represents
98.87% of allowable deflection.
Max. actual stress absolute value is 124.17 MPA
(18.01 KSI) in member 6,3 which represents
45.02% of allowable stress.
B- SIZE OPTIMIZATION FOR 25-BAR SPACE TRUSS.
32. C- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 25-BAR SPACE TRUSS.
The size, shape and topology optimization simultaneously will be considered with same data
input and constrains. For shape optimization case the coordinates limits for free node number 4
in X-direction From 20 to 60 inch and in Y-direction from 40 to 80 inch and in Z-direction from 90
to 130 inch where another free nodes 3,5 and 6 are symmetric to node number 4. And for
support node number 8 in X-direction From 40 to 80 inch and in Y-direction from 100 to 140
where another support nodes 7,9 and 10 are symmetric to node number 8.
Max. actual deflection absolute value is 8.8889 mm at node 1 in Y
direction which represents 99.87% of allowable deflection.
Max. actual stress absolute value is 119.62 MPA (17.35 KSI) in member
2,5 which represents 43.73% of allowable stress .
Member Area (in2) Length (in) Weight (lb.) Axial Force (lb.) Stress Abs. value (KSI)
1,2 Removed
2,6 0.10 123.76 1.24 844.30 8.44
1,5 0.10 123.76 1.24 1,549.30 15.49
2,3 0.10 123.76 1.24 748.60 7.49
1,4 Removed
1,6 0.90 96.06 8.65 12,136.50 13.49
1,3 0.90 96.06 8.65 7,639.20 8.49
2,5 0.90 96.06 8.65 15,618.60 17.35
2,4 0.90 96.06 8.65 6,334.20 7.04
6,5 Removed
3,4 Removed
5,4 Removed
6,3 Removed
4,9 0.10 233.70 2.34 351.30 3.51
5,8 0.10 233.70 2.34 72.70 0.73
6,7 0.10 233.70 2.34 193.50 1.94
3,10 0.10 233.70 2.34 398.90 3.99
6,9 0.10 176.71 1.77 255.90 2.56
5,10 0.10 176.71 1.77 96.10 0.96
4,7 0.10 176.71 1.77 464.70 4.65
3,8 0.10 176.71 1.77 527.60 5.28
5,9 1.00 148.65 14.87 1,142.00 1.14
6,10 1.00 148.65 14.87 3,042.00 3.04
4,8 1.00 148.65 14.87 5,524.00 5.52
3,7 1.00 148.65 14.87 6,272.00 6.27
Weight (lb.) 114.171 Max Stress 17.35
33. C- SIZE, SHAPE AND TOPOLOGY OPTIMIZATION FOR 25-BAR SPACE TRUSS.
34. Load Case 1 Max. actual deflection absolute value is 6.3 mm for node 17 in
X and Y direction which represents 99.21 % of allowable
deflection.
Max. Stress absolute value is 111.6 MPA (16.186 KSI) for
member 55 which represent 64.74% of allowable stress.
C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
35. Load case 2 Max. Stress absolute value is 4.206/0.1733 = 24.27 KSI for
members 55, 56, 57 and 58 which represent 97.08% of
allowable stress.
Max. Stress absolute value is 0.99949 mm for nodes 17, 18, 19
and 20 in X and Y directions which represents 15.74 % of
allowable deflection.
C- SIZE OPTIMIZATION FOR 72-BAR SPACE TRUSS BENCHMARK .
Two pages :
Motivation : optimization worth more studies
Objectives : the most important is reaching more optimized solution with less computations through …………….