Verifications and Validations in Finite Element Analysis (FEA) using Advanced Scientific and Engineering Services AdvanSES Material characterization Fatigue Testing Strain Gauging Engineering Services Ansys Abaqus LS-Dyna MSC-Marc
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.
The document provides an overview of the finite element method (FEM). It explains that FEM is a numerical technique used to approximate solutions to partial differential equations that describe physical phenomena. It works by dividing a complex geometry into small pieces called finite elements that can then be solved using a computer. The method was developed in the 1950s and has since become widely used in engineering fields to simulate systems like heat transfer, stress analysis, and fluid flow. The document outlines the basic approach of FEM and traces the history and development of its early software programs.
This document provides an overview of good practices in finite element analysis (FEA). It discusses various topics including the FEA process, analysis types, element types, mesh quality, and validation. The modern design process utilizes optimization and virtual testing with FEA earlier in the process compared to the traditional design-build-test approach. A variety of linear and nonlinear analysis types are described such as static, dynamic, and buckling analyses. The document emphasizes the importance of validation, quality assurance, and maintaining proper documentation of the FEA process.
The Finite Element Method (FEM) is a numerical technique for solving problems of engineering and mathematical physics. It subdivides a large problem into smaller, simpler parts that are called finite elements. FEM allows for complex geometries and loading conditions to be modeled. The process involves discretizing the domain into elements, deriving the governing equations for each element, assembling the element equations into a global system of equations, and solving the system to obtain the unknown variable values. FEM can handle a wide range of problems including nonlinear problems and transient problems.
The document discusses the finite element method (FEM) and structural modeling and analysis using FEM. It begins with basic concepts of FEM, which involves dividing a complex object into simple geometric elements. Examples of everyday applications are given. The document then discusses why FEM is used, its applications in engineering fields, and the basic procedure of a FEM analysis, which involves dividing a structure into elements, describing behavior on each element, assembling the system of equations, and solving for desired outputs. Finally, different types of finite elements are introduced, with the spring element used as a detailed example to derive the element stiffness matrix.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a complex structure into smaller, simpler parts called finite elements and solving sets of algebraic equations. Commercial FEM software programs allow users to analyze complex engineering problems without an in-depth knowledge of mathematics. The document gives examples of how FEM can be used to model different structures and its applications in fields like mechanics, thermal analysis, and biomechanics.
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.
The document provides an overview of the finite element method (FEM). It explains that FEM is a numerical technique used to approximate solutions to partial differential equations that describe physical phenomena. It works by dividing a complex geometry into small pieces called finite elements that can then be solved using a computer. The method was developed in the 1950s and has since become widely used in engineering fields to simulate systems like heat transfer, stress analysis, and fluid flow. The document outlines the basic approach of FEM and traces the history and development of its early software programs.
This document provides an overview of good practices in finite element analysis (FEA). It discusses various topics including the FEA process, analysis types, element types, mesh quality, and validation. The modern design process utilizes optimization and virtual testing with FEA earlier in the process compared to the traditional design-build-test approach. A variety of linear and nonlinear analysis types are described such as static, dynamic, and buckling analyses. The document emphasizes the importance of validation, quality assurance, and maintaining proper documentation of the FEA process.
The Finite Element Method (FEM) is a numerical technique for solving problems of engineering and mathematical physics. It subdivides a large problem into smaller, simpler parts that are called finite elements. FEM allows for complex geometries and loading conditions to be modeled. The process involves discretizing the domain into elements, deriving the governing equations for each element, assembling the element equations into a global system of equations, and solving the system to obtain the unknown variable values. FEM can handle a wide range of problems including nonlinear problems and transient problems.
The document discusses the finite element method (FEM) and structural modeling and analysis using FEM. It begins with basic concepts of FEM, which involves dividing a complex object into simple geometric elements. Examples of everyday applications are given. The document then discusses why FEM is used, its applications in engineering fields, and the basic procedure of a FEM analysis, which involves dividing a structure into elements, describing behavior on each element, assembling the system of equations, and solving for desired outputs. Finally, different types of finite elements are introduced, with the spring element used as a detailed example to derive the element stiffness matrix.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a complex structure into smaller, simpler parts called finite elements and solving sets of algebraic equations. Commercial FEM software programs allow users to analyze complex engineering problems without an in-depth knowledge of mathematics. The document gives examples of how FEM can be used to model different structures and its applications in fields like mechanics, thermal analysis, and biomechanics.
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and
offering a wide range of dental certified courses in different formats.for more details please visit
www.indiandentalacademy.com
The document provides an introduction to finite element analysis (FEA) including:
1) FEA involves discretizing a continuous structure into small substructures called finite elements connected at nodes. This process is called meshing.
2) The finite element method has three main phases - preprocessing (defining geometry, materials, mesh), solution (solving equations to obtain nodal results), and postprocessing (obtaining stresses, strains from nodal results).
3) FEA can model complex problems that cannot be solved analytically due to complicated geometry or materials, and is well-suited for solving problems in solid mechanics, heat transfer, and other fields on computers.
This document discusses sources of error in finite element analysis, including modeling errors due to simplifying assumptions, discretization errors from approximating solutions, and numerical errors from limited computer precision. It provides examples of common mistakes that can cause incorrect results, such as incorrect material properties or insufficient boundary constraints. It also discusses best practices for verifying models, such as element testing, mesh refinement studies, and checking results against analytical solutions or boundary conditions.
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
FEA Basic Introduction Training By Praveenpraveenpat
Finite Element Analysis (FEA) involves discretizing a structure into small pieces (elements) and using a mathematical model to simulate loads and stresses on the structure. The key steps are: 1) Discretizing the structure into elements, 2) Developing element equations, 3) Assembling equations into a global system, 4) Applying boundary conditions, 5) Solving for unknowns, and 6) Calculating derived variables like stresses and displacements. FEA is commonly used in engineering fields like automotive, aerospace, and mechanical engineering to analyze stresses, deflections, and other performance aspects of complex structures.
Introduction to CAE & CFD
It contains brief introduction to various types of numerical methods its advantages and disadvantages .steps involved in performing any CAE OR CFD related projects
Modeling of Granular Mixing using Markov Chains and the Discrete Element Methodjodoua
The document presents a method for modeling granular mixing using Markov chains and the discrete element method (DEM). It motivates the use of Markov chains to efficiently simulate granular mixing as an alternative to computationally expensive DEM simulations. The theory and definitions of Markov chains and operators are provided. The method is applied to simulate mixing in a cylindrical drum, and the effects of the number of states, time step, and learning time are investigated. Properties of the resulting operator like the invariant distribution and mixing rates are analyzed to characterize the mixing dynamics.
This document summarizes a finite element analysis of a cantilever beam using quadrilateral meshing elements. The beam is modeled and analyzed in Abaqus for three loading cases: a point load at the free end, a point load at the mid-section, and a distributed load along the length. Hand calculations are also performed and compared to Abaqus and MATLAB results. Increasing the number of elements improves accuracy of the models. Quadrilateral elements are preferred over triangular elements for beam bending problems. Maximum displacement occurs under a point load at the free end. The study concludes with recommendations for accurate beam modeling and design using finite element analysis.
Topics to be discussed-
Introduction
How Does FEM Works?
Types Of Engineering Analysis
Uses of FEM in different fields
How can the FEM Help the Design Engineer?
How can the FEM Help the Design Organization?
Basic Steps & Phases Involved In FEM
Advantages and disadvantages
The Future Scope
References.
This document provides an overview of a course on the finite element method for analyzing linear systems taught at the Swiss Federal Institute of Technology. The first lecture covers the motivation and organization of the course, introduces the use of finite elements by relating physical problems to mathematical modeling and finite element solutions, and discusses basic mathematical tools used in finite element analysis like vectors, matrices, and tensors.
The document discusses the simulation of the 1-dimensional Stefan problem using the extended finite element method (XFEM). It provides an overview of the Stefan problem, analytical solution, conventional numerical modeling techniques, and issues with those techniques. It then describes the implementation of XFEM to model the Stefan problem, including enrichment functions, determining enriched degrees of freedom, validation against analytical solutions, and issues encountered, such as determining initial values when the interface is located at a node. Potential extensions to 2D modeling and future work are also discussed.
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.
This document compares three popular discretization approaches in computational fluid dynamics (CFD): finite difference method (FDM), finite volume method (FVM), and finite element method (FEM). It explains that FDM replaces derivatives with difference formulas on a grid, FVM is based on integral forms of partial differential equations solved over finite volumes, and FEM uses piecewise basis functions over finite elements. While each method has advantages and disadvantages, FVM generally provides better conservation properties and can handle complex domains, though all three approaches make the modeling of fluid flows and related phenomena possible through computer-based simulation.
IRJET- Stress – Strain Field Analysis of Mild Steel Component using Finite El...IRJET Journal
This document analyzes the stress-strain field of a mild steel component under uniaxial loading using the finite element method. The component is modeled in MATLAB and Autodesk Fusion 360 using three elements and four nodes. Results are obtained for tensile forces of 1000N, 3000N, and 9000N. The displacement, stress, and strain values calculated in MATLAB are approximately similar to analytical solutions. Fusion 360 provides the maximum and minimum values within the component. The analysis demonstrates that finite element modeling can accurately determine stress-strain behavior under different loads.
Finite Element Method (FEM) is a numerical method to obtain an approximate solution for the problems related to engineering and mathematical physics. Copy the link given below and paste it in new browser window to get more information on Finite Element Method (FEM):- http://www.transtutors.com/homework-help/mechanical-engineering/finite-element-method.aspx
Structural Dynamic Reanalysis of Beam Elements Using Regression MethodIOSR Journals
This paper concerns with the reanalysis of Structural modification of a beam element based on
natural frequencies using polynomial regression method. This method deals with the characteristics of
frequency of a vibrating system and the procedures that are available for the modification of physical
parameters of vibrating structural system. The method is applied on a simple cantilever beam structure and Tstructure
for approximate structural dynamic reanalysis. Results obtained from the assumed conditions of the
problem indicates the high quality approximation of natural frequencies using finite element method and
regression method.
OUTLINE OF PRESENTATION:
1) Numerical Modeling and its types
2) Finite Volume Method and its comparison
3) How to decide a Modeling Technique
4) 2D vs 3D Modeling
5) FLAC3D Introduction and its features
6) Mesh, Types of Meshes and Mesh Quality
7) Mesh Generation Tools
8) FLAC3D Interface
The document discusses finite element methods and their applications in microelectromechanical systems (MEMS). It covers the basic formulation of finite element methods, including discretization, selection of displacement functions, derivation of element stiffness matrices, and assembly of global equations. It also discusses specific applications of finite element analysis to problems in MEMS like heat transfer analysis, thermal stress analysis, and static/modal analysis. The finite element method is well-suited for complex geometries and materials and can model irregular shapes, general loads/boundary conditions, and nonlinear behavior.
Failure analysis of polymer and rubber materialsKartik Srinivas
Rubber products are designed using engineering principles of loads and deflections applied to a certain volume of material. The use of engineering principles in the development of rubber products provide an application envelope in which the products are expected to perform. Most of the products do provide the required services for satisfactory lifetimes, however failures do occur. Failures occurring under field services conditions are expensive and it becomes imperative to identify the cause and rectify it as soon as possible. The failure mode of polymers sets limits to the process of engineering design.
Leverage Computational Modeling and Simulation for Device Design - OMTEC 2017April Bright
Computational modeling and simulation (CM&S) has the potential to revolutionize medical devices by accelerating innovation and providing comprehensive evidence of long-term safety. For example, CM&S can provide performance benchmarks, assess design parameter interdependencies, evaluate a variety of use conditions, provide visualization of complex processes and become a core element of device submissions and approvals. This presentation will begin with an overview of the use of CM&S throughout the orthopaedic implant lifecycle, followed by a review of the current regulatory direction regarding the use of CM&S in device submissions. Next, a series of case studies based on a variety of orthopaedic implants will demonstrate the application of CM&S at various phases of the product lifecycle in more detail. The examples will also highlight the effects of modeling assumptions on model credibility and some verification and validation best practices.
This presentation will position CM&S as a credible and common means for device companies and FDA to demonstrate the safety of medical devices, and thereby ensure safety, reduce cost and accelerate the pathway toward “first in the world” access to products in the U.S.
The document provides an introduction to the finite element method (FEM). It explains that FEM is a numerical method used to approximate solutions to partial differential equations. It works by dividing a complex problem into smaller, simpler parts called finite elements. This allows for the problem to be solved computationally. The document outlines the basic steps of FEM, including preprocessing (modeling, meshing), solving, and postprocessing (analyzing results). It also discusses applications, history, software, element types, meshing, convergence, and compatibility conditions of FEM.
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and
offering a wide range of dental certified courses in different formats.for more details please visit
www.indiandentalacademy.com
The document provides an introduction to finite element analysis (FEA) including:
1) FEA involves discretizing a continuous structure into small substructures called finite elements connected at nodes. This process is called meshing.
2) The finite element method has three main phases - preprocessing (defining geometry, materials, mesh), solution (solving equations to obtain nodal results), and postprocessing (obtaining stresses, strains from nodal results).
3) FEA can model complex problems that cannot be solved analytically due to complicated geometry or materials, and is well-suited for solving problems in solid mechanics, heat transfer, and other fields on computers.
This document discusses sources of error in finite element analysis, including modeling errors due to simplifying assumptions, discretization errors from approximating solutions, and numerical errors from limited computer precision. It provides examples of common mistakes that can cause incorrect results, such as incorrect material properties or insufficient boundary constraints. It also discusses best practices for verifying models, such as element testing, mesh refinement studies, and checking results against analytical solutions or boundary conditions.
The document provides an introduction to finite element analysis. It discusses the need for computational methods to solve problems involving complex geometries and boundary conditions that cannot be solved through closed-form analytical methods. The finite element method is introduced as a numerical technique that involves discretizing a continuous domain into discrete subdomains called elements, and approximating variations in dependent variables within each element. This allows setting up algebraic equations that can be solved to approximate the continuous solution. Advantages of the finite element method include its ability to model complex shapes and behaviors, and refine solutions through mesh refinement. Basic concepts such as element types, discretization, and derivation of element equations are described.
FEA Basic Introduction Training By Praveenpraveenpat
Finite Element Analysis (FEA) involves discretizing a structure into small pieces (elements) and using a mathematical model to simulate loads and stresses on the structure. The key steps are: 1) Discretizing the structure into elements, 2) Developing element equations, 3) Assembling equations into a global system, 4) Applying boundary conditions, 5) Solving for unknowns, and 6) Calculating derived variables like stresses and displacements. FEA is commonly used in engineering fields like automotive, aerospace, and mechanical engineering to analyze stresses, deflections, and other performance aspects of complex structures.
Introduction to CAE & CFD
It contains brief introduction to various types of numerical methods its advantages and disadvantages .steps involved in performing any CAE OR CFD related projects
Modeling of Granular Mixing using Markov Chains and the Discrete Element Methodjodoua
The document presents a method for modeling granular mixing using Markov chains and the discrete element method (DEM). It motivates the use of Markov chains to efficiently simulate granular mixing as an alternative to computationally expensive DEM simulations. The theory and definitions of Markov chains and operators are provided. The method is applied to simulate mixing in a cylindrical drum, and the effects of the number of states, time step, and learning time are investigated. Properties of the resulting operator like the invariant distribution and mixing rates are analyzed to characterize the mixing dynamics.
This document summarizes a finite element analysis of a cantilever beam using quadrilateral meshing elements. The beam is modeled and analyzed in Abaqus for three loading cases: a point load at the free end, a point load at the mid-section, and a distributed load along the length. Hand calculations are also performed and compared to Abaqus and MATLAB results. Increasing the number of elements improves accuracy of the models. Quadrilateral elements are preferred over triangular elements for beam bending problems. Maximum displacement occurs under a point load at the free end. The study concludes with recommendations for accurate beam modeling and design using finite element analysis.
Topics to be discussed-
Introduction
How Does FEM Works?
Types Of Engineering Analysis
Uses of FEM in different fields
How can the FEM Help the Design Engineer?
How can the FEM Help the Design Organization?
Basic Steps & Phases Involved In FEM
Advantages and disadvantages
The Future Scope
References.
This document provides an overview of a course on the finite element method for analyzing linear systems taught at the Swiss Federal Institute of Technology. The first lecture covers the motivation and organization of the course, introduces the use of finite elements by relating physical problems to mathematical modeling and finite element solutions, and discusses basic mathematical tools used in finite element analysis like vectors, matrices, and tensors.
The document discusses the simulation of the 1-dimensional Stefan problem using the extended finite element method (XFEM). It provides an overview of the Stefan problem, analytical solution, conventional numerical modeling techniques, and issues with those techniques. It then describes the implementation of XFEM to model the Stefan problem, including enrichment functions, determining enriched degrees of freedom, validation against analytical solutions, and issues encountered, such as determining initial values when the interface is located at a node. Potential extensions to 2D modeling and future work are also discussed.
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.
This document compares three popular discretization approaches in computational fluid dynamics (CFD): finite difference method (FDM), finite volume method (FVM), and finite element method (FEM). It explains that FDM replaces derivatives with difference formulas on a grid, FVM is based on integral forms of partial differential equations solved over finite volumes, and FEM uses piecewise basis functions over finite elements. While each method has advantages and disadvantages, FVM generally provides better conservation properties and can handle complex domains, though all three approaches make the modeling of fluid flows and related phenomena possible through computer-based simulation.
IRJET- Stress – Strain Field Analysis of Mild Steel Component using Finite El...IRJET Journal
This document analyzes the stress-strain field of a mild steel component under uniaxial loading using the finite element method. The component is modeled in MATLAB and Autodesk Fusion 360 using three elements and four nodes. Results are obtained for tensile forces of 1000N, 3000N, and 9000N. The displacement, stress, and strain values calculated in MATLAB are approximately similar to analytical solutions. Fusion 360 provides the maximum and minimum values within the component. The analysis demonstrates that finite element modeling can accurately determine stress-strain behavior under different loads.
Finite Element Method (FEM) is a numerical method to obtain an approximate solution for the problems related to engineering and mathematical physics. Copy the link given below and paste it in new browser window to get more information on Finite Element Method (FEM):- http://www.transtutors.com/homework-help/mechanical-engineering/finite-element-method.aspx
Structural Dynamic Reanalysis of Beam Elements Using Regression MethodIOSR Journals
This paper concerns with the reanalysis of Structural modification of a beam element based on
natural frequencies using polynomial regression method. This method deals with the characteristics of
frequency of a vibrating system and the procedures that are available for the modification of physical
parameters of vibrating structural system. The method is applied on a simple cantilever beam structure and Tstructure
for approximate structural dynamic reanalysis. Results obtained from the assumed conditions of the
problem indicates the high quality approximation of natural frequencies using finite element method and
regression method.
OUTLINE OF PRESENTATION:
1) Numerical Modeling and its types
2) Finite Volume Method and its comparison
3) How to decide a Modeling Technique
4) 2D vs 3D Modeling
5) FLAC3D Introduction and its features
6) Mesh, Types of Meshes and Mesh Quality
7) Mesh Generation Tools
8) FLAC3D Interface
The document discusses finite element methods and their applications in microelectromechanical systems (MEMS). It covers the basic formulation of finite element methods, including discretization, selection of displacement functions, derivation of element stiffness matrices, and assembly of global equations. It also discusses specific applications of finite element analysis to problems in MEMS like heat transfer analysis, thermal stress analysis, and static/modal analysis. The finite element method is well-suited for complex geometries and materials and can model irregular shapes, general loads/boundary conditions, and nonlinear behavior.
Failure analysis of polymer and rubber materialsKartik Srinivas
Rubber products are designed using engineering principles of loads and deflections applied to a certain volume of material. The use of engineering principles in the development of rubber products provide an application envelope in which the products are expected to perform. Most of the products do provide the required services for satisfactory lifetimes, however failures do occur. Failures occurring under field services conditions are expensive and it becomes imperative to identify the cause and rectify it as soon as possible. The failure mode of polymers sets limits to the process of engineering design.
Leverage Computational Modeling and Simulation for Device Design - OMTEC 2017April Bright
Computational modeling and simulation (CM&S) has the potential to revolutionize medical devices by accelerating innovation and providing comprehensive evidence of long-term safety. For example, CM&S can provide performance benchmarks, assess design parameter interdependencies, evaluate a variety of use conditions, provide visualization of complex processes and become a core element of device submissions and approvals. This presentation will begin with an overview of the use of CM&S throughout the orthopaedic implant lifecycle, followed by a review of the current regulatory direction regarding the use of CM&S in device submissions. Next, a series of case studies based on a variety of orthopaedic implants will demonstrate the application of CM&S at various phases of the product lifecycle in more detail. The examples will also highlight the effects of modeling assumptions on model credibility and some verification and validation best practices.
This presentation will position CM&S as a credible and common means for device companies and FDA to demonstrate the safety of medical devices, and thereby ensure safety, reduce cost and accelerate the pathway toward “first in the world” access to products in the U.S.
Configuration Navigation Analysis Model for Regression Test Case Prioritizationijsrd.com
Regression testing has been receiving increasing attention nowadays. Numerous regression testing strategies have been proposed. Most of them take into account various metrics like cost as well as the ability to find faults quickly thereby saving overall testing time. In this paper, a new model called the Configuration Navigation Analysis Model is proposed which tries to consider all stakeholders and various testing aspects while prioritizing regression test cases.
Analytical engineering uses both theoretical and empirical methods to inform product design decisions. Theoretical methods include mathematical modeling and simulation, while empirical methods involve physical testing and measurement. Early in design, theoretical tolerance analysis is used, while later empirical metrology data from prototypes is combined with simulation to validate models. For complex issues like component deflection under load, a hybrid approach using initial modeling followed by targeted physical testing and model validation is most effective. Combining methods alleviates limitations of any single approach and ensures high quality data at all stages of design.
This document discusses the foundations of chemical kinetic modeling and reaction models. It outlines the key pillars of knowledge required, including general chemistry, thermodynamics, chemical kinetics, and quantum chemistry. It then describes the step-wise process for constructing detailed chemical kinetic models, including determining elementary reactions, estimating thermo-chemical data and rate coefficients, validating models experimentally, and applying the models to reactor scale-up and design. Reactor scale-up requires satisfying similarity parameters between small and large-scale systems. The goal is to develop accurate predictive models and design safe, commercial-scale chemical reactors.
This document presents a process model for software measurement methods consisting of four main steps: 1) devising a measurement method, 2) applying the method to software, 3) producing results, and 4) exploiting results in quantitative models. It also discusses validation requirements for measurement methods, identifying checks needed to validate each step and sub-step in the process. While offering a knowledgeable discussion, the document notes that a complete validation framework addressing the full measurement process is still needed.
The operation research book that involves all units including the lpp problems, integer programming problem, queuing theory, simulation Monte Carlo and more is covered in this digital material.
This document discusses optimization problems in engineering applications. It begins by defining optimization and describing how it can be applied to engineering problems to minimize costs or maximize benefits. Some examples of engineering applications that can be optimized are described, such as designing structures for minimum cost or maximum efficiency. The document then discusses procedures for solving optimization problems, including recognizing and defining the problem, constructing a model, and implementing solutions. It also describes different types of optimization problems and methods for solving linear programming problems, including the graphical and simplex methods.
The document discusses a cost analysis of various metal hydroxide chemical (MHC) technologies used in printed wiring board manufacturing. It presents a framework for a hybrid cost formulation that uses computer simulation and activity-based costing to evaluate and compare the costs of different MHC processes. Key cost components considered include capital, production, maintenance, energy and water consumption, wastewater generation, and environmental costs. The analysis aims to determine the costs of fully operational MHC lines for a sample job size and evaluate the effects of critical cost variables through sensitivity analysis.
TRANSFORMING SOFTWARE REQUIREMENTS INTO TEST CASES VIA MODEL TRANSFORMATIONijseajournal
Executable test cases originate at the onset of testing as abstract requirements that represent system
behavior. Their manual development is time-consuming, susceptible to errors, and expensive. Translating
system requirements into behavioral models and then transforming them into a scripting language has the
potential to automate their conversion into executable tests. Ideally, an effective testing process should
start as early as possible, refine the use cases with ample details, and facilitate the creation of test cases.
We propose a methodology that enables automation in converting functional requirements into executable
test cases via model transformation. The proposed testing process starts with capturing system behavior in
the form of visual use cases, using a domain-specific language, defining transformation rules, and
ultimately transforming the use cases into executable tests.
This document summarizes a knowledge engineering approach using analytic hierarchy process (AHP) to resolve conflicts between experts in risk-related decision making. It proposes using a modified version of AHP to increase transparency in the analysis procedure. This allows identification of major causes of inter-expert discrepancy, which are differences in unstated assumptions and subjective weightings of risk factors. The document demonstrates how AHP can systematically decompose complex decision problems, evaluate alternatives based on multiple criteria, and aggregate results to provide an overall evaluation that incorporates differing expert opinions in a consistent manner.
POSTERIOR RESOLUTION AND STRUCTURAL MODIFICATION FOR PARAMETER DETERMINATION ...IJCI JOURNAL
When only a few lower modes data are available to evaluate a large number of unknown parameters, it is
difficult to acquire information about all unknown parameters. The challenge in this kind of updation
problem is first to get confidence about the parameters that are evaluated correctly using the available
data and second to get information about the remaining parameters. In this work, the first issue is resolved
employing the sensitivity of the modal data used for updation. Once it is fixed that which parameters are
evaluated satisfactorily using the available modal data the remaining parameters are evaluated employing
modal data of a virtual structure. This virtual structure is created by adding or removing some known
stiffness to or from some of the stories of the original structure. A 12-story shear building is considered for
the numerical illustration of the approach. Results of the study show that the present approach is an
effective tool in system identification problem when only a few data is available for updation.
This document discusses hierarchical design models for use in the mechatronic product development process, specifically for synchronous machines. It proposes a hierarchical design process where domain-specific design tasks are not fully integrated at the mechatronic level, but instead models cover different views and levels of detail of a system. Models represent structural, behavioral, and functional knowledge and views of a system. The approach is demonstrated through the design process of synchronous machines.
This document discusses self-adaptive evolutionary algorithms. It begins with an introduction that motivates the need for self-adaptive parameters in evolutionary algorithms. The document then provides an overview of evolutionary algorithms and defines different types of parameter control methods - deterministic, adaptive, and self-adaptive. Several examples of self-adaptive evolutionary algorithms that adapt mutation rates and other parameters are then described. The document concludes with a summary of self-adaptive evolutionary algorithms and prospects for future research.
Software Cost Estimation Using Clustering and Ranking SchemeEditor IJMTER
Software cost estimation is an important task in the software design and development process.
Planning and budgeting tasks are carried out with reference to the software cost values. A variety of
software properties are used in the cost estimation process. Hardware, products, technology and
methodology factors are used in the cost estimation process. The software cost estimation quality is
measured with reference to the accuracy levels.
Software cost estimation is carried out using three types of techniques. They are regression based
model, anology based model and machine learning model. Each model has a set of technique for the
software cost estimation process. 11 cost estimation techniques fewer than 3 different categories are
used in the system. The Attribute Relational File Format (ARFF) is used maintain the software product
property values. The ARFF file is used as the main input for the system.
The proposed system is designed to perform the clustering and ranking of software cost
estimation methods. Non overlapped clustering technique is enhanced with optimal centroid estimation
mechanism. The system improves the clustering and ranking process accuracy. The system produces
efficient ranking results on software cost estimation methods.
The document discusses mechatronics systems and their design process. It begins with an introduction to mechatronics, which is an interdisciplinary approach to design that integrates mechanical engineering with electrical and computer science principles. This leads to products with more synergy and flexibility. The design process involves modeling, simulation, project management, analysis, and real-time interfacing. Additional topics covered include the stages of mechatronic design, traditional vs mechatronics approaches, and case studies of mechatronic systems like pick-and-place robots.
Lect24-Efficient test suite mgt - IV.pptxvijay518229
This document discusses various techniques for prioritizing regression test cases based on data flow and module coupling. It describes how data flow based prioritization focuses on variable definitions and uses to detect errors. Module coupling based prioritization identifies highly affected modules when other modules change based on coupling information, then prioritizes test cases for those modules. An example demonstrates constructing module coupling and dependence matrices to determine which modules are most affected by changes in other modules, and thus which test cases should take highest priority in regression testing.
Calibration and Validation of Micro-Simulation ModelsWSP
Calibration and Validation of Micro-Simulation Models is a presentation delivered by François Bélisle, Eng., B.Sc., M.Sc., WSP | Parsons Brinckerhoff, Laurent Gauthier, Polytechnique Montréal and Nicolas Saunier, Polytechnique Montréal at the 2015 Transportation Association of Canada (TAC) Conference & Exhibition, from September 27 to 30.
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4. Verifications and Validations in Finite
Element Analysis (FEA)
1.1 Introduction
The finite element method (FEM) is a numerical method used to solve a mathematical
model of a given structure or system, which are very complex and for which analytical
solution techniques are generally not possible, the solution can be found using the finite
element method. The finite element method can thus be said to be a variational formulation
method using the principle of minimum potential energy where the unknown quantities of
interests are approximated by continuous piecewise polynomial functions. These quantities
of interest can be different according to the chosen system, as the finite element method
can be and is used in various different fields such as structural mechanics, fluid mechanics,
accoustics, electromagnetics, etc. In the field of structural mechanics the primary field of
interest is the displacements and stresses in the system.
It is important to understand that FEM only gives an approximate solution of the prob-
lem and is a numerical approach to get the real result of the variational formulation of
partial differential equations. A finite element based numerical approach gives itself to a
number of assumptions and uncertainties related to domain discretizations, mathematical
shape functions, solution procedures, etc. The widespread use of FEM as a primary tool
has led to a product engineering lifecycle where each step from ideation, design develop-
ment, to product optimization is done virtually and in some cases to the absence of even
1
5. prototype testing.
This fully virtual product development and analysis methodology leads to a situation
where a misinterpreted approximation or error in applying a load condition may be car-
ried out through out the engineering lifecycle leading to a situation where the errors get
cumulative at each stage leading to disastrous results. Errors and uncertainties in the ap-
plication of finite element method (FEM) can come from the following main sources, 1)
Errors that come from the inherent assumptions in the Finite element theory and 2) Errors
and uncertainties that get built into the system when the physics we are seeking to model
get transferred to the computational model. A common list of these kind of errors and
uncertainties are as mentioned below;
• Errors and uncertainties from the solver.
• Level of mesh refinement and the choice of element type.
• Averaging and calculation of stresses and strains from the primary solution variables.
• Uncertainty in recreating the geometrical domain on a computer.
• Approximations in the material properties of the model.
• Approximations and uncertainties in the loading and boundary conditions of the
model.
• Errors coming from chosing the right solver types for problems, e.g. Solvers for
eigen value problems.
The long list of error sources and uncertainties in the procedure makes it desirable that
a framework of rules and criteria are developed by the application of which we can make
sure that the finite element method performs within the required parameters of accuracy,
reliability and repeatability. These framework of rules serve as verification and validation
procedures by which we can consistently gauge the accuracy of our models, and sources of
errors and uncertainties be clearly identified and progressively improved to achieve greater
accuracy in the solutions. Verifications and Validations are required in each and every
2
6. development and problem solving FEA project to provide the confidence that the compu-
tational model developed performs within the required parameters. The solutions provided
by the model are sufficiently accurate and the model solves the intended problem it was
developed for.
Verification procedure includes checking the design, the software code and also inves-
tigate if the computational model accurately represents the physical system. Validation is
more of a dynamic procedure and determines if the computational simulation agrees with
the physical phenomenon, it examines the difference between the numerical simulation
and the experimental results. Verification provides information whether the computational
model is solved correctly and accurately, while validation provides evidence regarding the
extent to which the mathematical model accurately corelates to experimental tests.
In addition to complicated discretization functions, partial differential equations repre-
senting physical systema, CFD and FEA both use complicated matrices and PDE solution
algorithms to solve physical systems. This makes it imperative to carry out verification
and validation activities separately and incrementally during the model building to ensure
reliable processes. In order to avoid spurious results and data contamination giving out
false signals, it is important that the verification process is carried out before the valida-
tion assessment. If the verification process fails the the model building process should be
discontinued further until the verification is established. If the verification process suc-
ceeds, the validation process can be carried further for comparison with field service and
experimental tests.
1.2 Brief History of Standards and Guidelines for Verifi-
cations and Validations
Finite element analysis found widespread use with the release of NASA Structural Anal-
ysis Code in its various versions and flavous. The early adopters for FEA came from the
aerospace and nuclear engineering background. The first guidelines for verification and
validation were issued by the American Nuclear Society in 1987 as Guidelines for the Ver-
ification and Validation of Scientific and Engineering Computer Programs for the Nuclear
3
7. Industry. The first book on the subject was written by Dr. Patrick Roache in 1998 titled
Verification and Validation in Computational Science and Engineering, an update of the
book appeared in 2009.
In 1998 the Computational Fluid Dynamics Committee on Standards at the American
Institute of Aeronautics and Astronautics released the first standards document Guide for
the Verification and Validation of Computational Fluid Dynamics Simulations. The US
Depeartment of Defense through Defense Modeling and Simulation Office releaseed the
DoD Modeling and Simulation, Verification, Validation, and Accreditation Document in
2003.
The American Society of Mechanical Engineers (ASME) V and V Standards Commit-
tee released the Guide for Verification and Validation in Computational Solid Mechanics
(ASME V and V-10-2006).
In 2008 the National Aeronautics and Space Administration Standard for Models and
Simulations for the first time developed a set of guidelines that provided a numerical score
for verification and validation efforts.
American Society of Mechanical Engineers V and V Standards Committee V and V-20
in 2016 provided an updated Standard for Verification and Validation in Computational
Fluid Dynamics and Heat Transfer .
1.3 Verifications and Validations :- Process and Procedures
Figure(1.1) shows a typical product design cycle in a fast-paced industrial product de-
velopment group. The product interacts with the environment in terms of applied loads,
boundary conditions and ambient atmosphere. These factors form the inputs into the com-
putational model building process. The computational model provides us with predictions
and solutions of what would happen to the product under different service conditions.
It is important to note that going from the physical world to generating a computational
model involves an iterative process where all the assumptions, approximations and their
effects on the the quality of the computational model are iterated upon to generate the most
optimum computational model for representing the physical world.
4
8. Figure 1.1: Variation on the Sargent Circle Showing the Verification and Validation Pro-
cedures in a Typical Fast Paced Design Group
The validation process between the computational model and the physical world also
involves an iterative process, where experiments with values of loads and boundary con-
ditions are solved and the solution is compared to output from the physical world. The
computational model is refined based upon the feedbacks obtained during the procedure.
The circular shapes of the process representation emphasizes that computational mod-
eling and in particular verification and validation procedures are iterative in nature and
require a continual effort to optimize them.
The blue, red and green colored areas in Figure(1.3) highlight the iterative validation
and verification activities in the process. The standards and industrial guidelines clearly
mention the distinctive nature of code and solution verifications and validations at different
levels. The green highlighted region falls in the domain of the laboratory performing the
experiments, it is equally important that the testing laboratory understands both the process
and procedure of verification and validation perfectly.
Code verification seeks to ensure that there are no programming mistakes or bugs and
that the software provides the accuracy in terms of the implementation of the numerical al-
gorithms or construction of the solver. Comparing the issue of code verification and calcu-
lation verification of softwares, the main point of difference is that calculation verification
5
9. Figure 1.2: Verification and Validation Process
involves quantifying the discretization error in a numerical simulation. Code verification is
rather upstream in the process and is done by comparing numerical results with analytical
solutions.
6
11. 1.4 Guidelines for Verifications and Validations
The first step is the verification of the code or software to confirm that the software is work-
ing as it was intended to do. The idea behind code verification is to identify and remove
any bugs that might have been generated while implementing the numerical algorithms or
because of any programming errors. Code verification is primarily a responsibility of the
code developer and softwares like Abaqus, LS-Dyna etc., provide example problems man-
uals, benchmark manuals to show the verifications of the procedures and algorithms they
have implemented.
Next step of calculation verification is carried out to quantify the error in a computer
simulation due to factors like mesh discretization, improper convergence criteria, approxi-
mation in material properties and model generations. Calculation verification provides with
an estimation of the error in the solution because of the mentioned factors. Experience has
shown us that insufficient mesh discretization is the primary culprit and largest contributor
to errors in calculation verification.
Validation processes for material models, elements, and numerical algorithms are gen-
erally part of FEA and CFD software help manuals. However, when it comes to estab-
lishing the validity of the computational model that one is seeking to solve, the validation
procedure has to be developed by the analyst or the engineering group.
The following validation guidelines were developed at Sandia National Labs[Oberkampf
et al.] by experimentalists working on wind tunnel programs, however these are applicable
to all problems from computational mechanics.
Guideline 1: The validation experiment should be jointly designed by the FEA group
and the experimental engineers. The experiments should ideally be designed so that the
validation domain falls inside the application domain.
Guideline 2: The designed experiment should involve the full physics of the system,
including the loading and boundary conditions.
Guideline 3: The solutions of the experiments and from the computational model
should be totally independent of each other.
Guideline 4: The experiments and the validation process should start from the system
8
12. level solution to the component level.
Guideline 5: Care should be taken that operator bias or process bias does not contami-
nate the solution or the validation process.
1.5 Verification & Validation in FEA
1.5.1 Verification Process of an FEA Model
In the case of automotive product development problems, verification of components like
silent blocks and bushings, torque rod bushes, spherical bearings etc., can be carried. Fig-
ure(1.4) shows the rubber-metal bonded component for which calculations have been car-
ried out. Hill[11], Horton[12] and have shown that under radial loads the stiffness of the
bushing can be given by,
Figure 1.4: Geometry Dimensions of the Silent Bushing
Krs = βrsLG (1.1)
where,βrs =
80π A2 +B2
25(A2 +B2)ln B
A −9(A2 −B2)
(1.2)
9
13. Figure 1.5: Geometry of the Silent Bushing
and G= Shear Modulus = 0.117e0.034xHs, Hs = Hardness of the material. Replacing the
geometrical values from Figure(1.4),
Krs = 8170.23N/mm, (1.3)
for a 55 durometer natural rubber compound. The finite element model for the bushing
is shown in Figure(1.9) and the stiffness from the FEA comes to 8844.45 N/mm. The
verification and validation quite often recommends that a difference of less than 10% for a
comparison of solutions is a sound basis for a converged value.
For FEA with non-linear materials and non-linear geometrical conditions, there are
multiple steps that one has to carry out to ensure that the material models and the boundary
conditions provide reliable solutions.
• Unit Element Test: The unit element test as shown in in Figure(1.7) shows a unit
cube element. The material properties are input and output stress-strain plots are
compared to the inputs. This provides a first order validation of whether the material
10
14. Figure 1.6: Deformed Shape of the Silent Bushing
properties are good enough to provide sensible outputs. The analyst him/her self can
carry out this validation procedure.
• Experimental Characterization Test: FEA is now carried out on a characterization test
such as a tension test or a compression test. This provides a checkpoint of whether
the original input material data can be backed out from the FEA. This is a moderately
difficult test as shown in Figure(1.8). The reasons for the difficulties are because of
unquantified properties like friction and non-exact boundary conditions.
• Comparison to Full Scale Experiments: In these validation steps, the parts and com-
ponent products are loaded up on a testing rig and service loads and boundary con-
ditions are applied. The FEA results are compared to these experiments. This step
provides the most robust validation results as the procedure validates the finite ele-
ment model as well as the loading state and boundary conditions. Figure(1.9) shows
torque rod bushing and the validation procedure carried out in a multi-step analysis.
Experience shows that it is best to go linearly in the validation procedure from step 1
11
15. through 3, as it progressively refines one’s material model, loading, boundary conditions.
Directly jumping to step 3 to complete the validation process faster adds upto more time
with errors remaining unresolved, and these errors go on to have a cumulative effect on the
quality of the solutions.
Figure 1.7: Unit Cube Single Element Test
Figure 1.8: FEA of Compression Test
1.5.2 Validation Process of an FEA Model
Figure(1.7) shows the experimental test setup for validation of the bushing model. Radial
loading is chosen to be the primary deformation mode and load vs. displacement results
are compared. The verification process earlier carried out established the veracity of the
FEA model and the current validation analysis applies the loading in multiple Kilonewtons.
Results show a close match between the experimental and FEA results. Figures(1.10) and
12
16. Figure 1.9: Experimental Testing and Validation FEA for the Silent Bushing
(1.11) show the validation setup and solutions for a tire model and engine mount. The
complexity of a tire simulation is due to the nature of the tire geometry, and the presence
of multiple rubber compounds, fabric and steel belts. This makes it imperative to establish
the validity of the simulations.
13
17. Figure 1.10: Experimental Testing and Validation FEA for a Tire Model
Figure 1.11: Experimental Testing and Validation FEA for a Passenger Car Engine Mount
14
18. 1.6 Summary
An attempt was made in the article to provide information on the verification and validation
processes in computational solid mechanics. We went through the history of adoption
of verification and validation processes and their integration in computational mechanics
processes and tools. Starting from 1987 when the first guidelines were issued in a specific
field of application, today we are at a stage where the processes have been standardized and
all major industries have found their path of adoption.
Verification and validations are now an integral part of computational mechanics pro-
cesses to increase integrity and reliability of the solutions. Verification is done primarily at
the software level and is aimed at evaluating whether the code has the capability to offer the
correct solution to the problem, while validation establishes the accuracy of the solution.
ASME, Nuclear Society and NAFEMS are trying to make the process more standardized,
and purpose driven.
Uncertainty quantification has not included in this current review, the next update of
this article will include steps for uncertainty quantification in the analysis.
15
19. 1.7 References
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20