Finite element analysis (FEA) is a numerical technique used to approximate solutions to boundary value problems by dividing the domain into smaller elements. The document discusses the three main stages of FEA: building the model, solving the model, and displaying the results. It provides details on how to create nodes and finite elements to represent an object's geometry, assign material properties and constraints, define the type of analysis, and select parameters to display in the results. Examples of different types of FEA analyses are also listed, such as static, thermal, modal, and buckling analyses.
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
The finite element method is used to solve engineering problems involving stress analysis, heat transfer, and other fields. It involves dividing a structure into small pieces called finite elements and deriving the governing equations for each element. The element equations are assembled into a global stiffness matrix and force vector. Boundary conditions are applied and the system is solved for the unknown displacements at nodes. Results like stresses, strains, and temperatures are then determined. Key steps are discretization, deriving the element stiffness matrix, assembling the global matrix, applying boundary conditions, and solving for nodal displacements.
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.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
This document discusses the finite element method (FEM) for engineering analysis. It explains that FEM involves discretizing a continuous structure into smaller, finite elements and then solving the equations for each element. The general steps of FEM are: 1) discretizing the structure into elements connected at nodes, 2) numbering nodes and elements, 3) selecting displacement functions, 4) defining material behavior, 5) deriving element stiffness matrices, 6) assembling element equations, 7) applying boundary conditions, 8) solving for displacements, 9) computing element strains and stresses, and 10) interpreting results. One-, two-, and three-dimensional elements as well as axisymmetric elements are discussed.
INTRODUCTION TO FINITE ELEMENT ANALYSISAchyuth Peri
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It involves dividing a system into small elements and solving for variables within each element. This allows for analysis of complex geometries, loadings, and materials. The FEM process includes discretizing the system, selecting functions to approximate the solution, assembling element equations into a global system, applying boundary conditions, and calculating displacements, stresses, and strains. FEA offers advantages like analyzing irregular shapes and nonlinear problems, reducing testing costs, and optimizing designs.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
The finite element method is used to solve engineering problems involving stress analysis, heat transfer, and other fields. It involves dividing a structure into small pieces called finite elements and deriving the governing equations for each element. The element equations are assembled into a global stiffness matrix and force vector. Boundary conditions are applied and the system is solved for the unknown displacements at nodes. Results like stresses, strains, and temperatures are then determined. Key steps are discretization, deriving the element stiffness matrix, assembling the global matrix, applying boundary conditions, and solving for nodal displacements.
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.
This document discusses two-dimensional vector variable problems in structural mechanics. It describes plane stress, plane strain and axisymmetric problems, and provides the stress-strain relations for materials under these conditions. It also discusses thin structures like disks and long prismatic shafts. Additionally, it covers dynamic analysis and vibration of structures, describing free vibration, forced vibration and types of vibration. Equations of motion are developed using Lagrange's approach and the weak form method. Mass and stiffness matrices for axial rod and beam elements are also presented.
A short introduction presentation about the Basics of Finite Element Analysis. This presentation mainly represents the applications of FEA in the real time world.
This document discusses the finite element method (FEM) for engineering analysis. It explains that FEM involves discretizing a continuous structure into smaller, finite elements and then solving the equations for each element. The general steps of FEM are: 1) discretizing the structure into elements connected at nodes, 2) numbering nodes and elements, 3) selecting displacement functions, 4) defining material behavior, 5) deriving element stiffness matrices, 6) assembling element equations, 7) applying boundary conditions, 8) solving for displacements, 9) computing element strains and stresses, and 10) interpreting results. One-, two-, and three-dimensional elements as well as axisymmetric elements are discussed.
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 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 document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
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.
The document discusses the finite element method (FEM) for analyzing beam structures. FEM involves subdividing a structure into finite elements of simple shape and solving for the whole structure. Elements can be one-, two-, or three-dimensional, with accuracy increasing with more elements. Nodes are points where elements connect, and nodal displacements describe element deformation. FEM allows analyzing complex shapes like plates by treating them as assemblies of beams. A simple bar analysis example demonstrates deriving and solving the stiffness matrix to determine displacements and forces from applied loads.
This lecture provides an introduction to finite element analysis (FEA). It discusses the basic concepts of FEA, including dividing a complex object into simple finite elements and using polynomial terms to describe field quantities within each element. The lecture covers the history and applications of FEA, as well as the basic procedure, which involves meshing a structure into elements, describing element behavior, assembling elements at nodes, solving the system of equations, and calculating results. It also reviews matrix algebra concepts needed for FEA. Finally, it presents the simple example of a spring element and spring system to demonstrate the finite element modeling process.
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
1) Finite element analysis is a numerical method used to solve engineering problems by breaking structures down into small discrete elements. It involves modeling structures as assemblies of simple geometric shapes called finite elements.
2) The key steps in finite element analysis include discretizing the structure into elements, selecting element types, defining displacement and strain/stress relationships within each element, deriving the element stiffness matrix, and assembling individual element equations into a system of equations for the overall structure.
3) Common approaches include the displacement method, which uses nodal displacements as unknowns, and the force method, which uses internal forces. The displacement method is typically more suitable for computational analysis.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
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 Finite Element Analysis Madhan N R
This document discusses finite element analysis (FEA) and its applications in engineering. It introduces FEA as a numerical method to determine stress and deflection in structures. It covers FEA modeling techniques including meshing, element types, boundary conditions and assumptions. It also compares traditional design cycles to using FEA and discusses how FEA can replace physical testing.
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.
Finite Element Analysis (FEA) is a numerical method for solving complex engineering problems. The document discusses conducting FEA on a fixed-free cantilever beam to study the effect of mesh density on solution accuracy. Analytical solutions are derived and used to validate FEA results. A beam model is created in ABAQUS with varying element sizes. As element count increases, FEA results converge towards analytical solutions, though with increased computation time. An element count of 4125 provided an optimal balance between accuracy and cost.
The document discusses the finite element method (FEM) for numerical analysis of structures. It provides the following key points:
1) FEM divides a structure into discrete elements connected at nodes, resulting in a finite number of degrees of freedom and a set of simultaneous algebraic equations to solve.
2) It uses approximate methods like the Rayleigh-Ritz method to obtain solutions for complex geometries and boundary conditions. This involves assuming displacement fields and minimizing the total potential energy.
3) The Galerkin method is presented, which satisfies the governing differential equations in an integral sense by setting the residual equal to zero when multiplied by a weighting function.
4) Applications to 1D problems are discussed,
ME6603 - FINITE ELEMENT ANALYSIS UNIT - IV NOTES AND QUESTION BANKASHOK KUMAR RAJENDRAN
This document contains a collection of practice problems related to finite element analysis of two-dimensional vector variable problems, including axisymmetric problems. The problems cover derivation of element stiffness matrices and strain-displacement matrices for various element types under different conditions, calculation of element stresses and displacements, modeling of cylinders under pressure, and determination of global stiffness matrices for structures. The elements and conditions include constant strain triangles, linear strain triangles, axisymmetric triangles, plane stress, plane strain, and shells.
This document contains formulas and equations related to finite element analysis (FEA) for one-dimensional structural and heat transfer problems. It includes formulas for weighted residual methods, Ritz method, beam deflection and stress, springs, one-dimensional bars and frames, and one-dimensional heat transfer through walls and fins. Displacement functions, stiffness matrices, thermal loads, and conduction/convection equations are provided for linear and quadratic elements undergoing static structural and thermal analysis.
The document discusses the casting process for hydraulic cylinder pistons. It begins by introducing pistons and their use in hydraulic mechanisms. It then describes the casting process, noting that large pistons are typically gravity die cast while smaller pistons may be sand cast. The casting process involves pouring molten metal into a mold. Further processes include lathe work to machine diameters and faces and milling holes. Pistons are widely used in engines and hydraulics.
Design Reliability and Product Integrity on a Hydraulic Cylinderprashanth884
The document summarizes the design reliability process for a hydraulic cylinder used in trailer beds. It describes the initial design proposal, failure modes identified through design FMEA, prototype testing that revealed gland thread shear as the critical failure, and an alternate design using a retaining ring. Prototypes of the new design successfully passed tests up to 7,000 cycles without failure, establishing a design meeting the required reliability.
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 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 document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.
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.
The document discusses the finite element method (FEM) for analyzing beam structures. FEM involves subdividing a structure into finite elements of simple shape and solving for the whole structure. Elements can be one-, two-, or three-dimensional, with accuracy increasing with more elements. Nodes are points where elements connect, and nodal displacements describe element deformation. FEM allows analyzing complex shapes like plates by treating them as assemblies of beams. A simple bar analysis example demonstrates deriving and solving the stiffness matrix to determine displacements and forces from applied loads.
This lecture provides an introduction to finite element analysis (FEA). It discusses the basic concepts of FEA, including dividing a complex object into simple finite elements and using polynomial terms to describe field quantities within each element. The lecture covers the history and applications of FEA, as well as the basic procedure, which involves meshing a structure into elements, describing element behavior, assembling elements at nodes, solving the system of equations, and calculating results. It also reviews matrix algebra concepts needed for FEA. Finally, it presents the simple example of a spring element and spring system to demonstrate the finite element modeling process.
The document provides an introduction to the finite element method (FEM). It discusses how FEM can be used to obtain approximate solutions to boundary value problems in engineering. It outlines the general steps involved, including preprocessing (defining the model), solution/processing (computing unknown values), and postprocessing (analyzing results). Examples of FEM applications include structural analysis, fluid flow, heat transfer, and more. The key aspects of FEM include discretizing the domain into simple elements, choosing shape functions to approximate variations within each element, and assembling the element equations into a global system of equations to solve.
1) Finite element analysis is a numerical method used to solve engineering problems by breaking structures down into small discrete elements. It involves modeling structures as assemblies of simple geometric shapes called finite elements.
2) The key steps in finite element analysis include discretizing the structure into elements, selecting element types, defining displacement and strain/stress relationships within each element, deriving the element stiffness matrix, and assembling individual element equations into a system of equations for the overall structure.
3) Common approaches include the displacement method, which uses nodal displacements as unknowns, and the force method, which uses internal forces. The displacement method is typically more suitable for computational analysis.
The document discusses isoparametric finite elements. It defines isoparametric, superparametric, and subparametric elements. It provides examples of shape functions for 4-noded rectangular, 6-noded triangular, and 8-noded rectangular isoparametric elements. It also discusses coordinate transformation from the natural to global coordinate system using these shape functions and calculating the Jacobian.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
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 Finite Element Analysis Madhan N R
This document discusses finite element analysis (FEA) and its applications in engineering. It introduces FEA as a numerical method to determine stress and deflection in structures. It covers FEA modeling techniques including meshing, element types, boundary conditions and assumptions. It also compares traditional design cycles to using FEA and discusses how FEA can replace physical testing.
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.
Finite Element Analysis (FEA) is a numerical method for solving complex engineering problems. The document discusses conducting FEA on a fixed-free cantilever beam to study the effect of mesh density on solution accuracy. Analytical solutions are derived and used to validate FEA results. A beam model is created in ABAQUS with varying element sizes. As element count increases, FEA results converge towards analytical solutions, though with increased computation time. An element count of 4125 provided an optimal balance between accuracy and cost.
The document discusses the finite element method (FEM) for numerical analysis of structures. It provides the following key points:
1) FEM divides a structure into discrete elements connected at nodes, resulting in a finite number of degrees of freedom and a set of simultaneous algebraic equations to solve.
2) It uses approximate methods like the Rayleigh-Ritz method to obtain solutions for complex geometries and boundary conditions. This involves assuming displacement fields and minimizing the total potential energy.
3) The Galerkin method is presented, which satisfies the governing differential equations in an integral sense by setting the residual equal to zero when multiplied by a weighting function.
4) Applications to 1D problems are discussed,
ME6603 - FINITE ELEMENT ANALYSIS UNIT - IV NOTES AND QUESTION BANKASHOK KUMAR RAJENDRAN
This document contains a collection of practice problems related to finite element analysis of two-dimensional vector variable problems, including axisymmetric problems. The problems cover derivation of element stiffness matrices and strain-displacement matrices for various element types under different conditions, calculation of element stresses and displacements, modeling of cylinders under pressure, and determination of global stiffness matrices for structures. The elements and conditions include constant strain triangles, linear strain triangles, axisymmetric triangles, plane stress, plane strain, and shells.
This document contains formulas and equations related to finite element analysis (FEA) for one-dimensional structural and heat transfer problems. It includes formulas for weighted residual methods, Ritz method, beam deflection and stress, springs, one-dimensional bars and frames, and one-dimensional heat transfer through walls and fins. Displacement functions, stiffness matrices, thermal loads, and conduction/convection equations are provided for linear and quadratic elements undergoing static structural and thermal analysis.
The document discusses the casting process for hydraulic cylinder pistons. It begins by introducing pistons and their use in hydraulic mechanisms. It then describes the casting process, noting that large pistons are typically gravity die cast while smaller pistons may be sand cast. The casting process involves pouring molten metal into a mold. Further processes include lathe work to machine diameters and faces and milling holes. Pistons are widely used in engines and hydraulics.
Design Reliability and Product Integrity on a Hydraulic Cylinderprashanth884
The document summarizes the design reliability process for a hydraulic cylinder used in trailer beds. It describes the initial design proposal, failure modes identified through design FMEA, prototype testing that revealed gland thread shear as the critical failure, and an alternate design using a retaining ring. Prototypes of the new design successfully passed tests up to 7,000 cycles without failure, establishing a design meeting the required reliability.
This document provides examples of using FEMAP to analyze vibration modes of different structures. Example 1 analyzes a cantilever beam using beam elements. Example 2 analyzes a square plate using plate elements. Example 3 analyzes a wing box geometry made of multiple surfaces using shell elements. The steps include creating geometry, defining materials and properties, meshing, applying constraints, and performing modal analysis to obtain vibration modes.
In this presentation, we explain the basics of FEA, which stands for finite element analysis, a type of engineering method in product development.
For more information on RGBSI, visit: www.rgbsi.com
The document discusses different types of hydraulic cylinders and rotary actuators. It describes single acting cylinders that work in one direction, double acting cylinders that work in both directions, and telescopic cylinders for large strokes or limited spaces. It also covers properties of cylinders, calculations, buckling checks, and cushioning cylinders at the end of strokes. Rotary actuators discussed include vane, piston, and limited angle types.
ANSYS is an engineering simulation software founded by John Swanson. It develops CAE products like ANSYS Mechanical and ANSYS Multiphysics, which are used for numerically solving mechanical problems involving structural analysis, heat transfer, and fluid dynamics. These products allow modeling using finite elements and solving the resulting equations to analyze how engineering components will react to real-world forces, temperatures, pressures and other physical effects.
This document discusses the design and manufacturing of hydraulic cylinders. It defines hydraulic cylinders as devices that convert the energy of pressurized fluid into linear mechanical force and motion. It then describes the key components of hydraulic cylinders including the piston rod, seals, guide bush, gland bush, end plug, flanges, and bleed ports. The document focuses on explaining the purpose and design considerations for each of these important parts.
Introduction of finite element analysis1ssuser2209b4
The document provides an introduction to the finite element method (FEM). It discusses the different numerical, analytical, and experimental methods used to solve engineering problems. FEM involves discretizing a continuous domain into smaller, finite pieces called elements and using a mathematical representation to approximate the solution. It describes how FEM builds a stiffness matrix and assembles element equations to solve for unknown displacements. The document outlines the general FEM steps and highlights the merits and limitations of FEM, giving examples of its applications in stress analysis of industrial parts, fluid flow analysis, electromagnetic problems, and medical procedures.
This document outlines the objectives, course outcomes, and units covered in a finite element analysis course. The objective is to equip students with fundamentals of FEA and introduce the steps involved in discretization, applying boundary conditions, assembling stiffness matrices, and solving problems. The course covers basic FEA concepts, one-dimensional elements, two-dimensional elements, axisymmetric problems, isoparametric elements, and dynamic analysis. Students will learn to formulate and solve structural and heat transfer problems using various finite elements.
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 describes a case study analyzing the maximum deflection of a cantilever beam using finite element analysis software ANSYS. It first provides background on finite element analysis and its general steps. It then outlines the specific steps taken in ANSYS to model and analyze a cantilever beam with an end load, including preprocessing, solution, and postprocessing stages. The results found the maximum deflection to be 0.73648m and the von-mises stress to be 286.19 N/m. The document concludes with thanks for reading.
The document discusses the finite element method (FEM). FEM is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small, simpler elements that are solved using relations between each other. There are three phases: pre-processing to mesh the geometry and apply properties/conditions, solution to derive equations and solve for quantities, and post-processing to validate solutions. FEM can model various problem types like static, dynamic, structural, vibrational, and heat transfer analyses. It has advantages like handling complex geometries and loadings but also disadvantages like requiring approximations and computational resources.
Finite element analysis (FEA) is a numerical technique used to find approximate solutions to partial differential equations. It divides a complex problem into small elements that can be solved together. FEA uses a grid of nodes and meshes to model how a structure will react to loads based on its material properties. It can be used for structural, vibrational, fatigue, and heat transfer analysis to help engineers design structures with irregular shapes or complex conditions.
Part 1_Methods for mechanically analysing a solid structure(1).pdfSajawalNawaz5
The document provides an overview of finite element analysis (FEA) theory. It discusses the basic principles of FEA, including reducing complex structures into small elements defined by nodes. The behavior of each element is described using mechanics equations, and the overall structural behavior is calculated by assembling the equations. The document outlines different types of 2D and 3D elements that can be used, such as truss, beam, membrane, and plate elements. It also discusses meshing and node properties.
1. The document describes a study that used finite element analysis to simulate the burst pressure of a vibration welded plastic vessel and determine the yield stress at the weld bead.
2. An experimental hydrostatic pressure test showed rupture occurred at the weld bead, so the goal was to model this and obtain the stress at the weld bead.
3. Various meshing techniques were tested in the FEA software ABAQUS to find the best correlation with experimental data, including different element types, sizes, and modeling of the weld bead. The results showed second order elements with two layers of dragged elements for the weld bead membrane provided the most accurate stresses at the weld bead.
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.
Introduction of Finite Element AnalysisMuthukumar V
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 system to solve for displacements, and computing stresses and strains. FEM can be used to solve structural and non-structural problems and overcomes limitations of experimental and analytical methods for complex systems. The key aspects are subdividing the domain, selecting interpolation functions, deriving element equations, assembling the global system, applying boundary conditions, and solving for unknowns.
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.
*Need of finite element analysis
*Introduction to approaches used in Finite Element Analysis such as direct approach and energy approach
*Boundary conditions: Types
*Rayleigh-Ritz Method
*Galerkin Method
This document discusses using LS-DYNA software to simulate the thermoforming process. It introduces the geometry and finite element model created in HyperMesh and LS-Prepost. Shell elements are used to model the thin structures. Material models are defined for the rigid tools and deformable fabric. The forming process is defined through contact definitions, prescribed motion of the punch, and blank holder force. Results of the fiber orientation and shear angle distribution are compared to previous work. Parameters like yarn thickness and friction could not be exactly determined and may contribute to differences in results.
This document discusses using LS-DYNA software to simulate the thermoforming process. It introduces the geometry and finite element model created in HyperMesh and LS-Prepost. Shell elements are used to model the thin structures. Material models are defined for the rigid tools and deformable fabric. The forming process is defined through contact definitions, movement constraints, loading, time steps and other simulation settings. Results of the fabric draping simulation are compared to previous work and a parametric study is performed on the effect of blankholder force. Future work is proposed to further validate and expand on the thermoforming process simulations.
Intro
Principle
How it works
Types of dynamic Experiments
Instrumentation
Construction
Preparation of samples
Types of analysers
DMA of glass transition of polymers
Advantages
Applications
Limitations
Latest Research
References
Unit I fdocuments.in_introduction-to-fea-and-applications.pptAdityaChavan99
The document provides an introduction to finite element analysis (FEA) and its applications to engineering problems. It discusses that FEA is a numerical method used to solve problems that cannot be solved analytically due to complex geometry or materials. It involves discretizing a continuous structure into small, well-defined substructures called finite elements. The key steps in FEA include preprocessing such as defining geometry, meshing and material properties, solving the problem, and postprocessing results such as stresses and strains. The document also discusses various element types, assembly of elements, sources of error in FEA, and its advantages such as handling complex geometry, loading and materials.
This document discusses various techniques for non-linear structural analysis using finite element methods. It covers the differences between linear and non-linear analysis, MATLAB-based truss and push-over analyses, using experimental data to build material models for tensile testing simulations, buckling analysis of a stiffened panel, ultimate strength analysis of a hull girder, and comparing the Smith method and finite element analysis for calculating ultimate strength. The goal is to demonstrate various non-linear analysis methods and validate models using experimental data.
ENGR7961 Finite Element MethodsAssessment I - Report SemesTanaMaeskm
ENGR7961 Finite Element Methods
Assessment I - Report
Semester 1 201
Topic Coordinators: Dr Rami Al-Dirini
Due Date: 22nd of April 2021
Part 1: Simulating dog-bone tensile testing (10%)
As an FE engineer designing a product that uses rubber, you need to ensure that you have accurate data on the material properties. Therefore, you are provided with standard uniaxial tensile set testing (ASTM D412) data for Neoprene rubber (attached)
Task: Using the data provided in the attached excel sheet (Neoprene_tensile_data.xlsx) and the dimensions on Figure 1, you are required to develop an FE model for this experiment in order to calibrate your material properties. Use the template provided to report your FE process and results.
You are expected to explore the use of different elements and element order (linear or quadrilateral) while developing your model
Figure 1: dog-bone sample dimensions and coordinate system
70 mm
50 mm
16 mm
8 mm
5 mm
Part 2: Testing design robustness for a steel clamp.
You are part of an engineering team designing a steel clamp that supports 3-dimensional tensile loads. Given that the clamp will be supported by 2 bolts (as shown in Figure 2), as an FE engineer, you are required to assess the robustness of the design under the expected loads:
Loads: simulate a force with the following components:
Fx = -5 x 105 N
Fy = 0 N
Fz = 5 x 105 N
Bolt
Bolt
Figure 2: Clamp with bolt locations shown
Figure 3: side view of the clamp with coordinate system showing the x (red) and z (blue) axes.
Task:
Using the attached CAD file (CAD_Fitting.igs) and the information above, you are required to develop an FE model assess the robustness of this design to the expected loads. You may consider the concept of safety factor and the fact that the yield stress for this type of structural steel is 360 MPa.
You are expected to explore the use of different elements and element order (linear or quadrilateral) while developing your model.
Tips
Importing CAD geometry files:
Right click on “Geometry” in the Static Structural module, then select “Import Geometry” to locate the CAD file (CAD_Fitting.igs). Once you have selected your file, double click on the “Geometry” to load the file. This will open a new window with SpaceClaim.
Once the model shows on your screen, close the screen and return to ANSYS Workbench.
Defining Mesh Element Type, Size and Order:
Controlling element type:
Right click on the “Mesh” in the model tree and select “Insert” > “Method”
You can select the appropriate “Method” and “Element Order” in the “Details” panel on the left of the screen.
Notes:
Use “Tetrahedrons” to generate a mesh with tetrahedral elements and “Cartesian” to generate a mesh with hexahedral elements. [footnoteRef:1] [1: Alternatively, you can use “Hex Dominant” method, however, this tends to fail for some geometries. ]
Controlling element size:
Right click on the “Mesh” in the model tree and ...
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
2. FEM (Finite Element Method)
Introduction
• Numerical technique for gaining an approximate answer to the problem by
representing the object by an assembly of rods, plates, blocks, bricks & etc.
• building elements is given the appropriate material properties and is
connected to adjacent elements at ‘nodes’ – special points on the ends, edges
and faces of the element.
• Selected nodes will be given constraints to fix them in position, temperature,
voltage, etc. depending on the problem (user defined).
The finite element method, therefore, has three main stages:
1) build the model
2) solve the model
3) display the results
3. Build the model
• create nodes in positions to represent the object’s shape or import from an existing
CAD model
• refine as required.
• create finite elements (beams, plates, bricks, etc) between the nodes
• assign material properties to the elements
• assign constraints to selected nodes
• assign applied forces to the appropriate nodes.
Solve the model
•define the type of analysis you want e.g. static linear, vibrational modes, dynamic
response with time, etc.
Display the results
• select which parameters you want to display e.g. displacement, principal stress,
temperature, voltage,
• display as 2D or 3D contour plots, and/or as tables of numerical values, before
inferring anything from the results, they must first be validated,
• validation requires confirming mesh convergence has occurred and that values are in
line with expectations from hand calculations, experiments or past experience,
• mesh convergence requires refining the mesh repeatedly and solving until the
results
no longer change appreciably.
4. The Work
Flow
1.1 Mesh
• A finite element mesh consists of nodes (points) and elements (shapes which link the nodes
together).
• Elements represent material so they should fill the volume of the object being modeled.
1.2 Analysis
• Global properties such as analysis type, physical constants, solver settings and output options
by editing the Analysis item in the outline tree
1.3 Geometry
If you generate a mesh from a STEP or IGES file exported from CAD then these files are shown in
the Geometry group. Each geometry item can be auto-meshed to generate a mesh.
1.4 Components & Materials
• A component is an exclusive collection of elements. Every element must belong to exactly one
component. The default component is created automatically and cannot be deleted.
• Each component containing some elements must have a material assigned to it. The same
material can be shared between several components.
1.5 Named Selections
• A named selection is a non-exclusive collection of nodes, elements or faces.
• Named selections are used for applying loads and constraints.
1.6 Loads & Constraints
• This group contains all the loads and constraints in the model. It can also contain load cases
with their own loads.
1.7 Solution
After solving, the results are shown under the Solution branch in the outline tree. You can click
on a field value to display a colored contour plot of it.
5. GUI graphic user interface
• the toolbars at the top, arranged into model-building tools and the graphics display options.
• the model structure and solution displayed in an outline tree in the left panel
• a graphic display area of the model
1.2.1_basic_graphics_tutorial.liml
6. Modelling
• uses only nodes and elements
• imported CAD models in stp & iges format
• model is a mesh of elements. Each element has nodes which are simply points on
the element. Elements can only be connected to other elements node-to-node.
• Elements themselves have very simple shapes like lines, triangles, squares, cubes
and pyramids.
Each element is formulated to obey a particular law of science. For example:
• static analysis - the elements are formulated to relate displacement and stress according to the
theory of mechanics of materials.
• modal vibration - the elements are formulated to obey deflection shapes and frequencies
according to the theory of structural dynamics.
• thermal analysis - the elements relate temperature and heat according to heat transfer theory.
7. • Always begin a manual mesh by
creating a coarse mesh; it can always be
refined later.
• finite elements are 3D. The elements
that appear flat and 2D do actually have
the third dimension, of thickness.
• 3D Elements usually be created from a
2D flat shape. This initial 2D mesh can
be created either by a combination of
nodes and elements or by using readymade template patterns.
• Editing tools are available for
modifying the 2Dmesh. Once the coarse
mesh is complete, whether it be 2D or
3D in appearance, it will need to be
refined before running the Solver.
8. Meshing Tools
creating tools, that bring into existence
a two dimensional mesh
editing tools, that form and modify the created 2D mesh
tools that will convert the two dimensional mesh
into 3D meshes
refinement tools for converging results
10. Analysis Types
Warning:
!
The finite element method uses a mathematical formulation of physical theory to represent physical
behavior. Assumptions and limitations of theory (like beam theory, plate theory, Fourier theory, etc.) must
not be violated by what we ask the software to do. A competent user must have a good physical grasp of the
problem so that errors in computed results can be detected and a judgment made as to whether the results
are to be trusted or not. Please validate your results!
• FEA follows the law of 'Garbage in, Garbage out'.
The choice of element type, mesh layout, correctness of applied constraints will directly affect the stability
and accuracy of the solution.
Tips:
The outline tree presents all the information needed about your
model and allows you to perform various actions on the model itself.
You will always begin at the top, changing the analysis type if you do
not want the default, 3D static analysis.
Items that appear in red indicate missing or erroneous information, so right
click them for a What's wrong? clue.
11. Analysis Types
Tips:
Apply your loads and constraints to element faces rather than nodes. Mesh refinements will automatically
transfer element face loads and constraints to the newly created elements, whereas loads and constraints
applied to nodes are not automatically transferred to the new Elements.
12. Analysis Types - examples
• Static analysis of a pressurized cylinder
• Thermal analysis of a plate being cooled
• Modal vibration of a cantilever beam
• Dynamic response of a crane frame
• Magnetostatic analysis of a current carrying wire
• DC circuit analysis
• Electrostatic analysis of a capacitor
• Acoustic analysis of an organ pipe
• Buckling of a column
• Fluid flow around a cylinder
13. Static analysis of a pressurized cylinder
A cylinder of 2m radius, 10m length, 0.2m thickness, Young's modulus 200e9 N/m2 and Poisson ratio 0.285 will be analyzed to
determine its hoop stress caused by an internal pressure of 100N. From shell theory, the circumferential or hoop stress for a thin
cylinder of constant radius and uniform internal pressure is given by :
σ = (pressure × radius) / thickness
σ = (100 × 2) / 0.2
σ = 1000 N/m2
14. Static analysis of a pressurized cylinder
A cylinder of 2m radius, 10m length, 0.2m thickness, Young's modulus 200e9 N/m2 and Poisson ratio 0.285 will be analyzed to
determine its hoop stress caused by an internal pressure of 100N. From shell theory, the circumferential or hoop stress for a thin
cylinder of constant radius and uniform internal pressure is given by :
σ = (pressure × radius) / thickness
σ = (100 × 2) / 0.2
σ = 1000 N/m2
15. Thermal analysis of a plate being cooled
A plate of cross-section thickness 0.1m at an initial temperature of 250°C is suddenly immersed in an oil bath of temperature
50°C. The material has a thermal conductivity of 204W/m/°C, heat transfer coefficient of 80W/m2/°C, density 2707 kg/m3 and
a specific heat of 896 J/kg/°C. It is required to determine the time taken for the slab to cool to a temperature of 200*C.
For Biot numbers less than 0.1, the temperature anywhere in the cross-section will be the same with time.
Bi = hL/k = (80)(0.1)/(204) = 0.0392
From classical heat transfer theory the following lumped analysis heat transfer formula can be used.
(T(t)-Ta)/(To-Ta) = e-(mt)
Ta = temperature of oil bath, To = initial temperature
where m = h/ ρ Cp(L/2), h = heat transfer coefficient
ρ = density, Cp = specific heat, L = thickness
m = 80/[(2707)(896)(0.1/2)]
m = 1/1515.92 s-1
(200 - 50) / (250 - 50) = e(-t/1515.92)
t = ln (4) X 1515.92
t = 436 s
16. Modal vibration of a cantilever beam
A cantilever beam of length 1.2m, cross-section 0.2m × 0.05m, Young's modulus 200×10 9 Pa, Poisson
ratio 0.3 and density 7860 kg/m3. The lowest natural frequency of this beam is required to be
determined.
For thin beams, the following analytical equation is used to calculate the first natural frequency :
f = (3.52/2π)[(k / 3 × M)]1/2
f = frequency, M = mass
M = density × volume
M = 7860 × 1.2 × 0.05 × 0.2
M = 94.32 kg
k = spring stiffness
k = 3×E×I / L3
I = moment of inertia of the cross-section.
E = Young's modulus, L = beam length
I = (1/12)(bh3)
I = (1/12) (0.2 x 0.053)
I = 2.083×10-6 m4
k = (3 × 200×109 × 2.083×10-6) / 1.23
k = 723.379×103 N/m
f = (3.52/2 × 3.14) [(723.379×103/ 3 × 94.32)]1/2
f = 28.32 Hz
Beginners guide:pg 42
18. Buckling of a column
The eigen value buckling of a column with a fixed end will be solved. The column has a length of 100mm, a
square cross-section of 10mm and Young's modulus 200000 N/mm2 .
The critical load for a fixed end Euler column is π2EI/(4L2)
E = Young's modulus, I = moment of inertia
I = 104/12 = 833.33mm4
L = length
Critical load = π2 200000 × 833.33 / (4×1002)= 41123.19 N
Beginners guide:pg 76
19. Fluid flow around a cylinder
A confined streamlined flow around a cylinder will be analyzed for the flow potentials and velocity
distributions around the cylinder. The inward flow velocity is 1 m/s . The ambient pressure is 1×10 5 Pa,
density 1000 kg/m3 .
20. Modeling Errors
Results can only be as accurate as your model. Use rough estimates from hand calculations, experiment or
experience to check whether or not the results are reasonable. If the results are not as expected, your model
may have serious errors which need to be identified.
Too coarse a mesh
• the narrower the rectangles, the more
accurate will be the result.
• Concentrate the mesh refinement in those
areas where the accuracy can be improved,
while leaving unchanged those areas that
are already accurate.
• Run at least one model to identify the
areas where the values are changing a lot
and the areas where values are remaining
more or less the same. The second run will
be the refined model.
21. Modeling Errors
Wrong choice of elements
• Plate-like geometries such as walls, where the thickness is less in comparison to its other dimensions,
should be modeled with either shell elements or quadratic solid elements .
• Shell, beam and membrane elements should not be used where their simplified assumptions do not apply.
For example beams that are too thick, membranes that are too thick for plane stress and too thin
for plane strain, or shells
Linear elements
Linear elements (elements with no mid-side nodes) are too stiff in
bending so they typically have to be refined more than quadratic
elements (elements with mid-side nodes) for results to converge.
4.5.4 Severely distorted elements
Element shapes that are compact and regular give the greatest accuracy. The ideal triangle is
equilateral, the ideal quadrilateral is square, the ideal hexahedron is a cube of equal side length, etc.
Distortions tend to reduce accuracy by making the element stiffer than it would be otherwise, usually
degrading stresses more than displacements.
Shape distortions will occur in FE modeling because it is quite impossible to represent structural geometry
with perfectly shaped elements. Any deterioration in accuracy will only be in the vicinity of the badly shaped
elements and will not propagate through the model (St. Venant's principle).
These artificial disturbances in the field values should not be erroneously accepted as actually being
present.
22. Modeling Errors
Severely distorted elements
• Element shapes that are compact and regular give the greatest accuracy. The ideal triangle is equilateral,
the ideal quadrilateral is square, the ideal hexahedron is a cube of equal side length, etc.
• Distortions tend to reduce accuracy by making the element stiffer than it would be otherwise, usually
degrading stresses more than displacements.
• Shape distortions will occur in FE modeling because it is quite impossible to represent structural geometry
with perfectly shaped elements. Any deterioration in accuracy will only be in the vicinity of the badly shaped
elements and will not propagate through the model (St. Venant's principle).
These artificial disturbances in the field values should not be erroneously accepted as actually being
present.
Avoid large aspect ratios. A length to breadth
ratio of generally not more than 3.
Avoid strongly curved sides in quadratic
elements.
Highly skewed. A skewed angle of generally
not more than 30 degrees.
Off center mid-side nodes.
A quadrilateral should not look almost like a
triangle.
23. Modeling Errors
Mesh discontinuities
• Element sizes should not change abruptly from fine to coarse.
Rather they should make the transition gradually.
• Nodes cannot be connected to element
edges. Such arrangements will result in
gaps and penetrations that do not occur in
reality.
• Corner nodes of quadratic elements
should not be connected to mid-side
nodes. Although both edges deform
quadratically, they are not deflecting in
sync with each other.
• Linear elements (no mid-side node) should not be connected to the
midside nodes of quadratic elements, because the edge of the
quadratic element deforms quadratically whereas the edges of the
linear element deform linearly.
• Avoid using linear elements with quadratic elements as the mid side node
will open a gap or penetrate the linear element.
24. Modeling Errors
Non-linearities
• Some FEA software can model only the linear portion
of the stress-strain curve and large deformations where
the stiffness or load changes with deformation.
• Shell elements under bending loads should not deform
by more than half their thickness otherwise
non-linear membrane action occurs in the real world to
resist further bending.
Improper constraints
Fixed supports will result in less deformation that simple supports which permit material to move within
the plane of support.
Rigid body motion
In static analysis, for a structure to be stressed all rigid body motion must be eliminated. For 2D problems there
are two translational (along the X- & Y-axes) and one rotational (about the Z-axis) rigid body motions. For 3D
problems there are three translational (along the X-, Y- & Z-axes) and three rotational (about the X-,Y- & Z-axes)
rigid body motions. Rigid body motion can be eliminated by applying constraints such as fixed support,
displacement and rotx, roty and rotz.