Rent 9780534929640 | First Course in the Finite Element Method

Summary Table of Contents

This third edition provides a simple, basic approach to the finite element method that can be understood by both undergraduate and graduate students. It does not have the usual prerequisites (such as structural analysis) required by most available texts in this area. The book is written primarily as a basic learning tool for the undergraduate student in civil and mechanical engineering whose main interest is in stress analysis and heat transfer. The text is geared toward those who want to apply the finite element method as a tool to solve practical physical problems.

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Introduction Prologue
Brief History
Introduction to Matrix Notation
Role of the Computer
General Steps of the Finite Element of Method
Applications of the Finite Element Methods
Advantages of the Finite Element Method
Computer Programs for the Finite Element Method
References
Problems
Introduction to the Stiffness (Displacement) Method Introduction
Definitions of the Stiffness Matrix
Derivation of the Stiffness Matrix for a Spring Element
Example of a Spring Assemblage
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
Boundary Conditions
Potential Energy Approach to Derive Spring Element Equations
References
Problems
Development of Truss Equations Introduction
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
Selecting Approximation Functions for Displacements
Transformation of Vectors in Two Dimensions
Global Stiffness Matrix
Computation of Stress for a Bar in the x-y Plane
Solution of a Plane Truss
Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
Use of Symmetry in Structure
Inclined, or Skewed, Supports
Potential Energy Approach to Derive Bar Element Equations
Comparison of Finite Element Solution to Exact Solution for Bar
Galerkin's Residual Method and Its Application to a One-Dimensional Bar
References
Problems
Development of Beam Equations Introduction
Beam Stiffness
Example of Assemblage of Beam Stiffness Matrices
Examples of Beam Analysis Using the Direct Stiffness Method
Distributed Loading
Comparison of Finite Element Solution to the Exact Solution for a Beam
Beam Element with Nodal Hinge
Potential Energy Approach to Derive Beam Element Equations
Galerkin's Method for Deriving Beam Element Equations
References
Problems
Frame and Grid Equations Introduction
Two-Dimensional Arbitrarily Oriented Beam Element
Rigid Plane Frame Examples
Inclined or Skewed Supports-Frame Element
Grid Equations
Beam Element Arbitrarily Oriented in Space
Concepts of Substructure Analysis
References
Problems
Development of the Plane Stress and Plane Strain Stiffness Equations Introduction
Basic Concepts of Plane Stress and Plane Strain
Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations
Treatment of Body and Surface Forces
Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
Finite Element Solution of a Plane Stress Problem
References
Problems
Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis
Introduction
Finite Element Modeling
Equilibrium and Compatibility of Finite Element Results
Convergence of Solution
Interpretation of Stresses
Static Condensation
Flowchart for the Solution of Plane Stress Problems
Computer Program Results for Some Plane Stress/Strain Problems
References
Problems
Development of the Linear-Strain Triangle Equations Introduction
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations
Example LST Stiffness Determination
Comparison of Elements
References
Problems
Axisymmetric Elements Introduction
Derivation of the Stiffness Matrix
Solutions of an Axisymmetric Pressure Vessel
Applications of Axisymmetric Elements
References
Problems
Isoparametric Formulation
Introduction
Isoparametric Formulation of the Bar Element Stiffness Matrix
Rectangular Plane Stress Element
Isoparametric Formulation of the Plane Element Stiffness Matrix
Gaussian Quadrature (Numerical Integration)
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
Higher-Order Shape Functions
References
Problems
Three-Dimensional Stress Analysis
Introduction
Three Dimensional Stress and Strain
Tetrahedral Element
Isoparametric Formulation
References
Problems
Plate Be
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First Course in the Finite Element Method

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