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A First Course in the Finite Element Analysis 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. This revised fourth edition includes the addition of a large number of new problems (including SI… More problems), an appendix for mechanical and thermal properties, and more civil applications.Less

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Book details

List price: $368.95 Edition: 4th Copyright year: 2007 Publisher: Course Technology Publication date: 7/25/2006 Binding: Hardcover Pages: 752 Size: 7.75" wide x 9.50" long x 1.50" tall Weight: 3.190 Language: English

AuthorTable of Contents

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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