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A First Course in the Finite Element Method,9780534552985
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A First Course in the Finite Element Method

by
Edition:
4th
ISBN13:

9780534552985

ISBN10:
0534552986
Format:
Hardcover
Pub. Date:
7/25/2006
Publisher(s):
CL Engineering
List Price: $303.33

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Summary

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 problems), an appendix for mechanical and thermal properties, and more civil applications.

Table of Contents

Introduction
1(27)
Prologue
1(1)
Brief History
2(2)
Introduction to Matrix Notation
4(2)
Role of the Computer
6(1)
General Steps of the Finite Element Method
7(8)
Applications of the Finite Element Method
15(4)
Advantages of the Finite Element Method
19(4)
Computer Programs for the Finite Element Method
23(5)
References
24(3)
Problems
27(1)
Introduction to the Stiffness (Displacement) Method
28(37)
Introduction
28(1)
Definition of the Stiffness Matrix
28(1)
Derivation of the Stiffness Matrix for a Spring Element
29(5)
Example of a Spring Assemblage
34(3)
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
37(2)
Boundary Conditions
39(13)
Potential Energy Approach to Derive Spring Element Equations
52(13)
References
60(1)
Problems
61(4)
Development of Truss Equations
65(86)
Introduction
65(1)
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
66(6)
Selecting Approximation Functions for Displacements
72(3)
Transformation of Vectors in Two Dimensions
75(3)
Global Stiffness Matrix
78(4)
Computation of Stress for a Bar in the x-y Plane
82(2)
Solution of a Plane Truss
84(8)
Transformation, Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
92(8)
Use of Symmetry in Structure
100(3)
Inclined, or Skewed, Supports
103(6)
Potential Energy Approach to Derive Bar Element Equations
109(11)
Comparison of Finite Element Solution to Exact Solution for Bar
120(4)
Galerkin's Residual Method and Its Use to Derive the One-Dimensional Bar Element Equations
124(3)
Other Residual Methods and Their Application to a One-Dimensional Bar Problem
127(24)
References
132(1)
Problems
132(19)
Development of Beam Equations
151(63)
Introduction
151(1)
Beam Stiffness
152(9)
Example of Assemblage of Beam Stiffness Matrices
161(2)
Examples of Beam Analysis Using the Direct Stiffness Method
163(12)
Distributed Loading
175(13)
Comparison of the Finite Element Solution to the Exact Solution for a Beam
188(6)
Beam Element with Nodal Hinge
194(5)
Potential Energy Approach to Derive Beam Element Equations
199(2)
Galerkin's Method for Deriving Beam Element Equations
201(13)
References
203(1)
Problems
204(10)
Frame and Grid Equations
214(90)
Introduction
214(1)
Two-Dimensional Arbitrarily Oriented Beam Element
214(4)
Rigid Plane Frame Examples
218(19)
Inclined or Skewed Supports---Frame Element
237(1)
Grid Equations
238(17)
Beam Element Arbitrarily Oriented in Space
255(14)
Concept of Substructure Analysis
269(35)
References
275(1)
Problems
275(29)
Development of the Plane Stress and Plane Strain Stiffness Equations
304(46)
Introduction
304(1)
Basic Concepts of Plane Stress and Plane Strain
305(5)
Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations
310(14)
Treatment of Body and Surfaces Forces
324(5)
Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
329(2)
Finite Element Solution of a Plane Stress Problem
331(19)
References
342(1)
Problems
343(7)
Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis
350(48)
Introduction
350(1)
Finite Element Modeling
350(13)
Equilibrium and Compatibility of Finite Element Results
363(4)
Convergence of Solution
367(1)
Interpretation of Stresses
368(1)
Static Condensation
369(5)
Flowchart for the Solution of Plane Stress/Strain Problems
374(1)
Computer Program Assisted Step-by-Step Solution, Other Models, and Results for Plane Stress/Strain Problems
374(24)
References
381(1)
Problems
382(16)
Development of the Linear-Strain Triangle Equations
398(14)
Introduction
398(1)
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations
398(5)
Example LST Stiffness Determination
403(3)
Comparison of Elements
406(6)
References
409(1)
Problems
409(3)
Axisymmetric Elements
412(31)
Introduction
412(1)
Derivation of the Stiffness Matrix
412(10)
Solution of an Axisymmetric Pressure Vessel
422(6)
Applications of Axisymmetric Elements
428(15)
References
433(1)
Problems
434(9)
Isoparametric Formulation
443(47)
Introduction
443(1)
Isoparametric Formulation of the Bar Element Stiffness Matrix
444(5)
Rectangular Plane Stress Element
449(3)
Isoparametric Formulation of the Plane Element Stiffness Matrix
452(11)
Gaussian and Newton-Cotes Quadrature (Numerical Integration)
463(6)
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
469(6)
Higher-Order Shape Functions
475(15)
References
484(1)
Problems
484(6)
Three-Dimensional Stress Analysis
490(24)
Introduction
490(1)
Three-Dimensional Stress and Strain
490(3)
Tetrahedral Element
493(8)
Isoparametric Formulation
501(13)
References
508(1)
Problems
509(5)
Plate Bending Element
514(20)
Introduction
514(1)
Basic Concepts of Plate Bending
514(5)
Derivation of a Plate Bending Element Stiffness Matrix and Equations
519(4)
Some Plate Element Numerical Comparisons
523(1)
Computer Solution for a Plate Bending Problem
524(10)
References
528(1)
Problems
529(5)
Heat Transfer and Mass Transport
534(59)
Introduction
534(1)
Derivation of the Basic Differential Equation
535(3)
Heat Transfer with Convection
538(1)
Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h
539(1)
One-Dimensional Finite Element Formulation Using a Variational Method
540(15)
Two-Dimensional Finite Element Formulation
555(9)
Line or Point Sources
564(2)
Three-Dimensional Heat Transfer Finite Element Formulation
566(3)
One-Dimensional Heat Transfer with Mass Transport
569(1)
Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method
569(5)
Flowchart and Examples of a Heat-Transfer Program
574(19)
References
577(1)
Problems
577(16)
Fluid Flow
593(24)
Introduction
593(1)
Derivation of the Basic Differential Equations
594(4)
One-Dimensional Finite Element Formulation
598(8)
Two-Dimensional Finite Element Formulation
606(5)
Flowchart and Example of a Fluid-Flow Program
611(6)
References
612(1)
Problems
613(4)
Thermal Stress
617(30)
Introduction
617(1)
Formulation of the Thermal Stress Problem and Examples
617(30)
Reference
640(1)
Problems
641(6)
Structural Dynamics and Time-Dependent Heat Transfer
647(61)
Introduction
647(1)
Dynamics of a Spring-Mass System
647(2)
Direct Derivation of the Bar Element Equations
649(4)
Numerical Integration in Time
653(12)
Natural Frequencies of a One-Dimensional Bar
665(4)
Time-Dependent One-Dimensional Bar Analysis
669(5)
Beam Element Mass Matrices and Natural Frequencies
674(7)
Trusts, Plane Frame, Plane Stress/Strain Axisymmetric, and Solid Element Mass Matrices
681(5)
Time-Dependent Heat Transfer
686(7)
Computer Program Example Solutions for Structural Dynamics
693(15)
References
702(1)
Problems
702(6)
Appendix A Matrix Algebra
708(14)
Introduction
708(1)
Definition of a Matrix
708(1)
Matrix Operations
709(7)
Cofactor or Adjoint Method to Determine the Inverse of a Matrix
716(2)
Inverse of a Matrix by Row Reduction
718(4)
References
720(1)
Problems
720(2)
Appendix B Methods for Solution of Simultaneous Linear Equations
722(22)
Introduction
722(1)
General Form of the Equations
722(1)
Uniqueness, Nonuniqueness, and Nonexistence of Solution
723(1)
Methods for Solving Linear Algebraic Equations
724(11)
Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods
735(9)
References
741(1)
Problems
742(2)
Appendix C Equations from Elasticity Theory
744(8)
Introduction
744(1)
Differential Equations of Equilibrium
744(2)
Strain/Displacement and Compatibility Equations
746(2)
Stress/Strain Relationships
748(4)
Reference
751(1)
Appendix D Equivalent Nodal Forces
752(3)
Problems
752(3)
Appendix E Principle of Virtual Work
755(4)
References
758(1)
Appendix F Properties of Structural Steel and Aluminum Shapes
759(14)
Answers to Selected Problems 773(26)
Index 799


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