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A First Course in the Finite Element Method,9780534385170
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A First Course in the Finite Element Method

by
Edition:
3rd
ISBN13:

9780534385170

ISBN10:
0534385176
Format:
Hardcover
Pub. Date:
4/5/2001
Publisher(s):
CL Engineering
List Price: $228.99
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Summary

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

Table of Contents

Introduction
1(25)
Prologue
1(1)
Brief History
2(1)
Introduction to Matrix Notation
3(3)
Role of the Computer
6(1)
General Steps of the Finite Element Method
6(7)
Applications of the Finite Element Method
13(5)
Advantages of the Finite Element Method
18(1)
Computer Programs for the Finite Element Method
19(7)
References
22(3)
Problems
25(1)
Introduction to the Stiffness (Displacement) Method
26(37)
Introduction
26(1)
Definition of the Stiffness Matrix
26(1)
Derivation of the Stiffness Matrix for a Spring Element
27(5)
Example of a Spring Assemblage
32(3)
Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
35(2)
Boundary Conditions
37(13)
Potential Energy Approach to Derive Spring Element Equations
50(13)
References
58(1)
Problems
59(4)
Development of Truss Equations
63(74)
Introduction
63(1)
Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
63(6)
Selecting Approximation Functions for Displacements
69(2)
Transformation of Vectors in Two Dimensions
71(3)
Global Stiffness Matrix
74(4)
Computation of Stress for a Bar in the x-y Plane
78(2)
Solution of a Plane Truss
80(7)
Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
87(5)
Use of Symmetry in Structure
92(3)
Inclined, or Skewed, Supports
95(6)
Potential Energy Approach to Derive Bar Element Equations
101(11)
Comparison of Finite Element Solution to Exact Solution for Bar
112(4)
Galerkin's Residual Method and Its Application to a One-Dimensional Bar
116(21)
References
119(1)
Problems
120(17)
Development of Beam Equations
137(51)
Introduction
137(1)
Beam Stiffness
138(5)
Example of Assemblage of Beam Stiffness Matrices
143(2)
Examples of Beam Analysis Using the Direct Stiffness Method
145(9)
Distributed Loading
154(11)
Comparision of the Finite Element Solution to the Exact Solution for a Beam
165(6)
Beam Element with Nodal Hinge
171(5)
Potential Energy Approach to Derive Beam Element Equations
176(3)
Galerkin's Method for Deriving Beam Element Equations
179(9)
References
181(1)
Problems
181(7)
Frame and Grid Equations
188(76)
Introduction
188(1)
Two-Dimensional Arbitrarily Oriented Beam Element
188(4)
Rigid Plane Frame Examples
192(19)
Inclined or Skewed Supports-Frame Element
211(1)
Grid Equations
212(17)
Beam Element Arbitrarily Oriented in Space
229(5)
Concept of Substructure Analysis
234(30)
References
240(1)
Problems
240(24)
Development of the Plane Stress and Plane Strain Stiffness Equations
264(43)
Introduction
264(1)
Basic Concepts of Plane Stress and Plane Strain
265(5)
Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations
270(14)
Treatment of Body and Surface Forces
284(5)
Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
289(2)
Finite Element Solution of a Plane Stress Problem
291(16)
References
301(1)
Problems
301(6)
Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis
307(37)
Introduction
307(1)
Finite Element Modeling
308(10)
Equilibrium and Compatibility of Finite Element Results
318(2)
Convergence of Solution
320(1)
Interpretation of Stresses
321(2)
Static Condensation
323(4)
Flowchart for the Solution of Plane Stress/Strain Problems
327(1)
Computer Program Results for Some Plane Stress/Strain Problems
328(16)
References
331(1)
Problems
332(12)
Development of the Linear-Strain Triangle Equations
344(14)
Introduction
344(1)
Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations
344(5)
Example LST Stiffness Determination
349(3)
Comparision of Element
352(6)
References
354(1)
Problems
355(3)
Axisymmetric Elements
358(28)
Introduction
358(1)
Derivation of the Stiffness Matrix
358(10)
Solution of an Axisymmetric Pressure Vessel
368(8)
Applications of Axisymmetric Elements
376(10)
References
380(1)
Problems
381(5)
Isoparametric Formulation
386(35)
Introduction
386(1)
Isoparametric Formulation of the Bar Element Stiffness Matrix
386(6)
Rectangular Plane Stress Element
392(3)
Isoparametric Formulation of the Plane Element Stiffness Matrix
395(9)
Gaussian Quadrature (Numerical Integration)
404(3)
Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
407(6)
Higher-Order Shape Functions
413(8)
References
417(1)
Problems
417(4)
Three-Dimensional Stress Analysis
421(20)
Introduction
421(1)
Three-Dimensional Stress and Strain
421(2)
Tetrahedral Element
423(7)
Isoparametric Formulation
430(11)
References
436(1)
Problems
436(5)
Plate Bending Element
441(17)
Introduction
441(1)
Basic Concepts of Plate Bending
441(4)
Derivation of a Plate Bending Element Stiffness Matrix and Equations
445(5)
Some Plate Element Numerical Comparisions
450(2)
Computer Solution for a Plate Bending Problem
452(6)
References
454(1)
Problems
455(3)
Heat Transfer and Mass Transport
458(50)
Introduction
458(1)
Derivation of the Basic Differential Equation
459(3)
Heat Transfer with Convection
462(1)
Typical Units: Thermal, Conductivities, K; and Heat-Transfer Coefficients, h
463(1)
One-Dimensional Finite Element Formulation Using a Variational Method
464(14)
Two-Dimensional Finite Element Formulation
478(9)
Line or Point Sources
487(3)
One-Dimensional Heat Transfer with Mass Transport
490(1)
Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method
491(4)
Flowchart and Examples of a Heat-Transfer Program
495(13)
References
499(1)
Problems
499(9)
Fluid Flow
508(24)
Introduction
508(1)
Derivation of the Basic Differential Equations
508(5)
One-Dimensional Finite Element Formulation
513(8)
Two-Dimensional Finite Element Formulation
521(5)
Flowchart and Example of a Fluid-Flow Program
526(6)
References
527(1)
Problems
528(4)
Thermal Stress
532(27)
Introduction
532(1)
Formulation of the Thermal Stress Problem and Examples
532(27)
References
553(1)
Problems
554(5)
Structural Dynamics and Time-Dependent Heat Transfer
559(57)
Introduction
559(1)
Dynamics of a Spring-Mass System
559(2)
Direct Derivation of the Bar Element Equations
561(4)
Numerical Integration in Time
565(12)
Natural Frequencies of a One-Dimensional Bar
577(4)
Time-Dependent One-Dimensional Bar Analysis
581(5)
Beam Element Mass Matrices and Natural Frequencies
586(5)
Truss, Plane Frame, Plane Stress/Strain, Axisymmetric, and Solid Element Mass Matrices
591(4)
Time-Dependent Heat Transfer
595(7)
Computer Program Example Solutions for Structural Dynamics
602(14)
References
609(1)
Problems
610(6)
Appendix A Matrix Algebra 616(14)
Introduction
616(12)
A.1 Definition of a Matrix
616(1)
A.2 Matrix Operations
617(7)
A.3 Cofactor or Adjoint Method to Determine the Inverse of a Matrix
624(2)
A.4 Inverse of a Matrix by Row Reduction
626(2)
References
628(1)
Problems
628(2)
Appendix B Methods for Solution of Simultaneous Linear Equations 630(22)
Introduction
630(19)
B.1 General Form of the Equations
630(1)
B.2 Uniqueness, Nonuniqueness, and Nonexistence of Solution
631(1)
B.3 Methods for Solving Linear Algebraic Equations
632(11)
B.4 Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods
643(6)
References
649(1)
Problems
650(2)
Appendix C Equations from Elasticity Theory 652(8)
Introduction
652(7)
C.1 Differential Equations of Equilibrium
652(2)
C.2 Strain/Displacement and Compatibility Equations
654(2)
C.3 Stress/Strain Relationships
656(3)
Reference
659(1)
Appendix D Equivalent Nodal Forces 660(3)
Problems
660(3)
Appendix E Principle of Virtual Work 663(4)
References
666(1)
Answers to Selected Problems 667(22)
Index 689


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