有限要素法の初歩(第5版)<br>A First Course in the Finite Element Method : SI Edition (5TH)

有限要素法の初歩(第5版)
A First Course in the Finite Element Method : SI Edition (5TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 925 p.
  • 言語 ENG,ENG
  • 商品コード 9780495668275
  • DDC分類 621

基本説明

Provides a simple, basic approach to the course material that can be understood by both undergraduate and graduate students without the usual prerequisites (i.e. structural analysis).

Full Description


A FIRST COURSE IN THE FINITE ELEMENT METHOD provides a simple, basic approach to the course material that can be understood by both undergraduate and graduate students without the usual prerequisites (i.e. structural analysis). 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.

Table of Contents

Preface                                            xii
Preface to SI Edition xv
1 Introduction 1 (30)
Chapter Objectives 1 (1)
Prologue 1 (1)
1.1 Brief History 2 (2)
1.2 Introduction to Matrix Notation 4 (2)
1.3 Role of the Computer 6 (1)
1.4 General Steps of the Finite Element 7 (8)
Method
1.5 Applications of the Finite Element 15 (8)
Method
1.6 Advantages of the Finite Element 23 (2)
Method
1.7 Computer Programs for the Finite 25 (2)
Element Method
References 27 (2)
Problems 29 (2)
2 Introduction to the Stiffness 31 (41)
(Displacement) Method
Chapter Objectives 31 (1)
Introduction 31 (1)
2.1 Definition of the Stiffness Matrix 32 (1)
2.2 Derivation of the Stiffness Matrix 32 (6)
for a Spring Element
2.3 Example of a Spring Assemblage 38 (2)
2.4 Assembling the Total Stiffness Matrix 40 (2)
by Superposition (Direct Stiffness Method)
2.5 Boundary Conditions 42 (14)
2.6 Potential Energy Approach to Derive 56 (9)
Spring Element Equations
Summary Equations 65 (1)
References 66 (1)
Problems 66 (6)
3 Development of Truss Equations 72 (94)
Chapter Objectives 72 (1)
Introduction 72 (1)
3.1 Derivation of the Stiffness Matrix 73 (6)
for a Bar Element in Local Coordinates
3.2 Selecting Approximation Functions for 79 (3)
Displacements
3.3 Transformation of Vectors in Two 82 (3)
Dimensions
3.4 Global Stiffness Matrix for Bar 85 (5)
Arbitrarily Oriented in the Plane
3.5 Computation of Stress for a Bar in 90 (2)
the x-y Plane
3.6 Solution of a Plane Truss 92 (8)
3.7 Transformation Matrix and Stiffness 100(9)
Matrix for a Bar in Three-Dimensional
Space
3.8 Use of Symmetry in Structure 109(3)
3.9 Inclined, or Skewed, Supports 112(6)
3.10 Potential Energy Approach to Derive 118(11)
Bar Element Equations
3.11 Comparison of Finite Element 129(4)
Solution to Exact Solution for Bar
3.12 Galerkin's Residual Method and Its 133(3)
Use to Derive the One-Dimensional Bar
Element Equations
3.13 Other Residual Methods and Their 136(5)
Application to a One-Dimensional Bar
Problem
3.14 Flowchart for Solution of 141(1)
Three-Dimensional Truss Problems
3.15 Computer Program Assisted 141(3)
Step-by-Step Solution for Truss Problem
Summary Equations 144(1)
References 145(1)
Problems 146(20)
4 Development of Beam Equations 166(69)
Chapter Objectives 166(1)
Introduction 166(1)
4.1 Beam Stiffness 167(10)
4.2 Example of Assemblage of Beam 177(2)
Stiffness Matrices
4.3 Examples of Beam Analysis Using the 179(13)
Direct Stiffness Method
4.4 Distributed Loading 192(13)
4.5 Comparison of the Finite Element 205(6)
Solution to the Exact Solution for a Beam
4.6 Beam Element with Nodal Hinge 211(7)
4.7 Potential Energy Approach to Derive 218(3)
Beam Element Equations
4.8 Galerkin's Method for Deriving Beam 221(2)
Element Equations
Summary Equations 223(1)
References 224(1)
Problems 225(10)
5 Frame and Grid Equations 235(93)
Chapter Objectives 235(1)
Introduction 235(1)
5.1 Two-Dimensional Arbitrarily Oriented 235(4)
Beam Element
5.2 Rigid Plane Frame Examples 239(19)
5.3 Inclined or Skewed Supports---Frame 258(1)
Element
5.4 Grid Equations 259(18)
5.5 Beam Element Arbitrarily Oriented in 277(13)
Space
5.6 Concept of Substructure Analysis 290(6)
Summary Equations 296(2)
References 298(1)
Problems 299(29)
6 Development of the Plane Stress and Plane 328(56)
Strain Stiffness Equations
Chapter Objectives 328(1)
Introduction 328(1)
6.1 Basic Concepts of Plane Stress and 329(5)
Plane Strain
6.2 Derivation of the Constant-Strain 334(15)
Triangular Element Stiffness Matrix and
Equations
6.3 Treatment of Body and Surface Forces 349(5)
6.4 Explicit Expression for the 354(2)
Constant-Strain Triangle Stiffness Matrix
6.5 Finite Element Solution of a Plane 356(11)
Stress Problem
6.6 Rectangular Plane Element (Bilinear 367(6)
Rectangle, Q4)
Summary Equations 373(3)
References 376(1)
Problems 377(7)
7 Practical Considerations in Modeling; 384(53)
Interpreting Results; and Examples of Plane
Stress---Strain Analysis
Chapter Objectives 384(1)
Introduction 384(1)
7.1 Finite Element Modeling 385(13)
7.2 Equilibrium and Compatibility of 398(4)
Finite Element Results
7.3 Convergence of Solution 402(3)
7.4 Interpretation of Stresses 405(2)
7.5 Static Condensation 407(4)
7.6 Flowchart for the Solution of Plane 411(1)
Stress---Strain Problems
7.7 Computer Program-Assisted 411(6)
Step-by-Step Solution, Other Models, and
Results for Plane Stress---Strain Problems
References 417(3)
Problems 420(17)
8 Development of the Linear-Strain Triangle 437(15)
Equations
Chapter Objectives 437(1)
Introduction 437(1)
8.1 Derivation of the Linear-Strain 437(5)
Triangular Element Stiffness Matrix and
Equations
8.2 Example LST Stiffness Determination 442(3)
8.3 Comparison of Elements 445(3)
Summary Equations 448(1)
References 448(1)
Problems 449(3)
9 Axisymmetric Elements 452(34)
Chapter Objectives 452(1)
Introduction 452(1)
9.1 Derivation of the Stiffness Matrix 452(11)
9.2 Solution of an Axisymmetric Pressure 463(6)
Vessel
9.3 Applications of Axisymmetric Elements 469(5)
Summary Equations 474(2)
References 476(1)
Problems 476(10)
10 Isoparametric Formulation 486(48)
Chapter Objectives 486(1)
Introduction 486(1)
10.1 Isoparametric Formulation of the Bar 487(5)
Element Stiffness Matrix
10.2 Isoparametric Formulation of the 492(11)
Plane Quadrilateral Element Stiffness
Matrix
10.3 Newton-Cotes and Gaussian Quadrature 503(6)
10.4 Evaluation of the Stiffness Matrix 509(6)
and Stress Matrix by Gaussian Quadrature
10.5 Higher-Order Shape Functions 515(10)
Summary Equations 525(3)
References 528(1)
Problems 528(6)
11 Three-Dimensional Stress Analysis 534(38)
Chapter Objectives 534(1)
Introduction 534(1)
11.1 Three-Dimensional Stress and Strain 535(2)
11.2 Tetrahedral Element 537(8)
11.3 Isoparametric Formulation 545(8)
Summary Equations 553(3)
References 556(1)
Problems 556(16)
12 Plate Bending Element 572(27)
Chapter Objectives 572(1)
Introduction 572(1)
12.1 Basic Concepts of Plate Bending 572(5)
12.2 Derivation of a Plate Bending 577(5)
Element Stiffness Matrixand Equations
12.3 Some Plate Element Numerical 582(2)
Comparisons
12.4 Computer Solutions for Plate Bending 584(4)
Problems
Summary Equations 588(2)
References 590(1)
Problems 590(9)
13 Heat Transfer and Mass Transport 599(75)
Chapter Objectives 599(1)
Introduction 599(2)
13.1 Derivation of the Basic Differential 601(3)
Equation
13.2 Heat Transfer with Convection 604(1)
13.3 Typical Units; Thermal 605(2)
Conductivities, K; and Heat-Transfer
Coefficients, h
13.4 One-Dimensional Finite Element 607(19)
Formulation Using a Variational Method
13.5 Two-Dimensional Finite Element 626(9)
Formulation
13.6 Line or Point Sources 635(3)
13.7 Three-Dimensional Heat Transfer by 638(3)
the Finite Element Method
13.8 One-Dimensional Heat Transfer with 641(1)
Mass Transport
13.9 Finite Element Formulation of Heat 641(5)
Transfer with Mass Transport by
Galerkin's Method
13.10 Flowchart and Examples of a 646(7)
Heat-Transfer Program
References 653(1)
Problems 654(20)
14 Fluid Flow in Porous Media and Through 674(54)
Hydraulic Networks; and Electrical Networks
and Electrostatics
Chapter Objectives 674(1)
Introduction 674(1)
14.1 Derivation of the Basic Differential 675(5)
Equations
14.2 One-Dimensional Finite Element 680(12)
Formulation
14.3 Two-Dimensional Finite Element 692(5)
Formulation
14.4 Flowchart and Example of a 697(1)
Fluid-Flow Program
14.5 Electrical Networks 698(4)
14.6 Electrostatics 702(14)
Summary Equations 716(4)
References 720(1)
Problems 720(8)
15 Thermal Stress 728(35)
Chapter Objectives 728(1)
Introduction 728(1)
15.1 Formulation of the Thermal Stress 728(24)
Problem and Examples
Reference 752(1)
Summary Equations 753(2)
Problems 755(8)
16 Structural Dynamics and Time-Dependent 763(66)
Heat Transfer
Chapter Objectives 763(1)
Introduction 763(1)
16.1 Dynamics of a Spring-Mass System 763(3)
16.2 Direct Derivation of the Bar Element 766(4)
Equations
16.3 Numerical Integration in Time 770(12)
16.4 Natural Frequencies of a 782(4)
One-Dimensional Bar
16.5 Time-Dependent One-Dimensional Bar 786(5)
Analysis
16.6 Beam Element Mass Matrices and 791(7)
Natural Frequencies
16.7 Truss, Plane Frame, Plane Stress, 798(5)
Plane Strain, Axisymmetric, and Solid
Element Mass Matrices
16.8 Time-Dependent Heat Transfer 803(7)
16.9 Computer Program Example Solutions 810(9)
for Structural Dynamics
Summary Equations 819(4)
References 823(1)
Problems 824(5)
Appendix A Matrix Algebra 829(16)
Introduction 829(1)
A.1 Definition of a Matrix 829(1)
A.2 Matrix Operations 830(7)
A.3 Cofactor or Adjoint Method to 837(2)
Determine the Inverse of a Matrix
A.4 Inverse of a Matrix by Row Reduction 839(2)
A.5 Properties of Stiffness Matrices 841(1)
References 842(1)
Problems 842(3)
Appendix B Methods for Solution of 845(22)
Simultaneous Linear Equations
Introduction 845(1)
B.1 General Form of the Equations 845(1)
B.2 Uniqueness, Nonuniqueness, and 846(1)
Nonexistence of Solution
B.3 Methods for Solving Linear Algebraic 847(11)
Equations
B.4 Banded-Symmetric Matrices, Bandwidth, 858(7)
Skyline, and Wavefront Methods
References 865(1)
Problems 865(2)
Appendix C Equations from Elasticity Theory 867(8)
Introduction 867(1)
C.1 Differential Equations of Equilibrium 867(2)
C.2 Strain/Displacement and Compatibility 869(2)
Equations
C.3 Stress---Strain Relationships 871(3)
Reference 874(1)
Appendix D Equivalent Nodal Forces 875(3)
Problems 875(3)
Appendix E Principle of Virtual Work 878(4)
References 881(1)
Appendix F Properties of Structural Steel 882(3)
Shapes
Answers to Selected Problems 885(25)
Index 910