### 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.

`Preface                                            xiiPreface 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)  ShapesAnswers to Selected Problems                       885(25)Index                                              910`