本书详细介绍了有限元分析的基本理论和方法，以及ANSYS软件在有限元分析中的应用。全书详细介绍了一维和二维有限元公式的推导以及实例问题的分析方法，简单阐述了三维有限元分析方法；讨论了桁架、轴力构件、梁、框架、热传递、流体流动和动力学问题的有限元分析；通过实例详细介绍了利用ANSYS进行有限元分析的基本方法和步骤。每章均先介绍相关的基本概念和有限元公式的推导过程，然后基于有限元分析方法手工求解一些简单的实例问题，进而再利用ANSYS进行问题求解。本书特别强调分析结果的验证，在一些章的章末均提出了针对不同问题的分析结果的验证方法。

Contents 1 Introduction 1 1.1 Engineering Problems 2 1.2 Numerical Methods 5 1.3 A Brief History of the Finite Element Method and ANSYS 6 1.4 Basic Steps in the Finite Element Method 6 1.5 Direct Formulation 8 1.6 Minimum Total Potential Energy Formulation 37 1.7 Weighted Residual Formulations 43 1.8 Verification of Results 48 1.9 Understanding the Problem 49 Summary 54 References 54 Problems 54 2 Matrix Algebra 66 2.1 Basic Definitions 66 2.2 Matrix Addition or Subtraction 69 2.3 Matrix Multiplication 69 2.4 Partitioning of a Matrix 73 2.5 Transpose of a Matrix 77 2.6 Determinant of a Matrix 81 2.7 Solutions of Simultaneous Linear Equations 86 2.8 Inverse of a Matrix 94 2.9 Eigenvalues and Eigenvectors 98 2.10 Using MATLAB to Manipulate Matrices 102 2.11 Using Excel to Manipulate Matrices 106 2.12 Solutions of Simultaneous Nonlinear Equations 121 Summary 123 References 124 Problems 124 3 Trusses 129 3.1 Definition of a Truss 129 3.2 Finite Element Formulation 130 3.3 Space Trusses 155 3.4 Overview of the ANSYS Program 157 3.5 ANSYS Workbench Environment 165 3.6 Examples Using ANSYS 165 3.7 Verification of Results 197 Summary 199 References 199 Problems 199 4 Axial Members, Beams, and Frames 209 4.1 Members Under Axial Loading 209 4.2 Beams 217 4.3 Finite Element Formulation of Beams 222 4.4 Finite Element Formulation of Frames 238 4.5 Three-Dimensional Beam Element 244 4.6 An Example Using ANSYS 246 4.7 Verification of Results 271 Summary 273 References 274 Problems 275 5 One-Dimensional Elements 287 5.1 Linear Elements 287 5.2 Quadratic Elements 291 5.3 Cubic Elements 293 5.4 Global, Local, and Natural Coordinates 296 5.5 Isoparametric Elements 298 5.6 Numerical Integration: Gauss?CLegendre Quadrature 300 5.7 Examples of One- Dimensional Elements in ANSYS 305 Summary 305 References 305 Problems 305 6 Analysis of One-Dimensional Problems 312 6.1 Heat Transfer Problems 312 6.2 A Fluid Mechanics Problem 331 6.3 An Example Using ANSYS 335 6.4 Verification of Results 350 6.5 Members Under Axial Loading with Temperature Change 351 Summary 353 References 353 Problems 353 7 Two-Dimensional Elements 357 7.1 Rectangular Elements 357 7.2 Quadratic Quadrilateral Elements 361 7.3 Linear Triangular Elements 366 7.4 Quadratic Triangular Elements 371 7.5 Axisymmetric Elements 375 7.6 Isoparametric Elements 380 7.7 Two-Dimensional Integrals: Gauss?CLegendre Quadrature 383 7.8 Examples of Two-Dimensional Elements in ANSYS 384 Summary 385 References 385 Problems 386 8 More ANSYS 393 8.1 ANSYS Program 393 8.2 ANSYS Database and Files 394 8.3 Creating a Finite Element Model with ANSYS: Preprocessing 396 8.4 h-Method Versus p-Method 410 8.5 Applying Boundary Conditions, Loads, and the Solution 410 8.6 Results of Your Finite Element Model: Postprocessing 413 8.7 Selection Options 418 8.8 Graphics Capabilities 419 8.9 Error-Estimation Procedures 421 8.10 More on ANSYS Workbench Environment 422 8.11 An Example Problem 428 Summary 441 References 442 9 Analysis of Two-Dimensional Heat Transfer Problems 443 9.1 General Conduction Problems 443 9.2 Formulation with Rectangular Elements 450 9.3 Formulation with Triangular Elements 461 9.4 Axisymmetric Formulation of Three-Dimensional Problems 480 9.5 Unsteady Heat Transfer 487 9.6 Conduction Elements Used by ANSYS 497 9.7 Examples Using ANSYS 498 9.8 Verification of Results 538 Summary 538 References 540 Problems 540 10 Analysis of Two-Dimensional Solid Mechanics Problems 552 10.1 Torsion of Members with Arbitrary Cross-Section Shape 552 10.2 Plane-Stress Formulation 568 10.3 Isoparametric Formulation: Using a Quadrilateral Element 576 10.4 Axisymmetric Formulation 583 10.5 Basic Failure Theories 585 10.6 Examples Using ANSYS 586 10.7 Verification of Results 608 Summary 608 References 610 Problems 610 11 Dynamic Problems 619 11.1 Review of Dynamics 619 11.2 Review of Vibration of Mechanical and Structural Systems 633 11.3 Lagrange’s Equations 650 11.4 Finite Element Formulation of Axial Members 652 11.5 Finite Element Formulation of Beams and Frames 661 11.6 Examples Using ANSYS 675 Summary 694 References 694 Problems 694 12 Analysis of Fluid Mechanics Problems 701 12.1 Direct Formulation of Flow Through Pipes 701 12.2 Ideal Fluid Flow 713 12.3 Groundwater Flow 719 12.4 Examples Using ANSYS 722 12.5 Verification of Results 743 Summary 744 References 745 Problems 746 13 Three-Dimensional Elements 751 13.1 The Four-Node Tetrahedral Element 751 13.2 Analysis of Three-Dimensional Solid Problems Using Four-Node Tetrahedral Elements 754 13.3 The Eight-Node Brick Element 759 13.4 The Ten-Node Tetrahedral Element 761 13.5 The Twenty-Node Brick Element 762 13.6 Examples of Three-Dimensional Elements in ANSYS 764 13.7 Basic Solid-Modeling Ideas 768 13.8 A Thermal Example Using ANSYS 779 13.9 A Structural Example Using ANSYS 796 Summary 809 References 809 Problems 809 14 Design and Material Selection 818 14.1 Engineering Design Process 819 14.2 Material Selection 822 14.3 Electrical, Mechanical, and Thermophysical Properties of Materials 823 14.4 Common Solid Engineering Materials 825 14.5 Some Common Fluid Materials 832 Summary 834 References 834 Problems 834 15 Design Optimization 836 15.1 Introduction to Design Optimization 836 15.2 The Parametric Design Language of ANSYS 840 15.3 Examples of Batch Files 842 Summary 853 References 854 Problems 854 Appendix A Mechanical Properties of Some Materials 855 Appendix B Thermophysical Properties of Some Materials 859 Appendix C Properties of Common Line and Area Shapes 861 Appendix D Geometrical Properties of Structural Steel Shapes 865 Appendix E Conversion Factors 869 Appendix F An Introduction to MATLAB 871 Appendix G Workbench Examples 905