有限单元法

《有限单元法：基本原理及其在土木、水利、机械和航天工程中的应用》系统地阐述了有限单元法的基本原理及其在工程问题中的应用，包括弹性力学平面问题和空间问题、薄板、薄壳、厚板、厚壳、弹性稳定、塑性力学、大位移、断裂、动力反应、徐变、岩土力学、混凝土与钢筋混凝土、流体力学、热传导、工程反分析、仿真计算、网络自动生成、误差估计及自适应技术。该书内容丰富、取材新颖，概念清晰，可供土木、水利、机械、航空、力学专业的设计、科研人员使用，并可用做高等院校有关专业的教材。

Preface About the Author 1 Introduction to Finite Element Method and Matrix Analysis of Truss 1．1 Introduction to Finite Element Method 1．2 Truss Analysis Overview 1．3 Stiffness Matrix of Horizontal Bar Element 1．4 Stiffness Matrix oflnclined Bar Element 1．5 Coordinate Transformation 1．6 Nodal Equilibrium Equation and Global Stiffness Matrix 1．7 Treatment ofBoundary Conditions Bibliography 2 Plane Problems in Theory of Elasticity 2．1 Discretization ofContinuous Medium 2．2 DisplacementFunction 2．3 Element Strain 2．4 InitiaIStrain 2．5 ElementStress 2．5．1Isotropic Body： Plane Stress 2．5．2Isotropic Body： Plane Strain 2．5．3 AnisotropicBody 2．6 Equivalent Nodal Force and Element Stiffness Matrix 2．7 NodalLoads 2．7．1 Equivalent Nodal Loads of Distributed Boundary Forces 2．7．2 Nodal Loads ofUniform Volume Force 2．7．3 Nodal Loads Due to Potential ofVolume Force 2．7．4 Nodal Loads Caused by Initial Strain 2．8 Nodal Equilibrium Equation and Global Stiffness Matrix 2．9 Establish the Global Stiffness Matrix by the Coding Method 2．10 Calculation Example 2．10．1 Stress Concentration near the Circular Hole 2．10．2Stress Analysis ofl Beam with a Hole in Web 2．10．3 Stress Analysis ofthe Concrete Gravity Dam Bibliography 3 ElementAnalysis 3．1 Principle ofVirtual Displacement 3．2 ElementDisplacement 3．3 Element Strain and Stress 3．4 Nodal Force and Element Stiffness Matrix 3．5 NodaILoad 3．5．1 Distributed Volume Force 3．5．2 Distributed Surface Force 3．5．3 Initial Strain and Initial Stress 3．6 Application Examples of the Principle of Virtual Displacements： Beam Element 3．7 Strain Energy and Complementary Strain Energy 3．8 Principle ofMinimum PotentiaIEnergy 3．9 Minimum Complementary Energy Principle 3．10 Hybrid Element 3．11 Hybrid Element Example： Plane Rectangular Element 3．12 Mixed Energy Principle 3．13 Composite Element Bibliography 4 GlobaI Analysis 4．1 Nodal Equilibrium Equation 4．2 Application of the Principle of Minimum Potential Energy 4．3 The Low Limit Property ofthe Solution of Minimum Potential Energy 4．4 The Convergence of Solutions 4．5 Analysis of the Substructure 4．5．1 Multiple Substructures 4．5．2 Condensation of the Internal Degrees of Freedom of Substructures 4．5．3 Coordinate Transformatio'n Bibliography 5 High-Order Element of Plane Problem 5．1 RectangularElements 5．2 Area Coordinates 5．3 High-Order Triangular Element 5．3．16-Node Quadratic Triangular Element 5．3．2 10-Node 3-Order Triangular Element 5．3．3 3-Node 18 DOF Triangular Element Bibliography 6 Axisymmetrical Problems in Theory of Elasticity 6．1 Stresses Due to AxisymmetricaI Loads 6．1．1 Displacement Function …… 7 Spatial Problems in Theory of Elasticity 8 Shape Function， Coordinate Transformation，Isoparametric Element，and lnfinite Element 9 Comparison and Application Instances of Various Planar and SpatiaI Elements 10 Elastic Thin Plate …… 26 Back Analysis of Engineering 27 Automatic Mesh Generation， Error Estimation， and Auto-adaptation Technique 28 Matrix 29 Linear Algebraic Equation Set 30 VariationaI Method 31 Weighted ResiduaI Method Appendix A Appendix B Index

朱伯芳，中国工程院院士，1951年毕业于上海交通大学土木系后，参加我国首批三座大坝设计，1957年调至中国水科院，1995年当选院士，发表论文210篇出版著作10本，曾获国家自然科学奖1项，国家科技进步奖2项。国际大坝会议奖1项，部奖8项，建立了混凝土温度应力，拱坝优化等新学科。首次把有限元引入混凝土温度应力和水坝仿真计算。

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