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Mechanics of Elastic Solids 弹性固体力学(英文版)


作者:
张俊乾,宋亦诚,吕浡,著
定价:
139.00 元
版面字数:
490千字
开本:
16开
装帧形式:
平装
版次:
1
最新版次
印刷时间:
2026年
ISBN:
978-7-04-067317-3
物料号:
67317-00
出版时间:
2026-08-17
读者对象:
学术著作
一级分类:
自然科学
二级分类:
力学
三级分类:
固体力学

本书为国家级一流本科课程配套教材,聚焦弹性固体力学领域,采用英文编写。全书共10章,系统涵盖绪论、应力分析、变形分析、本构方程、实际问题的弹性力学建模、平面应力和平面应变小变形问题的应力函数解法、三维弹性小变形问题解法、多物理场问题、弹性力学的变分方法、薄板和圆柱壳等核心内容。本书作为改革尝试,新增和重构了弹性力学教材内容,具有显著变化的特色内容包括:变形分析一章论述有限变形的应变度量、并以一维到三维的自然推广方法讲述;本构关系一章包括了各向异性线弹性本构关系、小应变大转动弹性本构关系、超弹性本构关系;独立一章讲述实际问题力学建模的过程、方法和实例;多物理场问题通过引入具有普适性的特征应变方法进行论述。精简了平面问题解法和柱体扭转等内容。

为了克服新增内容的难度挑战性,本书每一章节的写作都具有自身的特点,力学新概念和方法都是通过简单情形和直观物理图像进行阐述,然后推广到一般情况。针对弹性力学问题,有机结合其物理图像和物理逻辑,开展相关数学工具的应用和理论推导。

本书英文讲义自2008年起在上海大学历经长期教学实践检验,教学体系成熟。

本书可作为高等学校力学类专业本科生和力学、土木工程、机械工程等专业研究生的教材,也可作为相关领域科学研究和工程技术人员的自学和参考用书。

  • 目录
    • 前辅文
      • Nomenclature
        • 1 Introduction
          • 1.1 Basic Hypotheses of Elastic Solids
            • 1.2 Brief History of Elastic Solid Mechanics
              • References
              • 2 Analysis of Stress
                • 2.1 Traction, Stress Tensor and Cauchy Formula
                  • 2.1.1 Traction (or Stress Vector)
                    • 2.1.2 Stress Tensor
                      • 2.1.3 Cauchy Formula
                      • 2.2 Index Notation and Transformation of Coordinates
                        • 2.2.1 Index Notation for Vectors, Tensors and Equations
                          • 2.2.2 Coordinate Transformation of Components of Traction and Stress Tensor
                          • 2.3 Principal Stresses and Stress Invariants
                            • 2.3.1 Principal Stresses and Principal Stress Directions
                              • 2.3.2 Stress Invariants
                              • 2.4 Maximum Shear Stress
                                • 2.5 Hydrostatic Stress, Deviatoric Stress and von Mises Stress
                                  • 2.6 Equations of Motion (or Equilibrium)
                                    • Problems
                                      • References
                                      • 3 Analysis of Deformation
                                        • 3.1 One-Dimensional Deformation
                                          • 3.1.1 Strain-Displacement Relations for Uniform Deformation
                                            • 3.1.2 Strain-Displacement Relations for Non-Uniform Deformation
                                            • 3.2 Displacement Field and Deformation Gradient
                                              • 3.3 Stretch Tensors and Strain Measures
                                                • 3.3.1 Elongation of a Differential Line
                                                  • 3.3.2 Change in Angle Between Any Two Line Elements
                                                    • 3.3.3 Typical Three-Dimensional Strain Measures
                                                    • 3.4 Principal Deformation Directions, Principal Stretches and Deformation Invariants
                                                      • 3.4.1 Principal Deformation Directions and Principal Stretches
                                                        • 3.4.2 Deformation Invariants
                                                        • 3.5 Strain-Displacement Relation
                                                          • 3.5.1 Explicit Strain-Displacement Relations
                                                            • 3.5.2 Calculation of Engineering Strain, Logarithmic Strain and Cauchy Strain from a Displacement Field
                                                            • 3.6 Deformation Rate and Material Derivative
                                                              • 3.7 Infinitesimal Strain and Infinitesimal Deformation
                                                                • 3.7.1 Infinitesimal Strain
                                                                  • 3.7.2 Infinitesimal Deformation
                                                                  • 3.8 Strain Compatibility for Infinitesimal Deformation
                                                                    • Problems
                                                                      • References
                                                                      • 4 Constitutive Equations
                                                                        • 4.1 Hooke’s Law for Isotropic Materials Undergoing Infinitesimal Deformation
                                                                          • 4.1.1 Determination by Conducting Material Mechanics Experiments
                                                                            • 4.1.2 Strain Energy Density
                                                                              • 4.1.3 Stress Derived from Strain Energy Density Function
                                                                              • 4.2 Hooke’s Law for Anisotropic Materials Undergoing Infinitesimal Deformation
                                                                                • 4.2.1 Orthotropic Materials
                                                                                  • 4.2.2 Transversely Isotropic Materials
                                                                                  • 4.3 Stress-Strain Relation for Infinitesimal Strain but Large Rotation
                                                                                    • 4.4 Hyperelasticity
                                                                                      • 4.4.1 Stress Derived from Strain Energy Density Function
                                                                                        • 4.4.2 Incompressible Materials
                                                                                          • 4.4.3 Strain Energy Density Functions for Isotropic Incompressible Materials
                                                                                            • 4.4.4 Determination of Material Constants of Incompressible Materials
                                                                                              • 4.4.5 Strain Energy Density Functions for Isotropic Compressible Materials
                                                                                              • Problems
                                                                                                • References
                                                                                                • 5 Construction of Elastic Solid Mechanics Models for Actual Problems
                                                                                                  • 5.1 Constructing an Elastic Solid Mechanics Model
                                                                                                    • 5.1.1 Deciding What Mechanical Quantities to Compute
                                                                                                      • 5.1.2 Defining the Geometry of the Model
                                                                                                        • 5.1.3 Defining Material Behavior
                                                                                                          • 5.1.4 Field Equations
                                                                                                            • 5.1.5 Simplifying Loads and Replicating Boundary Conditions
                                                                                                              • 5.1.6 Interface Models
                                                                                                                • 5.1.7 Examples for Constructing Elastic Solid Mechanics Models
                                                                                                                • 5.2 Boundary Value Problems of Mechanical Models
                                                                                                                  • Problems
                                                                                                                    • References
                                                                                                                    • 6 Solutions for Infinitesimal Plane Stress and Strain Problems
                                                                                                                      • 6.1 Plane Stress and Plane Strain Models
                                                                                                                        • 6.1.1 Plane Strain Model
                                                                                                                          • 6.1.2 Plane Stress Model
                                                                                                                            • 6.1.3 Basic Equations for Boundary Value Problems in Cartesian Coordinates
                                                                                                                            • 6.2 Airy Stress Function in Cartesian Coordinates
                                                                                                                              • 6.3 Solutions for Rectangular Beams by Polynomial Stress Functions
                                                                                                                                • 6.4 Solutions for Rectangular Beams by Separation of Variables
                                                                                                                                  • 6.5 Airy Stress Function Solutions in Polar Coordinates
                                                                                                                                    • 6.5.1 General Equations
                                                                                                                                      • 6.5.2 Solutions for Typical Problems
                                                                                                                                      • Problems
                                                                                                                                        • Reference
                                                                                                                                        • 7 Solutions for Infinitesimal Three-Dimensional Problems
                                                                                                                                          • 7.1 Two Mathematical Tools
                                                                                                                                            • 7.1.1 Integration by Parts for Higher Dimensions
                                                                                                                                              • 7.1.2 Solution of Poisson’s Equation by Green’s Function
                                                                                                                                              • 7.2 Helmholtz Decomposition of Displacement and Body Force
                                                                                                                                                • 7.3 A Particular Solution of Navier’s Equation with Body Force
                                                                                                                                                  • 7.4 Papkovich–Neuber Solution
                                                                                                                                                    • 7.5 Indentation of an Elastic Half-Space by a Flat Rigid Punch
                                                                                                                                                      • 7.6 Frictionless Contact Between Two Elastic Spheres Problems
                                                                                                                                                      • 8 Multiphysics Field Problems
                                                                                                                                                        • 8.1 Eigen-Strain and Its Physical Origins
                                                                                                                                                          • 8.2 Generalized Hooke’s Law Involving Eigen-Strain
                                                                                                                                                            • 8.3 One-Way Coupling Initial-Boundary Value Problems for Isotropic Solids
                                                                                                                                                              • 8.4 One-Dimensional Problems of Eigen-Strain
                                                                                                                                                                • 8.4.1 Inhomogeneous Eigen-Strain in a Plate
                                                                                                                                                                  • 8.4.2 Inhomogeneous Eigen-Strain in Spheres
                                                                                                                                                                    • 8.4.3 Inhomogeneous Eigen-Strain in Disks and Cylinders
                                                                                                                                                                    • 8.5 Eshelby Inclusion Problems
                                                                                                                                                                      • 8.6 Displacement Potential Method for Eigen-Strain Problems
                                                                                                                                                                        • 8.7 Brief Introduction to Two-Way Coupling Problems
                                                                                                                                                                          • Problems
                                                                                                                                                                            • References
                                                                                                                                                                            • 9 Variational Methods for Infinitesimal Deformation Problems
                                                                                                                                                                              • 9.1 Variation of Functionals
                                                                                                                                                                                • 9.2 Principles of Virtual Work and Complementary Virtual Work
                                                                                                                                                                                  • 9.3 Principle of Minimum Potential Energy
                                                                                                                                                                                    • 9.4 Applications of Principle of Minimum Potential Energy for Reducing Dimensionality of Models
                                                                                                                                                                                      • 9.4.1 Elementary Theory of Beams
                                                                                                                                                                                        • 9.4.2 Saint–Venant Torsion of Shafts
                                                                                                                                                                                        • 9.5 Rayleigh–Ritz Method
                                                                                                                                                                                          • 9.6 Principle of Minimum Complementary Energy
                                                                                                                                                                                            • 9.7 Applications of Principle of Minimum Complementary Energy
                                                                                                                                                                                              • 9.7.1 Derivation of the Governing Equations of Saint–Venant Torsion
                                                                                                                                                                                                • 9.7.2 Numerical Solution for Problems of Saint–Venant Torsion
                                                                                                                                                                                                • Problems
                                                                                                                                                                                                  • References
                                                                                                                                                                                                  • 10 Thin Plates and Circular Cylindrical Shells
                                                                                                                                                                                                    • 10.1 Basic Equations of Thin Plates
                                                                                                                                                                                                      • 10.2 Solutions for Bending of Thin Plates
                                                                                                                                                                                                        • 10.2.1 Pure Bending of Rectangular Plates
                                                                                                                                                                                                          • 10.2.2 Simply Supported Rectangular Plates
                                                                                                                                                                                                            • 10.2.3 Rectangular Plates Simply Supported at Two Opposite Edges
                                                                                                                                                                                                              • 10.2.4 Axisymmetric Bending of Circular Plates
                                                                                                                                                                                                              • 10.3 Vibration of Thin Plates
                                                                                                                                                                                                                • 10.3.1 Free Vibration of Simply Supported Rectangular Plates
                                                                                                                                                                                                                  • 10.3.2 Free Vibration of Rectangular Plates Simply Supported at Two Opposite Edges
                                                                                                                                                                                                                  • 10.4 Buckling of Thin Plates Under Compression
                                                                                                                                                                                                                    • 10.4.1 Buckling of Simply Supported Rectangular Plates Under Compression
                                                                                                                                                                                                                      • 10.4.2 Buckling of Circular Plates
                                                                                                                                                                                                                      • 10.5 Buckling of Cylindrical Shells Subjected to Axially Compressive Loads
                                                                                                                                                                                                                        • Problems
                                                                                                                                                                                                                          • References
                                                                                                                                                                                                                          • Appendix A Basic Equations in Polar, Cylindrical and Spherical Coordinate Systems, and Coordinate Transformation for Stresses and Displacements
                                                                                                                                                                                                                            • A.1 Equations in Polar Coordinates
                                                                                                                                                                                                                              • A.2 Equations in Cylindrical Coordinates
                                                                                                                                                                                                                                • A.3 Equations in Spherical Coordinates
                                                                                                                                                                                                                                • Index

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