目录 Chapter 1 Mathematical Prerequisites 1.1 Index Notation 1.1.1 Range convention 1.1.2 Summation convention 1.1.3 The Kronecker delta 1.1.4 The permutation symbol 1.2 Vector Operations and Some Useful Integral Theorems 1.2.1 The scalar product of two vectors 1.2.2 The vector product of two vectors 1.2.3 The scalar triple product 1.2.4 The gradient of a scalar function 1.2.5 The divergence of a vector function 1.2.6 The curl of a vector function 1.2.7 Laplacian of a scalar function 1.2.8 Divergence theorem (Gauss's theorem) 1.2.9 Stokes' theorem 1.2.10 Green's theorem 1.3 Cartesian Tensors and Transformation Laws Problems 1 Chapter 2 Analysis of Stress 2.1 Continuum 2.2 Forces 2.3 Cauchy's Formula 2.4 Equations of Equilibrium 2.5 Stress as a Second-order Tensor 2.6 Principal Stresses 2.7 Maximum Shears 2.8 Yields Criteria Problems 2 Chapter 3 Analysis of Strain 3.1 Differential Element Considerations 3.2 Linear Deformation and Strain 3.3 Strain as a Second-order Tensor 3.4 Principal Strains and Strain Measurement 3.5 Compatibility Equations 3.6 Finite Deformation Problems 3 Chapter 4 Linear Elastic Materials, Framework of Problems of Elasticity 4.1 Introduction 4.2 Uniaxial Stress-Strain Relations of Linear Elastic Materials 4.3 Hooke's Law 4.3.1 Isotropic materials 4.3.2 Orthotropic materials 4.3.3 Transversely isotropic materials 4.4 Generalized Hooke's Law 4.5 Elastic Constants as Components of a Fourth-order Tensor 4.6 Elastic Symmetry 4.6.1 One plane of elastic symmetry (monoclinic material) 4.6.2 Two planes of elastic symmetry 4.6.3 Three planes of elastic symmetry (orthotropic material)
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