《Elasticity THEORY AND APPLICATIONS》求取 ⇩

1Mathematical Preliminaries1

1.1 The Summation Convention1

1.2 The Symbols δij and eijk3

1.3 Determinants5

1.4 Scalars and Vectors8

1.5 Coordinate Rotations12

1.6 Cartesian Tensors15

1.7 Tensor Algebra17

1.8 Quotient Laws18

1.9 Scalar and Vector Fields19

1.10 Orthogonal Curvilinear Coordinates22

1.11 The Divergence Theorem31

2Stress44

2.1 The Stress Vector Concept44

2.2 Equilibrium45

2.3 The Stress Tensor Concept49

2.4 Principal Axes and Stresses51

2.5 An Example55

2.6 Principal Shearing Stresses57

2.7 Mohr Circles59

2.8 The Octahedral Shear Stress65

2.9 The Stress Deviator67

2.10 Curvilinear Coordinates71

3Deformation and Strain83

3.1 Kinematics of a Deformable Solid83

3.2 The Strain Tensor Concept85

3.3 Geometry of Deformation90

3.4 Small Strain94

3.5 Linear Strain98

3.6 Rigid Body Motion103

3.7 Compatibility of the Linear Strain Field106

3.8 Curvilinear Coordinates109

4Elasticity and its Limits128

4.1 Hooke's Law and the Elasticity Tensor128

4.2 Isotropy129

4.3 Physical Interpretation of the Elastic Constants133

4.4 The Tension Test136

4.5 Yield Criteria138

4.6 An Example143

5.Formulation and..Exact..Soiutions of Some Linear Elasticity Problems151

5.1 The Spherical Shell under Internal and External Pressure152

5.2 The Cylindrical Shell under Internal and External Pressure(Plane Strain Solution)155

5.3 Torsion of Prismatic Members158

5.4 Pure Bending of a Beam173

5.5 The Cantilever Beam under Transverse End Load175

5.6 Two-Dimensional Problems185

6Structural Mechanics207

6.1 The Rod in Tension or Compression208

6.2 The Rod in Torsion212

6.3 The Timoshenko Beam217

6.4 The Euler-Bernoulli Beam226

6.5 Plate Theory230

6.6 Classical Plate Theory240

7Energy Principles225

7.1 The Strain Energy Concept225

7.2 The Rate of Work Equation261

7.3 Strain Energy in Beams and Plates263

7.4 The Principle of Virtual Work266

7.5 Applications of the Principle of Virtual Work269

7.6 Theorem of Minimum Potential Energy276

7.7 The Complementary Energy Concept277

7.8 The Principle of Complementary Virtual Work280

7.9 Theorem of Minimum Complementary Energy285

7.10 Castigliano's Theorems286

7.11 Reciprocal Theorems of Betti and Rayleigh290

7.12 Kirchhoff's Uniqueness Theorem293

7.13 The Variational Principle of Hellinger and Reissner296

8Numerical Methods308

8.1 The Ritz Method309

8.2 Applications of the Ritz Method312

8.3 The Kantorovich Method327

8.4 Weighted Residual Methods328

8.5 Finite Difference Methods333

8.6 Finite Element Methods340

9The Initially Stressed Solid-Elastic Instability378

9.1 Strain and Deformation379

9.2 Stress and Equilibrium382

9.3 The Initial Stress Problem386

9.4 Energy Considerations388

9.5 The Initially Stressed Beam390

9.6 The Initially Stressed Plate398