Elasticity: Theory, Applications, and Numerics

✍ Scribed by Martin H. Sadd

• Publisher: Academic Press Inc
• Year: 2004
• Tongue: English
• Leaves: 474
• Category: Library

✦ Synopsis

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. Complemented by a Solutions Manual and including MatLab codes and coding, this text is an excellent book teaching guide. - Contains exercises for student engagement as well as the integration and use of MATLAB Software - Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of engineering interest - Presents applications of contemporary interest

✦ Table of Contents

Cover Page......Page 1
Title Page......Page 4
ISBN 0126058113......Page 5
Preface......Page 6
Text Contents......Page 7
The Subject......Page 8
Feedback......Page 9
4 Material Behavior—Linear Elastic Solids......Page 10
10 Complex Variable Methods......Page 11
Appendix C MATLAB Primer......Page 12
About the Author......Page 13
PART I FOUNDATIONS AND ELEMENTARY APPLICATIONS......Page 14
1.1 Scalar, Vector, Matrix, and Tensor Definitions......Page 16
1.2 Index Notation......Page 17
1.3 Kronecker Delta and Alternating Symbol......Page 19
1.4 Coordinate Transformations......Page 20
1.5 Cartesian Tensors......Page 22
1.6 Principal Values and Directions for Symmetric Second-Order Tensors......Page 25
1.7 Vector, Matrix, and Tensor Algebra......Page 28
1.8 Calculus of Cartesian Tensors......Page 29
1.9 Orthogonal Curvilinear Coordinates......Page 32
References......Page 37
Exercises......Page 38
2.1 General Deformations......Page 40
2.2 Geometric Construction of Small Deformation Theory......Page 43
2.3 Strain Transformation......Page 47
2.4 Principal Strains......Page 48
2.5 Spherical and Deviatoric Strains......Page 49
2.6 Strain Compatibility......Page 50
2.7 Curvilinear Cylindrical and Spherical Coordinates......Page 54
Exercises......Page 56
3.1 Body and Surface Forces......Page 62
3.2 Traction Vector and Stress Tensor......Page 64
3.3 Stress Transformation......Page 67
3.4 Principal Stresses......Page 68
3.5 Spherical and Deviatoric Stresses......Page 71
3.6 Equilibrium Equations......Page 72
3.7 Relations in Curvilinear Cylindrical and Spherical Coordinates......Page 74
Exercises......Page 77
4.1 Material Characterization......Page 82
4.2 Linear Elastic Materials—Hooke’s Law......Page 84
4.3 Physical Meaning of Elastic Moduli......Page 87
4.4 Thermoelastic Constitutive Relations......Page 90
Exercises......Page 92
5.1 Review of Field Equations......Page 96
5.2 Boundary Conditions and Fundamental Problem Classifications......Page 97
5.3 Stress Formulation......Page 101
5.4 Displacement Formulation......Page 102
5.5 Principle of Superposition......Page 104
5.6 Saint-Venant’s Principle......Page 105
5.7 General Solution Strategies......Page 106
References......Page 111
Exercises......Page 112
6.1 Strain Energy......Page 116
6.2 Uniqueness of the Elasticity Boundary-Value Problem......Page 121
6.3 Bounds on the Elastic Constants......Page 122
6.4 Related Integral Theorems......Page 123
6.5 Principle of Virtual Work......Page 125
6.6 Principles of Minimum Potential and Complementary Energy......Page 127
6.7 Rayleigh-Ritz Method......Page 131
Exercises......Page 133
7.1 Plane Strain......Page 136
7.2 Plane Stress......Page 139
7.3 Generalized Plane Stress......Page 142
7.4 Antiplane Strain......Page 144
7.5 Airy Stress Function......Page 145
7.6 Polar Coordinate Formulation......Page 146
References......Page 148
Exercises......Page 149
8.1 Cartesian Coordinate Solutions Using Polynomials......Page 152
8.2 Cartesian Coordinate Solutions Using Fourier Methods......Page 162
8.3 General Solutions in Polar Coordinates......Page 170
8.4 Polar Coordinate Solutions......Page 173
References......Page 204
Exercises......Page 205
9.1 General Formulation......Page 214
9.2 Extension Formulation......Page 215
9.3 Torsion Formulation......Page 216
9.4 Torsion Solutions Derived from Boundary Equation......Page 226
9.5 Torsion Solutions Using Fourier Methods......Page 232
9.6 Torsion of Cylinders With Hollow Sections......Page 236
9.7 Torsion of Circular Shafts of Variable Diameter......Page 240
9.8 Flexure Formulation......Page 242
9.9 Flexure Problems Without Twist......Page 246
References......Page 250
Exercises......Page 251
PART II ADVANCED APPLICATIONS......Page 256
10.1 Review of Complex Variable Theory......Page 258
10.2 Complex Formulation of the Plane Elasticity Problem......Page 265
10.3 Resultant Boundary Conditions......Page 269
10.4 General Structure of the Complex Potentials......Page 270
10.5 Circular Domain Examples......Page 272
10.6 Plane and Half-Plane Problems......Page 277
10.7 Applications Using the Method of Conformal Mapping......Page 282
10.8 Applications to Fracture Mechanics......Page 287
10.9 Westergaard Method for Crack Analysis......Page 290
References......Page 291
Exercises......Page 292
11.1 Basic Concepts......Page 296
11.2 Material Symmetry......Page 298
11.3 Restrictions on Elastic Moduli......Page 304
11.4 Torsion of a Solid Possessing a Plane of Material Symmetry......Page 305
11.5 Plane Deformation Problems......Page 312
11.6 Applications to Fracture Mechanics......Page 325
References......Page 328
Exercises......Page 329
12.1 Heat Conduction and the Energy Equation......Page 332
12.2 General Uncoupled Formulation......Page 334
12.3 Two-Dimensional Formulation......Page 335
12.4 Displacement Potential Solution......Page 338
12.5 Stress Function Formulation......Page 339
12.6 Polar Coordinate Formulation......Page 342
12.7 Radially Symmetric Problems......Page 343
12.8 Complex Variable Methods for Plane Problems......Page 347
Exercises......Page 355
13.1 Helmholtz Displacement Vector Representation......Page 360
13.2 Lame´’s Strain Potential......Page 361
13.3 Galerkin Vector Representation......Page 362
13.4 Papkovich-Neuber Representation......Page 367
13.5 Spherical Coordinate Formulations......Page 371
13.6 Stress Functions......Page 376
Exercises......Page 378
14 Micromechanics Applications......Page 384
14.1 Dislocation Modeling......Page 385
14.2 Singular Stress States......Page 389
14.3 Elasticity Theory with Distributed Cracks......Page 398
14.4 Micropolar/Couple-Stress Elasticity......Page 401
14.5 Elasticity Theory with Voids......Page 410
14.6 Doublet Mechanics......Page 416
References......Page 421
Exercises......Page 422
15 Numerical Finite and Boundary Element Methods......Page 426
15.1 Basics of the Finite Element Method......Page 427
15.2 Approximating Functions for Two-Dimensional Linear Triangular Elements......Page 429
15.3 Virtual Work Formulation for Plane Elasticity......Page 431
15.4 FEM Problem Application......Page 435
15.5 FEM Code Applications......Page 437
15.6 Boundary Element Formulation......Page 442
Exercises......Page 448
Appendix A Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates......Page 450
Equilibrium Equations......Page 451
Hooke’s Law......Page 452
Equilibrium Equations in Terms of Displacements (Navier’s Equations)......Page 453
Appendix B Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical Components......Page 455
Spherical Components from Cylindrical......Page 456
Spherical Components From Cartesian......Page 457
C.1 Getting Started......Page 458
C.2 Examples......Page 460
Reference......Page 469
Index......Page 470