Theory of Elasticity: Volume 7A comprehensive textbook covering not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids. |
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Contents
2 The stress tensor | 6 |
6 Deformations with change of temperature | 15 |
8 Equilibrium of an elastic medium bounded by a plane | 25 |
10 The elastic properties of crystals | 33 |
12 The equation of equilibrium for a plate | 45 |
14 Large deflections of plates | 51 |
16 | 59 |
20 Small deflections of rods | 81 |
35 The absorption of sound in solids | 137 |
36 Highly viscous fluids | 142 |
MECHANICS OF LIQUID CRYSTALS 37 Static deformations of nematics | 144 |
38 Straight disclinations in nematics | 147 |
39 Nonsingular axially symmetrical solution of the equilibrium equations for a nematic | 152 |
40 Topological properties of disclinations | 156 |
41 Equations of motion of nematics | 158 |
42 Dissipative coefficients of nematics | 163 |
ELASTIC WAVES | 87 |
23 Elastic waves in crystals | 93 |
25 | 99 |
The action of a stress field on a dislocation | 116 |
Distribution of interacting dislocations | 124 |
32 The equation of thermal conduction in solids | 133 |
33 Thermal conduction in crystals | 134 |
34 Viscosity of solids | 135 |
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Common terms and phrases
a₁ angle axes axis bending biharmonic equation boundary conditions Burgers vector clamped coefficient components compression constant contour corresponding cosē cross-section crystal crystallites curl deflection denote density derivatives Determine the deformation direction disclination dislocation line dispersion relation displacement vector edge equations of equilibrium equations of motion expression external forces F₁ force F formula free energy frequency function given gives glide plane grad div Hence integral internal stresses isotropic isotropic body K₁ length Let us consider longitudinal longitudinal waves medium moduli nematic non-zero obtain oscillations perpendicular plane plate polar coordinates propagation quantities radius relation result rotation satisfies shell smectics SOLUTION strain tensor stress tensor stretching Substituting surface symmetry temperature thermal thermodynamic torsion transverse transverse waves u₁ undeformed unit volume velocity w₁ wave vector xy-plane z-axis zero ди ду дх