Theory of Elasticity, Volume 7"This present volume of our Theoretical Physics deals with the theory of elasticity. Being written by physicists, and primarily for physicists, it naturally includes not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subjects, such as thermal conduction and viscosity in solids, and various problems in the theory of elastic vibration and waves."--Authors, 'Preface to the First English Edition. |
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Page 2
... small compared with the distance itself . In other words , the relative extensions are small compared with unity . In what follows we shall suppose that all strains are small . If a body is subjected to a small deformation , all the ...
... small compared with the distance itself . In other words , the relative extensions are small compared with unity . In what follows we shall suppose that all strains are small . If a body is subjected to a small deformation , all the ...
Page 58
... small compared with h . It should be emphasised , however , that the deformation itself must still be small , in the sense that the components of the strain tensor must be small . In practice , this usually implies the condition « l ...
... small compared with h . It should be emphasised , however , that the deformation itself must still be small , in the sense that the components of the strain tensor must be small . In practice , this usually implies the condition « l ...
Page 92
... comparable in magnitude if 8 ~ h . Thus , when a rod with fixed ends is bent , the equations of equilibrium can be used in the form ( 20.4 ) only if the deflection is small in comparison with the thickness of the rod . If 8 is not small ...
... comparable in magnitude if 8 ~ h . Thus , when a rod with fixed ends is bent , the equations of equilibrium can be used in the form ( 20.4 ) only if the deflection is small in comparison with the thickness of the rod . If 8 is not small ...
Contents
FUNDAMENTAL EQUATIONS | 1 |
2 The stress tensor | 11 |
8 Equilibrium of an elastic medium bounded by a plane | 29 |
Copyright | |
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Common terms and phrases
angle arbitrary axis bending biharmonic equation boundary conditions Burgers vector centre clamped coefficient components constant contour corresponding cross-section crystal crystallites curvature deflection denote derivatives Determine the deformation dislocation line displacement vector edge elastic wave element equations of equilibrium equations of motion expression external forces fluid force F forces acting forces applied formula free energy frequency function given gives grad div Hence HOOKE's law integral internal stresses isotropic isotropic body Let us consider longitudinal longitudinal waves medium moduli non-zero obtain parallel perpendicular plate PROBLEM quantities radius relation result rotation shear shell small compared SOLUTION strain tensor stress tensor stretching Substituting suffixes symmetry temperature thermal thermal conduction torsion transverse transverse waves two-dimensional undeformed unit length unit volume values velocity of propagation vibrations wave vector x-axis xy-plane z-axis zero σικ ди дхду дхк