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 13
... components of the strain and stress tensors , we see that all the components uk with i ‡ k are zero . For the remaining components we find uxx = Uyy = - 1/1 32μ 1 1/1 - P , Uzz = + 3K 3 3Κ με ( 5.1 ) The component uzz gives the relative ...
... components of the strain and stress tensors , we see that all the components uk with i ‡ k are zero . For the remaining components we find uxx = Uyy = - 1/1 32μ 1 1/1 - P , Uzz = + 3K 3 3Κ με ( 5.1 ) The component uzz gives the relative ...
Page 37
... components of a tensor of rank four having these symmetry properties is in general 21 . In accordance with the expression ( 10.1 ) for the free energy , the stress tensor for a crystal is given in terms of the strain tensor by әF | дик ...
... components of a tensor of rank four having these symmetry properties is in general 21 . In accordance with the expression ( 10.1 ) for the free energy , the stress tensor for a crystal is given in terms of the strain tensor by әF | дик ...
Page 38
... components Axim whose suffixes include an odd number of times ( 1 or 3 ) will change sign , while the other components will remain un- changed . By the symmetry of the crystal , however , all quantities characterising its properties ...
... components Axim whose suffixes include an odd number of times ( 1 or 3 ) will change sign , while the other components will remain un- changed . By the symmetry of the crystal , however , all quantities characterising its properties ...
Contents
FUNDAMENTAL EQUATIONS | 1 |
2 The stress tensor | 11 |
8 Equilibrium of an elastic medium bounded by a plane | 29 |
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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