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
... tensor utk is called the strain tensor . We see from its definition that it is symmetrical , i.e. uik = Uki . ( 1.4 ) This result has been obtained by writing the term 2 ( du / xx ) dx dxê in dľ ? in the explicitly symmetrical form диг ...
... tensor utk is called the strain tensor . We see from its definition that it is symmetrical , i.e. uik = Uki . ( 1.4 ) This result has been obtained by writing the term 2 ( du / xx ) dx dxê in dľ ? in the explicitly symmetrical form диг ...
Page 3
... strain tensor is given by Uik = 1 / ди дик · + . 2 дк дх ( 1.5 ) The relative extensions of the elements of length along the principal axes of the strain tensor ( at a given point ) are , to within higher - order quantities , √ ( 1 + ...
... strain tensor is given by Uik = 1 / ди дик · + . 2 дк дх ( 1.5 ) The relative extensions of the elements of length along the principal axes of the strain tensor ( at a given point ) are , to within higher - order quantities , √ ( 1 + ...
Page 12
... strain tensor in terms of the stress tensor . ( 4.8 ) Equation ( 4.7 ) shows that the relative change in volume ( uu ) in any deformation of an isotropic body depends only on the sum out of the diagonal components of the stress tensor ...
... strain tensor in terms of the stress tensor . ( 4.8 ) Equation ( 4.7 ) shows that the relative change in volume ( uu ) in any deformation of an isotropic body depends only on the sum out of the diagonal components of the stress tensor ...
Contents
FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |
2 The stress tensor | 4 |
3 The thermodynamics of deformation | 8 |
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angle arbitrary axes axis bending biharmonic equation boundary conditions Burgers vector clamped co-ordinates coefficient components constant contour corresponding crack cross-section crystal crystallite curvature deflection denote derivatives Determine the deformation dislocation line displacement vector edge element equations of equilibrium equations of motion expression external forces fluid force F formula free energy frequency function given gives grad div Hence integral internal stresses isotropic isotropic body k₁ Let us consider longitudinal longitudinal waves moduli non-zero obtain parallel perpendicular plane plate PROBLEM quadratic quantities radius relation result rotation satisfies shear shell small compared SOLUTION strain tensor stress tensor stretching Substituting surface symmetry temperature thermal conduction torsion transverse transverse waves two-dimensional u₁ undeformed unit volume values velocity of propagation vibrations wave vector x-axis xy-plane YOUNG's modulus z-axis zero σικ диг ду дх дхк