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 10
... body as a function of the strain tensor . This expression is easily obtained by using the fact that the deformation is small and expanding the free energy in powers of uk . We shall at present consider only isotropic bodies . The ...
... body as a function of the strain tensor . This expression is easily obtained by using the fact that the deformation is small and expanding the free energy in powers of uk . We shall at present consider only isotropic bodies . The ...
Page 122
... body , and the components of the tensor σ are now given by ( 26.2 ) , with & correct to the required accuracy . The tensor ok is no longer symmetrical . † PROBLEM Write down the general expression for the elastic energy of an isotropic body ...
... body , and the components of the tensor σ are now given by ( 26.2 ) , with & correct to the required accuracy . The tensor ok is no longer symmetrical . † PROBLEM Write down the general expression for the elastic energy of an isotropic body ...
Page 155
... isotropic body has only two independent components , and Y can be written in a form analogous to the expression ( 4.3 ) for the elastic energy of an isotropic body : η Y = n ( úík - Síkůπ ) 2 + } { ùn2 , ( 34.5 ) where and are the two ...
... isotropic body has only two independent components , and Y can be written in a form analogous to the expression ( 4.3 ) for the elastic energy of an isotropic body : η Y = n ( úík - Síkůπ ) 2 + } { ùn2 , ( 34.5 ) where and are the two ...
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