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 24
... derivatives of the stress function . SOLUTION . Since the required expressions cannot depend on the choice of the initial line of 4 , they do not contain & explicitly . Hence we can proceed as follows : we transform the Cartesian ...
... derivatives of the stress function . SOLUTION . Since the required expressions cannot depend on the choice of the initial line of 4 , they do not contain & explicitly . Hence we can proceed as follows : we transform the Cartesian ...
Page 50
... derivative aan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals in ... derivatives with respect to x and y in ( 12.6 ) and ( 12.7 ) into those in the directions of n and 1 , we obtain the ...
... derivative aan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals in ... derivatives with respect to x and y in ( 12.6 ) and ( 12.7 ) into those in the directions of n and 1 , we obtain the ...
Page 59
... derivatives of u are here omitted ; the same cannot , of course , be done with the derivatives of , since there are no corresponding first - order terms . The stress tensor oa due to the stretching of the plate is given by formula ...
... derivatives of u are here omitted ; the same cannot , of course , be done with the derivatives of , since there are no corresponding first - order terms . The stress tensor oa due to the stretching of the plate is given by formula ...
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