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 alan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals ... 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 alan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals ... 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 σαβ ...
... 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 σαβ ...
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