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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Results 1-3 of 11
Page 28
... dx ' dy ' . ( 8.14 ) We know from potential theory that a harmonic function ƒ which is zero at infinity and has a given normal derivative aflax on the plane z = 0 is given by the formula where 1 f ( x , y , z ) = - 2 = √ √ df ( x ...
... dx ' dy ' . ( 8.14 ) We know from potential theory that a harmonic function ƒ which is zero at infinity and has a given normal derivative aflax on the plane z = 0 is given by the formula where 1 f ( x , y , z ) = - 2 = √ √ df ( x ...
Page 32
... dx dy ' , TE 1 - o'2 u'z = TE ' f • Pz ( x ' , y ' ) dx ' dy ' , ( 9.5 ) where σ , o ' and E , E ' are the POISSON's ratios and the YOUNG's moduli of the two bodies . Since P2 = 0 outside the region of contact , the integration ex ...
... dx dy ' , TE 1 - o'2 u'z = TE ' f • Pz ( x ' , y ' ) dx ' dy ' , ( 9.5 ) where σ , o ' and E , E ' are the POISSON's ratios and the YOUNG's moduli of the two bodies . Since P2 = 0 outside the region of contact , the integration ex ...
Page 54
... dxdy ) дих 1 2uy + Px + P2 = 0 , ( 13.4 ) + Py = 0 . 2 ( 1 − a ) ôxây grad div u- ( 1 – σ ) curl curl u = - ( 1-02 ) P / Eh , ( 13.5 ) + \ 1 - σ2 ay2 2 ( 1 + 0 ) dx2 02 + These equations can be written in the two - dimensional vector ...
... dxdy ) дих 1 2uy + Px + P2 = 0 , ( 13.4 ) + Py = 0 . 2 ( 1 − a ) ôxây grad div u- ( 1 – σ ) curl curl u = - ( 1-02 ) P / Eh , ( 13.5 ) + \ 1 - σ2 ay2 2 ( 1 + 0 ) dx2 02 + These equations can be written in the two - dimensional vector ...
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