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
... given point . This means that , at any given point , we can choose co - ordinate axes ( the principal axes of the tensor ) in such a way that only the diagonal components U11 , U22 , u33 of the tensor utk are different from zero . These ...
... given point . This means that , at any given point , we can choose co - ordinate axes ( the principal axes of the tensor ) in such a way that only the diagonal components U11 , U22 , u33 of the tensor utk are different from zero . These ...
Page 50
... given part of the edge turns from its initial position is ( for small displacements ( ) the derivative alan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals in ( 12.3 ) are zero ...
... given part of the edge turns from its initial position is ( for small displacements ( ) the derivative alan . Thus the variations & and Sat / on must be zero at clamped edges , so that the contour integrals in ( 12.3 ) are zero ...
Page 137
... given by ( 29.2 ) and ( 29.6 ) , together with the dynamical equations pvi = dσik / dxk , ( 29.8 ) where σik = λiklmUlm = λiklmwim . The tensors pik and ji which appear in these equations are given functions of the co - ordinates ( and ...
... given by ( 29.2 ) and ( 29.6 ) , together with the dynamical equations pvi = dσik / dxk , ( 29.8 ) where σik = λiklmUlm = λiklmwim . The tensors pik and ji which appear in these equations are given functions of the co - ordinates ( and ...
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