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 8
... Let us consider some deformed body , and suppose that the deformation is changed in such a way that the displacement vector u changes by a small amount du ; and let us determine the work done by the internal stresses in this change ...
... Let us consider some deformed body , and suppose that the deformation is changed in such a way that the displacement vector u changes by a small amount du ; and let us determine the work done by the internal stresses in this change ...
Page 38
... Let us consider the class C .; we take a co - ordinate system with the xy - plane as the plane of symmetry . On reflection in this plane , the co - ordinates undergo the transformation xx , y → y , z →→ z . The components of a tensor ...
... Let us consider the class C .; we take a co - ordinate system with the xy - plane as the plane of symmetry . On reflection in this plane , the co - ordinates undergo the transformation xx , y → y , z →→ z . The components of a tensor ...
Page 39
... Let us consider the class C4v ; we take the axis C4 as the x - axis , and the x and y axes perpendicular to two of the vertical planes of symmetry . Reflections in these two planes signify transformations and x → -x , y → y ' , 2⇒2 x ...
... Let us consider the class C4v ; we take the axis C4 as the x - axis , and the x and y axes perpendicular to two of the vertical planes of symmetry . Reflections in these two planes signify transformations and x → -x , y → y ' , 2⇒2 x ...
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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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