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 38
Lev Davidovich Landau, Evgeniĭ Mikhaĭlovich Lifshit͡s, Evgeniĭ Mikhaĭlovich Lifshit︠s︡. be taken as zero . Then the independent quantities which describe the elastic properties of the crystal will be 18 non - zero moduli and 3 angles ...
Lev Davidovich Landau, Evgeniĭ Mikhaĭlovich Lifshit͡s, Evgeniĭ Mikhaĭlovich Lifshit︠s︡. be taken as zero . Then the independent quantities which describe the elastic properties of the crystal will be 18 non - zero moduli and 3 angles ...
Page 40
... non - zero value of the difference λgggz - Annnz . This , however , can be made to vanish by a suitable choice of the x and y axes . ( 6 ) Hexagonal system . Let us consider the class Ce ; we take the sixth- order axis as the z - axis ...
... non - zero value of the difference λgggz - Annnz . This , however , can be made to vanish by a suitable choice of the x and y axes . ( 6 ) Hexagonal system . Let us consider the class Ce ; we take the sixth- order axis as the z - axis ...
Page 98
... non - zero solution , it is sufficient to consider only the equation which contains the smaller of I , and I. Let I , < I. Then we seek a solution of the equation EI , X ( v ) + | T | X ” = 0 in the form X = A + B + C sin kz + D cos kz ...
... non - zero solution , it is sufficient to consider only the equation which contains the smaller of I , and I. Let I , < I. Then we seek a solution of the equation EI , X ( v ) + | T | X ” = 0 in the form X = A + B + C sin kz + D cos kz ...
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