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 51
... boundary condition ( 12.7 ) can be simplified by converting to the ... conditions in the form = 22L do ac < = 0 , + o- = 0 . an2 dl an ( 12.11 ) ... boundary conditions ( = 0 , d¿ / dr = 0 for r = The result is 【= ß ( Ra — r2 ) 3 . PROBLEM ...
... boundary condition ( 12.7 ) can be simplified by converting to the ... conditions in the form = 22L do ac < = 0 , + o- = 0 . an2 dl an ( 12.11 ) ... boundary conditions ( = 0 , d¿ / dr = 0 for r = The result is 【= ß ( Ra — r2 ) 3 . PROBLEM ...
Page 71
... boundary conditions on the surface of the rod , we note that , since the rod is thin , the external forces on its sides must be small com- pared with the internal stresses in the rod , and can therefore be put equal to zero in seeking ...
... boundary conditions on the surface of the rod , we note that , since the rod is thin , the external forces on its sides must be small com- pared with the internal stresses in the rod , and can therefore be put equal to zero in seeking ...
Page 83
... boundary conditions at the ends of a bent rod . Various cases are possible . The end of the rod is said to be clamped ( Fig . 4a , §12 ) if it cannot move either longitudinally or transversely , and moreover its direction ( i.e. the ...
... boundary conditions at the ends of a bent rod . Various cases are possible . The end of the rod is said to be clamped ( Fig . 4a , §12 ) if it cannot move either longitudinally or transversely , and moreover its direction ( i.e. the ...
Contents
FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |
2 The stress tensor | 4 |
3 The thermodynamics of deformation | 8 |
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Common terms and phrases
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