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 58
... deflections . The deflection is not now supposed small compared with h . It should be emphasised , however , that the deformation itself must still be small , in the sense that the components of the strain tensor must be small . In ...
... deflections . The deflection is not now supposed small compared with h . It should be emphasised , however , that the deformation itself must still be small , in the sense that the components of the strain tensor must be small . In ...
Page 61
... deflections of thin plates ( A. FÖPPL 1907 ) . These equations are very compli- cated , and cannot be solved exactly ... deflection of a plate as a function of the force on it when > h . SOLUTION . An estimate of the terms in equation ...
... deflections of thin plates ( A. FÖPPL 1907 ) . These equations are very compli- cated , and cannot be solved exactly ... deflection of a plate as a function of the force on it when > h . SOLUTION . An estimate of the terms in equation ...
Page 62
... deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The situation is entirely different in the defor- mation of shells : here the stretching is ...
... deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The situation is entirely different in the defor- mation of shells : here the stretching is ...
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