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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Results 1-3 of 38
Page 58
... bending of thin plates given in §§11-13 is applicable only to fairly small deflections . Anticipating the result given below , it may be mentioned here that the condition for that theory to be applicable is that the deflection { is ...
... bending of thin plates given in §§11-13 is applicable only to fairly small deflections . Anticipating the result given below , it may be mentioned here that the condition for that theory to be applicable is that the deflection { is ...
Page 62
... bending of a flat plate is a second- order effect in comparison with the bending deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The ...
... bending of a flat plate is a second- order effect in comparison with the bending deflection itself . This is seen , for example , from the fact that the strain tensor ( 14.1 ) , which gives this stretching , is quadratic in . The ...
Page 63
... bending energy is small compared with the stretching energy , it is clear that , if any given shell permits deformation without stretching , then such defor- mations will , in general , actually occur when arbitrary external forces act ...
... bending energy is small compared with the stretching energy , it is clear that , if any given shell permits deformation without stretching , then such defor- mations will , in general , actually occur when arbitrary external forces act ...
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