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 32
... curvature are R1 and R'1 . The radii of curvature are regarded as positive if the centre of curvature lies within the body con- cerned , and negative in the contrary case . This integral equation determines the distribution of the ...
... curvature are R1 and R'1 . The radii of curvature are regarded as positive if the centre of curvature lies within the body con- cerned , and negative in the contrary case . This integral equation determines the distribution of the ...
Page 62
... curvature tends to zero , and is therefore due to the curvature of the shell . Let R be the order of magnitude of the radius of curvature of the shell , which is usually of the same order as its dimension . Then the strain tensor for ...
... curvature tends to zero , and is therefore due to the curvature of the shell . Let R be the order of magnitude of the radius of curvature of the shell , which is usually of the same order as its dimension . Then the strain tensor for ...
Page 79
... curvature vector of the line ; its magnitude is 1 / R , where R is the radius of curvature , † and its direction is that of the principal normal to the curve . The change in a vector due to an infinitesimal rotation is equal to the ...
... curvature vector of the line ; its magnitude is 1 / R , where R is the radius of curvature , † and its direction is that of the principal normal to the curve . The change in a vector due to an infinitesimal rotation is equal to the ...
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