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 65
... corresponds to unstable equilibrium for a given p : bulges with larger values of H grow of their own accord , while ... corresponding total energy in the region of the bulge E ( h / R ) 2hr . With the condition ( 15.5 ) it is in fact ...
... corresponds to unstable equilibrium for a given p : bulges with larger values of H grow of their own accord , while ... corresponding total energy in the region of the bulge E ( h / R ) 2hr . With the condition ( 15.5 ) it is in fact ...
Page 119
... corresponding equations of motion are non - linear and do not admit simple periodic ( harmonic ) solutions . We shall consider here anharmonic effects of the third order , arising from terms in the elastic energy which are cubic in the ...
... corresponding equations of motion are non - linear and do not admit simple periodic ( harmonic ) solutions . We shall consider here anharmonic effects of the third order , arising from terms in the elastic energy which are cubic in the ...
Page 127
... corresponding co - ordinate axes ; the tensor di may be called the dislocation moment tensor . The components of the tensor Gy are first - order homogeneous functions of the co - ordinates x , y , z ( see §8 , Problem ) . We therefore ...
... corresponding co - ordinate axes ; the tensor di may be called the dislocation moment tensor . The components of the tensor Gy are first - order homogeneous functions of the co - ordinates x , y , z ( see §8 , Problem ) . We therefore ...
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