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 1
... displacement of this point due to the deformation is then given by the vector r ' - r , which we shall denote by u : thị = đt . ( 1.1 ) The vector u is called the displacement vector . The co - ordinates x ' of the displaced point are ...
... displacement of this point due to the deformation is then given by the vector r ' - r , which we shall denote by u : thị = đt . ( 1.1 ) The vector u is called the displacement vector . The co - ordinates x ' of the displaced point are ...
Page 18
... vector notation . The quantities 2x2 are components of the vector △ u , and duż / dxɩ = div u . Thus the equations ... displacement vector satisfies the biharmonic equation . These results remain valid in a uniform gravitational field ...
... vector notation . The quantities 2x2 are components of the vector △ u , and duż / dxɩ = div u . Thus the equations ... displacement vector satisfies the biharmonic equation . These results remain valid in a uniform gravitational field ...
Page 124
Lev Davidovich Landau, Evgeniĭ Mikhaĭlovich Lifshit͡s, Evgeniĭ Mikhaĭlovich Lifshit︠s︡. displacement of each point from its position in the ideal lattice is denoted by the vector u , the total increment of this vector around the ...
Lev Davidovich Landau, Evgeniĭ Mikhaĭlovich Lifshit͡s, Evgeniĭ Mikhaĭlovich Lifshit︠s︡. displacement of each point from its position in the ideal lattice is denoted by the vector u , the total increment of this vector around 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