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 54
Page 5
... integral over the surface . As we know from vector analysis , the integral of a scalar over an arbitrary volume can be transformed into an integral over the surface if the scalar is the divergence of a vector . In the present case we ...
... integral over the surface . As we know from vector analysis , the integral of a scalar over an arbitrary volume can be transformed into an integral over the surface if the scalar is the divergence of a vector . In the present case we ...
Page 46
... integral in ( 11.6 ) into two , and vary the two parts separately . The first integral can be written in the form ( A ) 2 df , where df = dx dy is a surface element and △ = 2 / dx2 + 02 / 02 is here ( and in §§13 , 14 ) the two ...
... integral in ( 11.6 ) into two , and vary the two parts separately . The first integral can be written in the form ( A ) 2 df , where df = dx dy is a surface element and △ = 2 / dx2 + 02 / 02 is here ( and in §§13 , 14 ) the two ...
Page 49
... integrals . The surface integral is Eh3 Δ ^ 25 — P \ 55 - ( 12 ( 1 —。2 ) ^ 25 — P 85 dƒ . - The variation › in this integral is arbitrary . The integral can therefore vanish only if the coefficient of d is zero , i.e. Eh3 12 ( 1 – σ2 ) ...
... integrals . The surface integral is Eh3 Δ ^ 25 — P \ 55 - ( 12 ( 1 —。2 ) ^ 25 — P 85 dƒ . - The variation › in this integral is arbitrary . The integral can therefore vanish only if the coefficient of d is zero , i.e. Eh3 12 ( 1 – σ2 ) ...
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