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 18
Page 77
... unit volume of the rod is σikuk = σzzUzz = Ex2 / R2 . Integrating over the cross - section of the rod , we have ( E / R2 ) x2 df . ( 17.5 ) This is the free energy per unit length of a bent rod . The radius of curvature R is that of the ...
... unit volume of the rod is σikuk = σzzUzz = Ex2 / R2 . Integrating over the cross - section of the rod , we have ( E / R2 ) x2 df . ( 17.5 ) This is the free energy per unit length of a bent rod . The radius of curvature R is that of the ...
Page 80
... unit length of the rod is a quadratic function of the deformation , i.e. , in this case , a quadratic function of the components of the vector 2. It is easy to see that there can be no terms in this quadratic form proportional to Ng and ...
... unit length of the rod is a quadratic function of the deformation , i.e. , in this case , a quadratic function of the components of the vector 2. It is easy to see that there can be no terms in this quadratic form proportional to Ng and ...
Page 134
... unit length acting on one dislocation in the stress field due to the other dislocation is determined from formula ( 28.4 ) , using the results of §27 , Problem 2. It is a radial force of magnitude ƒ : ub1b2 / 2πr . Dislocations of like ...
... unit length acting on one dislocation in the stress field due to the other dislocation is determined from formula ( 28.4 ) , using the results of §27 , Problem 2. It is a radial force of magnitude ƒ : ub1b2 / 2πr . Dislocations of like ...
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