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 65
Page 38
... expression for the elastic free energy of a crystal belonging to the monoclinic system is F = λxxxxxx2 + 1⁄2λyyyyUyy2 + } λzzzzUzz2 + λxxyyUxxUyy + λxxzzUxxUzz + + λyyzzUyyUzz + 2 \ xyxyuxy2 + 2λxzxzUxz2 + 2λyzyzUyz2 + 2λxxxyUxx2xy + + ...
... expression for the elastic free energy of a crystal belonging to the monoclinic system is F = λxxxxxx2 + 1⁄2λyyyyUyy2 + } λzzzzUzz2 + λxxyyUxxUyy + λxxzzUxxUzz + + λyyzzUyyUzz + 2 \ xyxyuxy2 + 2λxzxzUxz2 + 2λyzyzUyz2 + 2λxxxyUxx2xy + + ...
Page 80
... expression for the energy must be that obtained in §16 . Thus the term in 22 in the free energy is CQ2 . Finally , the terms quadratic in 2 and 2 , can be obtained by starting from the expression ( 17.7 ) for the energy of a slightly ...
... expression for the energy must be that obtained in §16 . Thus the term in 22 in the free energy is CQ2 . Finally , the terms quadratic in 2 and 2 , can be obtained by starting from the expression ( 17.7 ) for the energy of a slightly ...
Page 155
... expression ( 34.3 ) is exactly analogous to the expression ( 10.1 ) for the free energy of a crystal : the elastic modulus tensor is replaced by the tensor nikim , and uik by uk . Hence the results obtained in §10 for the tensor λikim ...
... expression ( 34.3 ) is exactly analogous to the expression ( 10.1 ) for the free energy of a crystal : the elastic modulus tensor is replaced by the tensor nikim , and uik by uk . Hence the results obtained in §10 for the tensor λikim ...
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