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 19
... quantities are independent of the co - ordinate z , the equations of equilibrium ( in the absence of external body ... quantities σxx , σxy , σyy can be expressed in terms of the two quantities ux , uy , and are therefore not independent ...
... quantities are independent of the co - ordinate z , the equations of equilibrium ( in the absence of external body ... quantities σxx , σxy , σyy can be expressed in terms of the two quantities ux , uy , and are therefore not independent ...
Page 27
... quantities gx , gy , ƒ z and were defined do not determine them uniquely . We can therefore impose an arbitrary additional condition on these quantities , and it is convenient to make the quantity in the braces in equations ( 8.9 ) ...
... quantities gx , gy , ƒ z and were defined do not determine them uniquely . We can therefore impose an arbitrary additional condition on these quantities , and it is convenient to make the quantity in the braces in equations ( 8.9 ) ...
Page 38
... quantities which describe the elastic properties of the crystal will be 18 non - zero moduli and 3 angles defining the orientation of the axes in the crystal . -2 . ( 2 ) Monoclinic system . Let us consider the class C .; we take a co ...
... quantities which describe the elastic properties of the crystal will be 18 non - zero moduli and 3 angles defining the orientation of the axes in the crystal . -2 . ( 2 ) Monoclinic system . Let us consider the class C .; we take a co ...
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