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 39
... axis C4 as the x - axis , and the x and y axes perpendicular to two of the vertical planes of symmetry . Reflections ... z - axis is unique ( along the axis C4 or S4 ) . The requirements of symmetry then allow a further component λxxxy ...
... axis C4 as the x - axis , and the x and y axes perpendicular to two of the vertical planes of symmetry . Reflections ... z - axis is unique ( along the axis C4 or S4 ) . The requirements of symmetry then allow a further component λxxxy ...
Page 40
... z ; since F is to be expressed in terms of the components of the strain tensor in the co - ordinates x , y , z , we ... axis as the x - axis , and again use the co - ordinates & = x + iy , n = x - iy . In a rotation through an angle ...
... z ; since F is to be expressed in terms of the components of the strain tensor in the co - ordinates x , y , z , we ... axis as the x - axis , and again use the co - ordinates & = x + iy , n = x - iy . In a rotation through an angle ...
Page 129
... z - axis along the disloca- tion line ; the Burgers vector is by = by = 0 , b2 = b . It is evident from symmetry that the displacement u is parallel to the x - axis and is independent of the co - ordinate z . The equation of equilibrium ...
... z - axis along the disloca- tion line ; the Burgers vector is by = by = 0 , b2 = b . It is evident from symmetry that the displacement u is parallel to the x - axis and is independent of the co - ordinate z . The equation of equilibrium ...
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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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