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 69
... torsion causes sufficiently distant cross- sections to turn through large angles . The generators on the sides of the rod , which are parallel to its axis , become helical in form under torsion . Let us consider a thin straight rod of ...
... torsion causes sufficiently distant cross- sections to turn through large angles . The generators on the sides of the rod , which are parallel to its axis , become helical in form under torsion . Let us consider a thin straight rod of ...
Page 74
... torsion angle : T = M / C . PROBLEMS ( 16.20 ) PROBLEM 1. Determine the torsional rigidity of a rod whose cross - section is a circle of radius R. SOLUTION . The solutions of Problems 1-4 are formally identical with those of problems of ...
... torsion angle : T = M / C . PROBLEMS ( 16.20 ) PROBLEM 1. Determine the torsional rigidity of a rod whose cross - section is a circle of radius R. SOLUTION . The solutions of Problems 1-4 are formally identical with those of problems of ...
Page 79
... torsion , the co - ordinate system rotates only about the axis of the rod , i.e. about the ( -axis . In this case , therefore , the vector is parallel to the axis of the rod , and is just the torsion angle 7 used in §16 ...
... torsion , the co - ordinate system rotates only about the axis of the rod , i.e. about the ( -axis . In this case , therefore , the vector is parallel to the axis of the rod , and is just the torsion angle 7 used in §16 ...
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