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. |
From inside the book
Results 1-3 of 73
Page 51
... result is B ( Ra — 3 ) 3 . = PROBLEM 2. The same as Problem 1 , but for a plate with supported edges . SOLUTION . The boundary conditions ( 12.11 ) for a circular plate are ¿ = 0 , dt d † + dr2 r dr = 0 . The solution is similar to that ...
... result is B ( Ra — 3 ) 3 . = PROBLEM 2. The same as Problem 1 , but for a plate with supported edges . SOLUTION . The boundary conditions ( 12.11 ) for a circular plate are ¿ = 0 , dt d † + dr2 r dr = 0 . The solution is similar to that ...
Page 52
... result is } = = 3f ( 1-02 ) 2πЕh3 - [ } ( R2 — r2 ) — r2 log ( R / r ) ] . PROBLEM 4. The same as Problem 3 , but for a plate with supported edges . SOLUTION . 5 = 3ƒ ( 102 ) [ 3 + σ , 4 Eh3 1 + o R - ( R2 — r2 ) — 2r2 log- PROBLEM 5 ...
... result is } = = 3f ( 1-02 ) 2πЕh3 - [ } ( R2 — r2 ) — r2 log ( R / r ) ] . PROBLEM 4. The same as Problem 3 , but for a plate with supported edges . SOLUTION . 5 = 3ƒ ( 102 ) [ 3 + σ , 4 Eh3 1 + o R - ( R2 — r2 ) — 2r2 log- PROBLEM 5 ...
Page 147
... result first derived by A. A. GRIFFITH ( 1920 ) . Let us now return to the consideration of the shape of the crack . When L - x≤d , the region L - έ ~ d is the most important in the integral in ( 31.6 ) . The integral can then be ...
... result first derived by A. A. GRIFFITH ( 1920 ) . Let us now return to the consideration of the shape of the crack . When L - x≤d , the region L - έ ~ d is the most important in the integral in ( 31.6 ) . The integral can then be ...
Contents
FUNDAMENTAL EQUATIONS | 1 |
2 The stress tensor | 11 |
8 Equilibrium of an elastic medium bounded by a plane | 29 |
Copyright | |
21 other sections not shown
Other editions - View all
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