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 63
Page 20
... function x satisfies the equation Δ Δχ = 0 , ( 7.11 ) i.e. it is biharmonic . This function is called the stress function . When the plane problem has been solved and the function x is known , the longitudinal stress σzz is determined ...
... function x satisfies the equation Δ Δχ = 0 , ( 7.11 ) i.e. it is biharmonic . This function is called the stress function . When the plane problem has been solved and the function x is known , the longitudinal stress σzz is determined ...
Page 24
... function . Taking the Laplacian of equation ( 3 ) , we then find that △ △ σx = 0 , i.e. the components σ are biharmonic functions . These results follow also from ( 7.6 ) and ( 7.7 ) , since σ and u are linearly related . PROBLEM 10 ...
... function . Taking the Laplacian of equation ( 3 ) , we then find that △ △ σx = 0 , i.e. the components σ are biharmonic functions . These results follow also from ( 7.6 ) and ( 7.7 ) , since σ and u are linearly related . PROBLEM 10 ...
Page 126
... function : bk = = [ riba8 ( E ) dfi . ( 27.5 ) where is the two - dimensional radius vector taken from the axis of the dis- location in the plane perpendicular to the vector τ at the point considered . Since the contour L is arbitrary ...
... function : bk = = [ riba8 ( E ) dfi . ( 27.5 ) where is the two - dimensional radius vector taken from the axis of the dis- location in the plane perpendicular to the vector τ at the point considered . Since the contour L is arbitrary ...
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