Some two- and three-dimensional stress analyses in solid mechanics.

摘要

This thesis addresses several important problems in solid mechanics. The subjects involved include plane anisotropic elasticity, plane isotropic plasticity and three-dimensional isotropic elasticity. The topics covered range from basic issues to specific problems.; A new proof of the equivalence of the stress and displacement formulation methods in plane anisotropic elasticity is provided in Chapter 2 along with a systematic study of the Lekhnitskii and Stroh formalisms. A new displacement method based on partial differential equation theory is also presented in this chapter. Chapter 3 develops a new hybrid experimental-numerical/analytical method for stress analysis of a finite three-dimensional isotropic elastic component. It uses measured surface stresses and Green's function method in potential theory to determine the displacements (and thus strains and stresses) in the interior of the component. The general procedure developed in this chapter can be directly applied to actual engineering components with finite geometry.; Chapter 4 presents an exact solution for the plane stress inclusion problem of an equibiaxially loaded elastic power-law plastic plate containing an elastic circular inhomogeneity, while Chapter 5 furnishes an analytical solution for the plane strain counterpart of the inclusion problem dealt with in Chapter 4. These two solutions can find applications in fiber-filled metal-matrix composites and opening and reinforcement designs of thin-walled spherical pressure vessels.