Date of Award
Doctor of Engineering Science in Mechanical Engineering
James L. Martin
Su Ling Cheng
A method is developed within the framework of Synge's function-space interpretation of problems in linear elasticity which allows the consideration of solutions to problems for anisotropic media in terms of the solutions of a corresponding isotropic problem and corresponding simpler anisotropic problems. The isotropic solution and simpler anisotropic solutions establish points in each of the statically and kinematically admissible spaces for the anisotropic problem. The established points are used to define sets of vectors in the statically and kinematically admissible spaces. The linear independence of these vectors can then be determined by a pair of criteria developed in this work. The independent vectors so established, when employed in Synge's hypercircle method, provide approximations to the solution of the anisotropic problem. Synge's expressions for the bounds on the approximations obtained are extended to allow more immediate usage. In addition the notion of the residual problem, which leads in some cases to an exact solution of the anisotropic problem, is developed.
Carman, Richard Clement, "On the classification of the solution space of linear anisotropic elasticity" (1970). Dissertations. 1348.