ANALYSIS OF TWO-DIMENSIONAL LINEAR FIELD PROBLEMS BY SCALED BOUNDARY FINITE ELEMENT METHOD

Abstract

This dissertation presents the development of an efficient and accurate numerical technique based upon the scaled boundary finite element method that is capable of solving two-dimensional, second-order, linear, multi-field problems. Basic governing equations are established in a general context allowing various classes of linear boundary value problems such as the steady-state heat conduction, the steady-state flow in porous media, linear elasticity, linear piezoelectricity, and other related couple-field problems to be treated in a unified fashion. The scaled boundary finite element equations are also formulated within a broad framework integrating the influence of the distributed body source, general boundary conditions, contributions of the side face with either prescribed surface flux or prescribed state variable, and the flexibility of the scaled boundary approximations. Several examples are solved and selected results are reported not only to verify the implemented technique but also to demonstrate its vast capability, computational efficiency, and robustness.