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Abstract
The Complex Variable Boundary Element Method (CVBEM) has been shown to be an effective numerical technique for the solution of two-dimensional potential problems such as ideal-fluid flow, Fickian diffusion, heat flow, and torsion of prismatic bars. It is based on the Cauchy integral of the theory of a complex variable which expresses an analytical function in a region in terms of its integral along the contour of the region. The method consists in discretizing the boundary into segments called complex boundary elements and replacing the analytic function on the boundary by interpolating functions which can be easily integrated analytically.
In this dissertation, the mathematical foundation of the CVBEM relevant to multiply connected regions is first developed. The method is then applied to solve the Saint-Venant torsion problem for composite cylindrical bars of arbitrary cross section. As numerical examples: (1) a square shaft with a square inclusion; (2) a square shaft with a circular inclusion; (3) an elliptical shaft with an elliptical inclusion; (4) an elliptical shaft with two elliptical inclusions are solved. The torsional rigidity and the resultant boundary shear stresses for each case are given and are compared with those available in the literature.
