A Study on Optimum Topology Using a Coordinate Transformation by Conformal Mapping.

Abstract

This paper presents a method to determine the optimum topology of 2-D elastic plane structures by making use of coordinate transformation. We use conformal mapping which is well known to be effective in two dimensional fluid mechanical, electromagnetical and elastic problems as a coordinate transformation function. First, we examine two quantities of stresses in conformal mapped elastic problem. We show that those two quantities of stresses can satisfy the Laplace equation, and then we clarify that a corresponding same relationship between fluid mechanics and electromagnetics can be also valid in the theory of elasticity. Then we proposed a simple design method for optimum topology by making use of coordinate transformation by conformal mapping. We also proposed a method to determine of the similarity qualitatively between the obtained optimum topologies. Finally, we treated several numerical examples by the proposed method. In numerical examples, we can examine the effectiveness of the proposed method.