A Study on Optimum Topology of Plate Structure Using Coordinate Transformation by Conformal Mapping

Abstract

This paper presents a new method to determine optimum topology of plate strucutres using conformal mapping which is used in fluid mechanics, electromagnetic, and elasticity. Fisrt we prove two invariants of bending moments satisfy Laplace equation. Then it is showed that corresponding relationship between fluid mechanics, electromagnetic and elasticity can be also valid in the theory of plate bending under a certain condition. Then a simple design method to optimum topology of plate strucutures is proposed. Several numerical examples are treated and it is confirmed the effectiveness and validity of proposed method.