On a Technique to Obtain an Optimum Strength Shape by the Finite Element Method : Application to the Problems under Body Force

In this paper, a technique to determine effectively an optimum shape of two-dimensional and axisymmetric bodies under body force is proposed. This technique is based on the iteration of a sequential search method consisting of the following steps. In the first step, the superiority or inferiority of a given shape, which satisfies the constrained conditions of design, is judged by the deviation from the design object stress value. In the second step, this given shape is modified to an optimum shape by the proportional transformation method of the finite elements, which is considered an effect of body force. By using this technique the optimum shapes of the basic problems under gravity load or centrifugal force are obtained and the results are compared with the corresponding shapes given by elementary theory. Moreover and optimum shape of the rotating disk with a rim and a bored hole is obtained by applying the optimization technique. The validity of this shape is examined experimentally by comparing with the fracture strength of a bored, uniform thickness disk.