March 19, 1998

SIZE, SHAPE, AND TOPOLOGY OPTIMIZATION OF STRUCTURES

by:

Ashok D. Belegundu, Associate Professor

Department of Mechanical Engineering

The Pennsylvania State University

ABSTRACT

Basic concepts and computer implementation is presented for structural optimization. Specifically, the talk deals with: sizing optimization involving determination of size related variables; with shape optimization dealing with x-y-z coordinates of boundary nodes; with topology optimization dealing with where material should and should not be. In sizing problems, the technique is straightforward although the problem dimension can be large. In special cases, “optimality criteria” methods can be used for handling large problems. In shape optimization, the main task is to generate basis shapes. In topology optimization, the challenge is to develop a material model which can relate material distribution densities to material properties. Here, the homogenization method is discussed. Computer implementation aspects are discussed and PC based program demonstrations will be given.