Topology optimization in structural design.

摘要

Topology optimization for general structures is considered in this dissertation. The objective of topology optimization is to find the best material distribution to maximize the structural stiffness in statics or dynamics with limited material usage, or to minimize structural weight under overall stiffness constraint. These objectives are achieved by using the density method in this dissertation.; Due to the large amount of design variables in topology optimization, the mathematical programming (MP) methods are not used in this dissertation. The method of optimality criteria (MOC) is adapted in this dissertation. A one-term posynomial is successfully utilized to approximate either the objective function or constraint. After approximating the objective function or constraint as an explicit function of design variables, the Lagrange multiplier technique is employed to obtain the optimum solution. This method is very effective in solving the optimum design since there is only a single constraint.; A FORTRAN program was developed to incorporate the one term posynomial optimization technique with MSC/NASTRAN. Several examples are presented for minimum compliance, maximum eigenvalue, and minimum weight design of general structures modeled by plate/shell elements. For topology optimization under dynamic loading, several formulations are presented and illustrated by plane truss examples.