A MIXED METHOD FOR SHAPE OPTIMIZATION OF SKELETAL STRUCTURES

Abstract

This paper presents a new efficient mixed method for minimum weight structural design (geometrical and member sizing) of structures. The objective function is approximated by a second-order Taylor series expansion and the constraints by first-order Taylor series expansions. In order to eliminate the tedious work in evaluating the Hessian matrix and performing its inversion, an approximating matrix employed by the variable metric method is used to approach the inverse of the Hessian matrix. Applying the Kuhn-Tucker conditions to the problem, the K-T multipliers can be determinated by quadratic programming, and finally, the problem is transformed to one of linear programming with intercomplementarity conditions. The examples show that the method is generally applicable, convenient to use and has rapid convergence.