Application of methods of feasible directions to structural optimization problems

Abstract

A general approach to structural optimization which has received much attention in recent years is that of using mathematical programming (numerical search) techniques. These techniques may be separated into direct and indirect methods. Of the direct methods of attack on general nonlinear inequality constrained problems, the largest class is called methods of feasible directions. This paper presents the application fo Zoutendijk's method of feasible directions [5] to structural optimization problems. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. A considerable improvement in convergence has been achieved by considering each pushoff factor as a linear function of the corresponding active constraint. A comparison of the half-step versus full-step search procedure is presented. An initial step length based on a present decrement of objective function is used. A discussion of the linear versus quadratic interpolations of a constraint function in search for a bound point is presented. The algorithm is demonstrated with elastic design of a 25-bar space tower, a 3-bay single storey and a double bay double storey rigid jointed plane frames. Data on the differences in the optimum designs obtained from different starting points is reported.