A basis for local minima of a symmetric frame topography

Abstract

Optimization of indeterminate frames involves non-convex stress constraint functions which form a non-convex design space that results in multiple local minima, unknown in number to begin with. The current state-of-the-art in this field recommends employment of different arbitrary initial designs to have a reasonable assurance of reaching every local minimum which, under a particular load, is associated with a specific material distribution. In this study a basis is laid down for (a) determination, at the very outset, of the number of local minima that possibly may exist in a frame of symmetric topography, (b) definition, in terms of relative member stiffnesses, of the material distribution pattern associated with each local minimum, and (c) a guideline for evaluation of member forces for initial proportioning of the pattern, The application of the proposed method for evaluation of local minima is illustrated with an example problem.