Optimization of singular problems

Abstract

A new optimization method is presented that optimizes singular structures. An example of a singular problem is deleting an inefficient member from a structure. As the member is deleted, the stresses in the member may increase above the allowables. When a member is deleted the nature of the analysis changes because the member stiffness becomes zero. This causes a local optima because stress constraints prevent inefficient members from zeroing. The problem is reformulated using the percent method so that the appropriate stress constraints are deleted as the member is deleted. Several examples show that the global optimal design is reached. Other methods to reach the global optima are appropriate only if the optimal structure is statically determinate. The percent optimization is also useful for optimization of discrete problems.