ON DESIGN DERIVATIVES FOR OPTIMIZATION WITH A CRITICAL-POINT CONSTRAINT

Design optimization of geometrically nonlinear structures with a criti cal point constraint is considered. A staggered scheme is applied to t he optimization problem and the reduced optimization problem is solved at the critical point. Derivatives of the objective function and cons traints are defined consistently with the algorithmic steps of the sta ggered scheme. It is noticed that different schemes require different design derivatives of the objective function and constraints. It is st ressed that a distinction must be made between the derivative of displ acements at the critical load and the derivative of critical displacem ents. For the sake of simplicity a nonlinear two-bar truss structure i s used to show that their properties are quite different; while the fi rst one grows to infinity when approaching the critical point and thus does not exist, the other exists at the critical point and is equal t o zero. Subsequently, two methods of computing the design derivative o f critical loads are analysed, and it is demonstrated, for the truss e xample, that both methods yield correct results. Then, two optimizatio n problems, i.e. the minimum volume problem and the maximum critical l oad problem, we formulated. Both problems are solved for the two-bar t russ, and yield results that compare favourably with those obtained an alytically. The solution scheme is shown to be insensitive to initial errors in the determination of the critical point.