Comparison of two staggered schemes for optimization with a critical point constraint

Abstract

Two staggered solution schemes for a minimum volume optimization problem with a critical point constraint are considered. Scheme 1 leads to optimization at a critical (maximum) point, while Scheme 2 results in optimization at a maximum load. The reduced optimization problems for each of the schemes are different, and the derivatives for them must be defined consistently with the step preceding optimization. Using an example of a simple nonlinear two-bar truss and performing a rigorous analysis of roots of the equilibrium equation and of their limits, we show that properties of the derivative of displacements at the critical load and the derivative of critical displacements are very different. Then the methods of calculating various design derivatives are described and both solution schemes are tested on the truss example. Conclusions are related to accuracy and rate of convergence of both schemes, as well as to their sensitivity to inaccuracies characteristic for large scale numerical implementations.