A first-order equivalent static loads algorithm for optimization of nonlinear static response

The Equivalent Static Loads (ESL) algorithm for nonlinear static response structural optimization is modified to promote convergence to designs satisfying first-order optimality conditions. The modifications involve first-order estimates of the equivalent static loads considered in the sub-problems and algorithmic stabilization through a trust-region approach.

The practical convergence properties of the original and modified algorithms are assessed through numerical experiments on a set of reproducible structural size optimization problems. The results demonstrate the capabilities of the proposed algorithm in finding optimized designs that satisfy first-order optimality conditions numerically with modest computational resources.