A Full-Space Method with Matrix Aggregates for Stress-Constrained Structural Optimization

Abstract

Stress-constrained structural optimization is challenging due to the nature of the local stress constraints that must be imposed point-wise everywhere within the structural domain. These constraints lead to optimization problems for which classical reduced-space methods scale poorly with increasing number of local stress constraints. To address this issue, a full-space barrier method is developed which is designed for problems with large numbers of constraints. Within this method, local stress constraints are formulated as matrix inequalities using convex optimization methods. Matrix aggregates are introduced which aggregate local stress constraints formulated as linear matrix inequalities. The advantage of the linear matrix inequality formulation is that the resulting stress constraints are convex in both the design and state variables, where non-convexity enters only through the governing equations. The proposed method is demonstrated on a plane stress problem.

Kona: A Parallel Optimization Library for Engineering-Design Problems

“…A similar formulation on the same PDE solver, with forcing applied as traction along the entire edge instead of a point load in the corner, has previously been solved using a full-space Newton-Krylov approach. 20 Here we will be using the FLECS-based reduced-space Newton-Krylov algorithm. Kona's abstraction layer is suitable for full-space optimization problems, but we have not yet implemented a fullspace (i.e.…”