Decomposition and optimization of linear structures using meta models

Abstract

Monolithic optimization of large mechanical systems can be expensive and cumbersome. Drivers of computational cost and integration effort are, e.g., the size of the design problem and the number of different components, models, and disciplines. Distributed optimization schemes decompose large problems into smaller subproblems; however, they typically require intense coordination effort. This paper proposes an approach for complete decoupling by decomposing a monolithic optimization into independent optimization subproblems that can be solved without need for coordination. This is accomplished by sampling the space of component performance, here represented by eigenvalues and eigenvectors of stiffness matrices, and establishing meta models that map the relevant component performance values onto feasibility and mass estimates. The optimization procedure consists of two steps: First, a system optimization problem is solved by assigning stiffness requirements to components that are approximately feasible and mass-optimal. Second, the component optimization problems are solved independently of each other such that stiffness requirements are satisfied. As information on feasibility and mass is provided during system optimization by meta models, the approach will be referred to as informed decomposition. The effectiveness of the approach is demonstrated by minimizing the mass of a simple two-component linear structure subject to a requirement on total stiffness. This is done for three different component models, a beam with constant cross-section, a beam with varying cross-sections, and an arbitrary 2-dimensional body, using parametric and topology optimization, respectively. The approach produces results that are at most 1 % heavier than the results obtained by monolithic optimization.