Efficient computation of states and sensitivities for compound structural optimisation problems using a Linear Dependency Aware Solver (LDAS)

Abstract

Real-world structural optimisation problems involve multiple loading conditions and design constraints, with responses typically depending on states of discretised governing equations. Generally, one uses gradient-based nested analysis and design approaches to solve these problems. Herein, solving both physical and adjoint problems dominates the overall computational effort. Although not commonly detected, real-world problems can contain linear dependencies between encountered physical and adjoint loads. Manually keeping track of such dependencies becomes tedious as design problems become increasingly involved. This work proposes using a Linear Dependency Aware Solver (LDAS) to detect and exploit such dependencies. The proposed algorithm can efficiently detect linear dependencies between all loads and obtain the exact solution while avoiding unnecessary solves entirely and automatically. Illustrative examples demonstrate the need and benefits of using an LDAS, including a run-time experiment.

Stress‐constrained topology optimization of structures subjected to nonproportional loading

“…The computational cost is, however, similar as the number of linear equations solved is approximately the same. However, if one were to use a linear elastic model, all load scenarios could be solved effectively in parallel using a direct solver, which would result in a substantial speed up as discussed in Koppen et al, 41 compared to using our hyperelastic model. In this work, several equilibrium states has to be solved separately using Newton's method, which contributes to the computational cost.…”