High-Resolution Topology Optimization with Stress and Natural Frequency Constraints

摘要

Topology optimization tools offer the potential to design novel aerospace structures that are subject to demanding strength and natural frequency requirements. However, algorithms for stress- and frequency-constrained topology optimization are more computationally expensive than compliance-based methods and are especially challenging to apply to large-scale high-resolution problems. To address this issue, stress constraints are formulated using a reconstruction of the displacement field that produces a stress field that is less mesh-sensitive and more amenable to stress-constrained optimization. To address the high computational cost of eigenvalue problems, the natural frequency problem is solved using a Jacobi-Davidson eigenvalue solution method that is compatible with iterative solution techniques. Novel eigenvector recycling strategies, which reuse eigenvector information, are proposed and evaluated. This combination of iterative eigenvalue solution method and recycling strategy enables the solution of high-resolution topology optimization problems with frequency constraints. The effectiveness of these techniques is demonstrated by solving mass minimization problems with combined stress and frequency constraints on a cantilever beam problem with 42 million degrees of freedom, and on a new orthogonal bracket problem with 16 million degrees of freedom.