Stress trajectory guided structural design and topology optimization

Density-based topology optimization using global and local volume constraints is a key technique to automatically design lightweight structures. It is known that stiffness optimal structures comprise spatially varying geometric patterns that span multiple length scales. However, both variants of topology optimization have challenges to efficiently converge to such a structural layout. In this paper, we investigate material layouts that are generated from stress trajectories, i.e., to compile a globally consistent structure by tracing the stress trajectories from finite element simulation of the solid design domain under external loads. This is particularly appealing from a computational perspective, since it avoids iterative optimization that involves finite element analysis on fine meshes. By regularizing the thickness of each trajectory using derived strain energy measures along them, stiff structural layouts can be generated in a highly efficient way. We then shed light on the use of the resulting structures as initial density fields in density-based topology optimization, i.e., to generate an initial density field that is then further optimized via topology optimization. We demonstrate that by using a stress trajectory guided density initialization in lieu of a uniform density field, convergence issues in density-based topology optimization can be significantly relaxed at comparable stiffness of the resulting structural layouts.