Design optimization of lattice structures with stress constraints

Abstract

This paper presents an experimentally validated framework used to perform topology and orientation (morphology) optimization of lattice structures subject to stress constraints. The effective stiffnesses and yield stresses of a unit cell are obtained using numerical homogenization and validated experimentally. Due to the orthotropic behavior of the unit cell, the modified Hill’s yield criterion is used to describe the lattice strength. The effective orthotropic properties are implemented via macrostructure topology optimization to further improve the lattice structure stiffness. Homogenization-based optimization is performed using a coarse mesh and the optimized design is projected onto a fine mesh. This reduces the computational cost significantly. Finally, the projected design is post-processed to ensure the fabrication feasibility of the optimized lattice structure. The framework is tested for two cases: an L-shaped bracket and a single-edge notched bend (SENB) problem. A comparison of the compliance-based and stress-constrained designs used in the two cases demonstrates that the changes in the optimal material distribution that occur upon implementing the stress constraint result in higher yield strength. The SENB lattice structures are additively manufactured and the stiffnesses and yield strength of the optimized designs are compared to those obtained numerically.

Keywords

• Topology optimization
• Morphology optimization
• Homogenization
• Cellular solids
• Additive manufacturing