Stress-constrained optimization using graded lattice microstructures

Abstract

In this work, we propose a novel method for predicting stress within a multiscale lattice optimization framework. On the microscale, a scalable stress is captured for each microstructure within a large, full factorial design of experiments. A multivariate polynomial response surface model is used to represent the microstructure material properties. Unlike the traditional solid isotropic material with a penalization-based stress approach or using the homogenized stress, we propose the use of real microscale stress components with macroscale strains through linear superposition. To examine the accuracy of the multiscale stress method, full-scale finite element simulations with non-periodic boundary conditions were performed. Using a range of microstructure gradings, it was determined that 6 layers of microstructures were required to achieve periodicity within the full-scale model. The effectiveness of the multiscale stress model was then examined. Using various graded structures and two load cases, our methodology was shown to replicate the von Mises stress in the center of the unit lattice cells to within 10% in the majority of the test cases. Finally, three stress-constrained optimization problems were solved to demonstrate the effectiveness of the method. Two stress-constrained weight minimization problems were demonstrated, alongside a stress-constrained target deformation problem. In all cases, the optimizer was able to sufficiently reduce the objective while respecting the imposed stress constraint.

Multiscale thermal and thermo-structural optimization of three-dimensional lattice structures

“…Provided local stress data from the microscale deformation analyses is captured, local stress response models can be generated to facilitate the derivation of stress-constrained optimal solutions. This is the subject of current research (Thillaithevan et al 2021). The principles of heterogeneous multiscale methods can be extended to acoustic, electro-magnetics as well as tailoring of structural properties to predefined resonant frequencies.…”

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

“…However, one of the challenges in M-TO is the high computational cost since one must generate and evaluate various microstructures (through homogenization) during each step of the optimization process ( [13,21,15,26]). To reduce this cost, researchers have proposed the use of graded variations of one or more pre-selected microstructural topologies ( [14,19,27]). [14] expressed the mechanical properties as a density function, with a B-spline-based interpolation.…”

Stress‐constrained multiscale topology optimization with connectable graded microstructures using the worst‐case analysis

“…38 Thillaithevan et al utilized the response surface model to design structures with graded lattice microstructures. 39 Yu et al handled the shell-lattice infill structural design under the von Mises stress-based and Tsai-Hill yield criteria-based constraints by using the level set method. 40 Zhao et al proposed a concurrent topology optimization approach for designing two-scale hierarchical structures under stress constraints without specifying the topology of the unit cell.…”

“…Based on the worst‐case analysis, 37 Zhang et al used the surrogate modeling technique to design the functionally graded lattice structure considering the strength performance 38 . Thillaithevan et al utilized the response surface model to design structures with graded lattice microstructures 39 . Yu et al handled the shell‐lattice infill structural design under the von Mises stress‐based and Tsai‐Hill yield criteria‐based constraints by using the level set method 40 .…”