An Integrated MATLAB Code for Homogenization-Based Topology Optimization and Generating Functionally Graded Surface Lattices for Additive Manufacturing

Triply periodic minimal surfaces (TPMS) lattices are gaining popularity for enhancing structural efficiency in many engineering applications. Functionally graded TPMS structures provide more customized mechanical properties and improved functionality compared to typical homogenous designs by deliberately altering material properties throughout the lattice. This study presents a novel framework by integrating a homogenization-based topology optimization method with functionally graded lattice creation, utilizing a streamlined and versatile MATLAB code. The methodology encompasses several essential phases, including preprocessing, finite element analysis, sensitivity analysis, density filtering, optimization, element density visualization, and lattice reconstruction. These steps facilitate the development of highly efficient lattice structures with varied attributes, rendering them optimal for additive manufacturing and full-scale analysis. To ensure the accuracy of the established methodology, three optimization case studies with different boundary conditions are defined, and the mechanical reactions of the optimized lattice structures in filled with different TPMS structures are extensively validated by comparing them to both full-scale finite element models and experiments. The comparative results demonstrate that the mechanical responses obtained from topological analysis closely correspond to those acquired from full-scale models and experiments.