Tailored Functionally Graded Materials design and concurrent topology optimization with implicit fields

Abstract

Tailored Functionally Graded Materials (FGMs) offer the ability to design and engineer materials with specific properties at a changing volume fraction and are widely used in various fields such as aerospace, biomedical engineering, etc. The precise control of physical properties and the connectivity of microstructural sequences are two main challenges in multiscale problems. This paper constructs a novel optimization model for generating FGMs under customized performance, employing an implicit field representation governed by tensor product B-splines. The cross-sectional profile aligns with a microstructure, and thus varying heights correspond to a sequence of microstructures. Fine-tuning the implicit field on connectable FGMs is achieved by optimizing specific properties and addressing the 2-norm problem under connectivity constraints. Therefore, these FGMs can serve as fundamental units for bottom-up multiscale infills. Additionally, we also develop a new model to investigate a more universally applicable concurrent topology optimization method without initial input restrictions. These multiscale optimization results demonstrate excellent performance under tested working conditions.