Multi-phase field topology optimization of polycrystalline microstructure for maximizing heat conductivity

IgaTop: an implementation of topology optimization for structures using IGA in MATLAB

“…Currently, several topology optimization methods with their specific functions have been developed in recent years, such as the Solid Isotropic Material with Penalization (SIMP) method (Zhou and Rozvany 1991;Bendsøe and Sigmund 1999), the Evolutionary Structural Optimization (ESO) method (Xie and Steven 1993), the Level-Set Method (LSM) (Wang et al 2003; Allaire et al 2004), the Moving Morphable Components/Voids (MMC/Vs) method (Guo et al 2014;Yang et al 2016;Zhang et al 2017) and etc.. Meanwhile, these developed topology optimization methods have been also applied to discuss several numerical optimization problems, such as, the concurrent topology optimization (Xia and Breitkopf 2014;Li et al 2016;Wang et al 2017a;Gao et al 2019b), materials design (Sigmund 1994;Xia and Breitkopf 2015), heat conduction (Kato et al 2018;Zhao et al 2020b) and etc.. As we know, the classic Finite Element Method (FEM) has achieved a broad of applications in topology optimization to solve the unknown structural responses in the numerical implementation. In the FEM, spline basis functions are employed in the construction of the Computer-Aided Design (CAD) model, whereas Lagrangian and Hermitian polynomials are used in Computer-Aided Engineering (CAE) model.…”