Parameterized level-set based topology optimization method considering symmetry and pattern repetition constraints

Symmetry and repetitive patterns are very common in both natural and artificial structures. Design with symmetry and pattern repetition (SPR) can be very useful in practical engineering. In this paper, we discuss a new optimal structural design method considering SPR constraints. The basic idea consists in combining a parameterized level-set method together with radial basis function (RBF) interpolation strategy, which allows for decoupling RBF knots from the finite element (FE) analysis mesh. The merits of the decoupled manner are that RBF knots can be mapped independently on regular or irregular design domain, and SPR constraints can be imposed by simply building a bijective relationship between RBF knots regardless of analysis mesh. Furthermore, due to parameterization of the level-set function, there are fewer numerical manipulations that need to be implemented than the conventional level-set method during the optimization process. Several numerical examples are presented to show feasibility and effectiveness of the proposed method.