MQ quasi-interpolation-based level set method for structural topology optimization

Parametric level set method (PLSM) using interpolation method, such as radial basis function (RBF) interpolation, exposes high computational cost and poor stability when solving structural topology optimization (STO) problems with large-scale nodes. However, the quasi-interpolation method can approximate the level set function (LSF) and its generalized functions without solving any system of linear equations. With this good property, this paper utilizes multiquadric (MQ) quasi-interpolation to parameterize the LSF and innovatively introduces it into the STO problem. Moreover, the MQ quasi-interpolation is utilized to compute the element density, which makes the level set band method (LSBM) more rigorous. The proposed methods were compared with the PLSM based on compactly supported radial basis functions (CSRBFs). The results show that the approximation accuracy, computational efficiency and stability of the evolution process of the proposed methods are better than those of CSRBFs when the shape parameter takes a suitable small value.