A meshless level set method for shape and topology optimization

This paper proposes a meshless Galerkin level set method for structural shape and topology optimization of continua. Design boundary is represented through the introduction of a scalar level set function as its zero level set. Compactly supported radial basis functions (CSRBFs) are used to parameterize level set function and construct the meshless shape functions. The meshless Galerkin global weak form is employed to implement the discretization of the state equations. This provides a pathway to simplify the numerical procedures in most conventional level set by unifying the two different stages just in terms of one set of scattered nodes. The proposed level set method has the capability of describing the implicit moving boundaries without remeshing for discontinuities. One benchmark example is used to demonstrate the effectiveness of the proposed method.