An Effective Topology Optimization Using Smoothed Bézier Curve-Fitting Based Level Set

In this paper, an extended finite element method and a curve-fitting procedure are incorporated into an implicit level set method to construct a topology optimization approach inspired for manufacturing fields. The extended finite element method plays an essential role in dealing with a weak discontinuous model after utilizing a zero level set to be divided into the solid and void areas in each element. A Hamilton–Jacobi partial differential equation is transformed into ordinary differential equations over the entire design domain and updated by an upwind scheme. The proposed method is implemented in the minimum compliance design framework that has been extensively studied in topology optimization. Numerical examples illustrate the success of the presented approach in the accuracy, convergence speed and insensitivity to initial designs. It is suggested that the introduction of the nodal density variables interpolation with a level set and smoothed curve-fitting approach can be promising in material topology optimization.