The localized radial basis functions for parameterized level set based structural optimization

The current work is mainly about the implementation of the local radial basis functions (LRBFs) within the level set framework for structural optimization of two-dimensional linear elastic problems. The implicit representation of the structural geometry is accomplished through the LRBFs based level set function (LSF), and the geometry modification during the optimization process is carried out through an update of the LSF using a system of coupled ordinary differential equations (ODEs) instead of the Hamilton-Jacobi (HJ) type equation. This new implementation of LRBFs and level set method (LSM) allows essential topological changes automatically, i.e hole nucleation, hole merging with each other, and with the boundary to obtain the optimal structures. The coefficient matrix of the LRBFs is less sensitive to the values of shape parameter as well as the proposed method is mesh independent as explored during the numerical experiments performed. This new implementation is applied to distinct benchmark problems for minimum compliance with single and multiple load cases. The numerical experiments performed reveal significant insightful of the use of radial basis functions (RBFs) within the LSM framework, which may be considered as a step forward for further exploration of their intrinsic capabilities and improved performance for the solution of structural optimization problems.