Moving Knots RBFs and Level Set Method
for Structural Optimization

This method is a parametric shape and topology optimization technique based on radial basis functions (RBFs) and level set methods. The shape and topology optimization problem is converted into a parameter optimization problem and design variables are positions of the knots of RBFs. We deduce sensitivities of the objective function and volume function through combining the shape derivative analysis with the Hamilton-Jacobi equation. According to these sensitivities, we can move knots to new positions using a proper optimization algorithm.

An important advantage of the parametric method is that we have more freedom to choose design variables with the RBF parameterization and we can control more parameters with sensitivity analysis. Another advantage of the parametric method is that we can use the mature optimization algorithms based on parameters sensitivity analysis, such as the method of moving asymptote (MMA) and the optimality criteria (OC) method.

• Research Grants Council of Hong Kong SAR (Grant Nos. CUHK416205, CUHK416206 and CUHK416507).