A Robust Topology Optimization Method Considering Bounded Field Parameters with Uncertainties Based on the Variable Time Step Parametric Level-Set Method

• A level-set based robust topology optimization method considering bounded field parameters is proposed. • A variable time step strategy based on the RBF gradient function is developed to realize the separation of time and space. • The bounded field parameters are characterized through the dimension reduction method and dimension-wise method. In this paper, a robust topology optimization method considering bounded field parameters with uncertainties based on the variable time step parametric level-set method is proposed. Firstly, a variable time step strategy for level set function evolution based on the gradient of the level set function that uses radial basis function interpolation to realize the separation of time and space is developed, which can achieve better design results during topology optimization. Beyond that, the dimension reduction method and dimension-wise method based on the polynomials are used for characterization and quantification of bounded field parameters with uncertainties. Finally, the sensitivity of the robust optimization model is derived based on the shape derivative principle, which provides the basis for the implementation of gradient based optimization algorithm. Three examples illustrate the effectiveness, necessity and influence of important parameters of the robust topology optimization method considering bounded field parameters with uncertainties based on the variable time step parametric level-set method from different aspects.