In this paper, we present an extension of the B-spline based density representation to a robust formulation of topology optimization. In our B-spline based topology optimization approach, we use separate representations for material density distribution and analysis. B-splines are used as a representation of density and the usual finite elements are used for analysis. The density undergoes a Heaviside projection to reduce the grayness in the optimized structures. To ensure minimal length control so the resulting designs are robust with respect to manufacturing imprecision, we adopt a three-structure formulation during the optimization. That is, dilated, intermediate and eroded designs are used in the optimization formulation. We give an analytical description of minimal length of features in optimized designs. Numerical examples have been implemented on three common topology optimization problems: minimal compliance, heat conduction and compliant mechanism. They demonstrate that the proposed approach is effective in generating designs with crisp black/white transition and is accurate in minimal length control.
