Influence of Filter Functions on Efficiency of Topology Optimization and Gray-scale Element

In order to enhance the efficiency of topology optimization and reduce the number of gray units, power function, composite exponential function and rational fraction function are introduced as filtering functions based on independent continuous mapping (ICM) method, and a topology optimization model with minimum weight as the objective and displacement as the constraint is fomulated. Numerical examples are employed to investigate the effects of three kinds of filter functions and the parameter ratio of element weight and element stiffness filter functions on the efficiency of topology optimization and gray units are studied. Numerical examples show that the rational fraction function can effectively reduce the number of intermediate gray units, improve the convergence speed and reduce the weight of the structure. For the power function, when the parameter ratio of element weight and element stiffness filter function is 1: 7, the effect is optimal. For the composite exponential function, when the parameter ratio of element weight and element stiffness filter function is 1.3 : 0.1, the effect is optimal. For the rational fraction filter function, when the parameter ratio of element quality and element stiffness filter function is 3: 63, the effect is optimal.