关键词: 插值方法, 变密度法, 位移约束, 拓扑优化

Abstract: A density-volume interpolation scheme applied in the variable density method was proposed, which was used for controlling grayscale elements in the topology optimization of continuum structures. In the new interpolation scheme, a linear relationship was established between the element stiffness and the relative density to ensure that the element stiffness changed smoothly with the changes of relative density in each iteration. And a penalty function was established between the element volume and the relative density in order to penalize the intermediate densities, which is better for reducing the number of grayscale elements acompained with the intermediate densities approaching both ends.The new interpolation scheme was introduced into the minimum volume optimization problems subjected to displacement constraints. The examples show that the optimization process changes little when increasing the penalty and it indicates that this algorithm is relatively stable. When solving the topology optimization problems with the same structures, it shows that there are less grayscale elements in the optimization results by using the new interpolation scheme than the results optimized by the SIMP and RAMP method. It is because a large penalty may be implemented on intermediate density in the new interpolation scheme.

Key words: interpolation scheme, variable density method, displacement constraint, topology optimization