载荷位置不确定条件下结构稳健性拓扑优化设计

Robust topology optimization of continuum structures with load position uncertainty

研究了在载荷作用位置不确定条件下,连续体结构的稳健性拓扑优化设计,为外载荷的有效传递提供可靠的传力路径。首先基于非概率方法,将载荷位置的不确定性用区间变量表示。其次通过载荷移动的一阶和二阶导数信息,推导出载荷位置改变后结构柔顺度对拓扑设计变量的一阶导数公式。最后运用变密度法中的SIMP模型以及移动渐近线法(MMA),对连续体结构进行稳健性拓扑优化设计。所得结构与传统载荷位置确定条件下的优化结构相比,稳健性明显更高,充分展示了考虑载荷位置变化对结构拓扑构型设计的影响及其重要性。

Robust topology optimization of continuum structures under the position uncertainty of an external load is performed with the objective of the structural compliance minimization.On the basis of the non-probabilistic representation method,the load position uncertainty is indicated with an interval variable.Then the sensitivity analyses of the structural compliance to the topological design variables are performed according to the quadratic Taylor series expansion with the first-and second-order derivatives of the load position movement.Based on the SIMP model and MMA algorithm,the robust topology optimal design is carried out,and the results are compared with those obtained under the deterministic load position.Numerical comparisons reveal that the present topology optimization solutions provide more reliable load transfer paths in the design domain with higher robustness to the load application point disturbances than the equivalent deterministic topology optimization.