考虑材料参数不确定性结构动力学稳健性拓扑优化设计

Robust dynamic topology optimization of structure with uncertain material parameters

本文在考虑材料参数不确定性的条件下,对连续体结构动力学稳健性拓扑优化设计进行研究。在使结构的第一阶固有频率最大化的同时,显著减小其对材料性能不确定性的影响。基于非概率凸集模型,将材料参数的不确定性用有界区间变量表示;建立了能够抑制频率改变的结构动力学拓扑优化模型,用单层优化策略求解稳健性优化设计问题。通过对材料参数的导数分析,获得了在材料性能不确定情形下结构第一阶固有频率的二阶泰勒展开式,并推导出了频率对拓扑变量的一阶灵敏度显性表达式。基于变密度法,开展了结构动力学稳健性拓扑优化设计,并与确定性优化结果进行对比,验证了用本文方法获得的结构第一阶固有频率稳健性更高,受材料参数不确定性扰动影响更小,展示了考虑材料参数不确定性的重要性。

The robust dynamic topology optimization of a continuum planar structure is studied to reduce its natural frequency varia-tion when the structural material parameter uncertainties are considered.The uncertainties of the material properties are represented with the uncertain-but-bounded interval variables based on the non-probabilistic convex model.The dynamic topology optimization model for maximizing the first natural frequency is constituted by mitigating its variation,such that the robust optimization problem can be simply solved into a single-level framework.By the derivative analysis of the material parameters,a quadratic Taylor series expansion of the first natural frequency is obtained,and the design sensitivity of the natural frequency is accordingly evaluated in an explicit form under the uncertain material properties.By means of the material density-based strategy,the robust dynamic topology optimization is implemented with the material volume constraint,and the results are compared with those of the deterministic topol-ogy optimization.Optimal results show that the first-order natural frequency obtained with the proposed method has a higher robust-ness against the material property uncertainties,which fully demonstrates the importance of considering the uncertainties of the ma-terial parameters in the structural design stage.