1.天津大学;2.合肥工业大学
中国博士后科学基金（2022M712358）;中央高校科研业务费基金（JZ2022HGTB0291）
1.Tianjin University;2.Hefei University of Technology
China Postdoctoral Science Foundation(2022M712358);Fundamental Research Funds for the Central Universities（JZ2022HGTB0291）
加筋板结构中加强筋的分布位置严重影响其结构性能，目前大部分关于加筋板结构设计方面的工作都是在确定性载荷工况下开展的，忽略了载荷不确定性因素对结构刚度的影响。本文针对加筋板结构加强筋的布局优化问题，提出一种考虑载荷不确定性的鲁棒性结构布局优化方法，以实现加强筋布局和尺寸的同步优化。基于基结构法建立了以表征加强筋的圆形截面梁半径为设计变量、以结构整体的质量为约束，以不确定性载荷下结构柔度的期望和方差的线性加权值为目标的鲁棒性布局优化模型；详细推导了结构柔度的期望和方差、及质量约束关于设计变量的解析灵敏度列式，采用移动渐进线方法对鲁棒性布局优化问题进行求解；最后两个优化算例验证了本文方法的有效性。
The distribution of stiffeners in the stiffened plate structure seriously affects its structural performance. At present, most of the work on the design of the stiffened plate structure is carried out under deterministic load conditions, where the effect of load uncertainty on the structural stiffness is ignored. This paper proposes a robust structural layout optimization method for layout optimization problem of stiffeners in stiffened plate structures considering load uncertainty, and realizes the simultaneous optimization of the layout and size of stiffeners. A robust layout optimization model is established based on the ground structure method, with the radius of the circular section beam representing the stiffener as the design variable, the mass of the entire structure as the constraint, and the linear weighted value of the expected and variance of the structural compliance under uncertain loads as the objective. The analytical sensitivity formula of the expectation and variance of the structural compliance and the mass constraint with respect to design variables are deduced in detail. The method of moving asymptotes is adopted to solve the robust layout optimization problem. Finally, two examples are performed to verify the effectiveness of the proposed method.
