基于灵敏度分析的结构-声学鲁棒优化设计

针对工程中普遍存在的结构-声场耦合系统，充分考虑系统本身及外载荷的不确定性，提出了求解系统响应范围的区间有限元分析方法及鲁棒优化设计模型.从耦合系统的平衡方程出发，利用中心差分方法得到了系统响应的灵敏度计算公式.引入区间变量来表征信息不足的不确定参数，借助一阶泰勒展式，可以快速估算系统响应的区间上下界.在结构鲁棒优化设计过程中，通过引入灵敏度指标，将原不确定单目标优化问题转化为确定的多目标优化问题.为保证结构性能更加稳定，利用区间可能度刻画约束条件的鲁棒性.数值算例通过某弹舱模型弹性板厚度的优化设计，验证了所建立的鲁棒优化模型及算法的有效性.

Robust optimization of coupled structural-acoustic systems based on sensitivity analysis

An interval finite element method and an interval robust optimization model were proposed for the coupled structural-acoustic field prediction and structural design with uncertainties both in the inherent parameters and external load. Based on the central difference method, the response sensitivity with respect to the system parameters was derived from the structural-acoustic dynamic equilibrium equation. Interval variables were used to quantitatively describe all the uncertain parameters with limited information. In terms of the first-order Taylor expansion, the lower and upper bounds of the uncertain structural-acoustic field could be quickly obtained. In the structural robust optimization, the original uncertain single-objective optimization problem was transformed into a deterministic multi-objective one by introducing a sensitivity index. To ensure a more stable performance of the structural design, the interval possible degree was adopted to describe the robustness of the constraints. Numerical results about a bomb bay were given to demonstrate the effectiveness of proposed robust model and algorithm.