应变能约束下多随机参数连续体结构的拓扑优化

研究几何和物理参数均为随机变量的平面连续体结构在结构总应变能约束下的拓扑优化设计问题．以结构总质量均值最小化为目标函数，以结构的形状拓扑信息为设计变量，以结构总应变能概率可靠性指标为约束条件，构建了随机结构的拓扑优化设计数学模型．利用代数综合法，导出了应变能响应的均值和均方差的计算表达式．采用双方向渐进结构优化的求解策略．通过两个算例验证了本模型及求解策略的合理性和有效性．

Topology optimization of the multi-random parameters continuum structure under the strain energy constraint

The topology optimization design problem for the planar continuum structure with the randomness of both the geometry and physical parameters under the structural total strain energy constraint is studied. A mathematical model for topology optimization design with a random structure is established, in which the minimum mean of structural weight is taken as the objective function, the structural shape topology information is taken as design variables, and the probabilistic reliability index of structural total strain energy is taken as the constraint condition. The computational expressions for the mean value and mean variance of the structural strain energy response are presented by the algebra method. The solution strategy of the bi-directional evolutionary structural optimization method is used in the optimization. Through two examples, the rationality and feasibility of the optimization model and solution strategy are validated.