中文摘要：

提出一种多工况应力约束下格栅结构的拓扑优化方法。优化目标结构是由无限细无限密的梁（或肋）构成的类格栅连续体（或加肋板）。采用正交异性增强复合材料模型模拟该类格栅连续体（或加肋板）的本构关系。以梁在结点处的密度和方向作为设计变量。根据有限元分析结果，采用满应力准则法优化各单工况下材料分布。按照多工况下材料的方向刚度与各单工况下材料的方向刚度最大值的差值最小为原则建立多工况下梁（或肋）的拓扑优化分布。经过少量迭代就可以建立优化的材料连续分布场。最后以3个算例演示拓扑优化的过程，并给出结点处梁的密度和方向分布。

英文摘要：

A method to optimize the topology of grillage structures under multiple load cases with stress constraints is presented. The optimal structures are grillage-like continua/stiffened-plates containing infinite number of beams/ribs of infinitesimal spacing. The fiber-reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of the grillage-like continua/stiffened-raft. The beams/ribs densities and orientations at the nodes are taken as design variables. The material distribution for each single load case is optimized by a fully-stressed criterion based on finite element analysis. The directional stiffness of the optimal structures in multiple load cases approach to the biggest of the stiffness defined for each single load case. The optimal continuous material distributive field is achieved after several iterations. Three examples are presented to demonstrate the effectiveness of the proposed approach. The beams/ribs densities and orientations distribution at the nodes are given finally.