连续体结构非概率可靠性拓扑优化

基于非概率可靠性指标的定义，考虑材料、几何及荷载大小的不确定性，提出以结构体积最小化为目标、具有位移非概率可靠性约束的三维连续体拓扑优化数学模型. 采用目标性能方法对优化模型进行转换，给出目标性能值的伴随法灵敏度分析算法，利用数学规划法实现优化问题的求解. 数值算例验证了所提出优化模型的正确性及算法的有效性，并指出相对于确定性优化而言，非概率可靠性拓扑优化能够给出在考虑不确定参数和荷载条件下更合理的材料分布.

NON-PROBABILISTIC RELIABILITY-BASED TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES

It is of great importance to incorporate uncertainties into structural topology optimization problems. Based on the definition of the non-probabilistic reliability index, this paper proposes a mathematical model for topology optimization of 3D continuum structures with non-probabilistic reliability constraints on deformation. In this model, the uncertainties in material properties, geometrical dimensions and loading conditions are accounted for. The Performance Measure Approach (PMA) is adopted for transformation of the constraints. In this context, the adjoint variable scheme for sensitivity analysis of the target performance is discussed, which facilitates a mathematical programming solution of the optimization problem. Numerical investigations illustrate the applicability and the validity of the present model as well as the proposed numerical techniques. The computational results show that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than the conventional deterministic approach.