非正态分布的连续体结构可靠性拓扑优化方法研究

Research on Reliability-Based Topological Optimization of Continuum Structure with Abnormal Distribution

针对连续体结构普遍存在不确定参数服从非正态分布的拓扑优化问题,利用当量正态化法(JC法)将结构不确定参数正态化,然后利用标准空间最小值问题求解连续体结构的可靠度,对隐式的可靠度约束进行显式化处理。以固体各向同性惩罚微结构模型(SIMP法)为插值模型和优化准则,以结构柔度最小为优化目标建立连续体拓扑优化模型,随后利用优化准则法(OC法)求解加入可靠度约束后的优化模型,得到同时满足材料最优分布和可靠度要求的优化结构。通过数值算例与确定性设计结果进行对比,结果表明,考虑了可靠度影响的拓扑优化结果要优于确定性参数的优化结果,且结构可靠度设计指标对最终优化形式有较大影响,同时表明该计算方法是可行的。

Aiming at solving the topology optimization problem for continuum structures when abnormal distribution uncertanity parameters exsited,techniques from equivalent normalization method(JC method)is employed to transform the abnormal random parameters to normal ones. Then,the structural reliability index is obtained by solving the minimum problem of standard space,which changed the index from implicit to explicit. The mathematical model,with the objective to minimize compliance,is worked out based on solid isotropic microstructures with penalization(SIMP)and Optimality Criteria method(OC method). We may obtain the optimized model with the optimum material distribution and meeting reliability requirements simultaneously when solving the optimization model,by using OC method,after reliability constraint added. The validity of methodology in this paper is demonstrated by several typical examples,and it found that the reliability target has great influence on the final optimization.