非正态分布的连续体结构可靠性拓扑优化设计

The Reliability-based Topological Optimization Design of Continuum Structural with Abnormal Distribution

由于具有不确定性参数的连续体结构普遍存在,因此研究不确定性参数连续体结构的可靠性拓扑优化问题具有十分重要的意义。在基本随机变量前四阶矩已知的情况下,利用四阶矩技术以及有限元方法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。将连续体的拓扑优化设计视为一种对单元的模式识别,将模式识别领域的K邻近方法引入到连续体结构拓扑优化设计领域,以结构的单元应力作为识别的变量,利用应力的欧拉距离作为判别的标准,对连续体结构进行可靠性拓扑优化设计。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,同时表明该计算方法是可行的。

Because of the continuum structural with uncertainty is common,the research of reliability-based topology optimization is of great significance.Techniques from the fourth prime matrix and the finite element method are employed to present the practical and effective method for the reliability-based topology optimization for continuum structural with abnormal distribution parameters in the case of given the first-forth moments of basic random variables.The topology optimization is described as pattern recognition to element and the K nearest neighbor method is extracted from the technique of pattern recognition to seek the optimized result with the element stress as variable and Euclidean distance of stress as recognition standard.Several numerical examples given to compare with optimized results with deterministic indicate that the approach proposed is a convenient and practical method.