基于可靠性的结构动态拓扑优化方法

发布时间：2018-10-30 09:44

【摘要】：实际工程结构设计往往在确定性范畴内进行,所得结构存在较大失效可能性.基于此,提出一种基于可靠性的连续体动态拓扑优化方法,将结构可靠性分析方法嵌套到连续体拓扑优化中.考虑了结构几何尺寸和材料体积的不确定性,并用高斯分布来度量.将结构可靠度作为约束嵌套到连续体拓扑优化中,属于二次嵌套优化问题,但计算效率低下,不适于工程应用.提出一种解耦策略将结构可靠性分析从连续体拓扑优化中解耦出来,使结构可靠性分析与动态拓扑优化为两个独立的优化循环,大大提高了计算效率.建立以结构基频最大为优化目标,满足一定体积约束和可靠度要求的优化问题,利用各向同性材料惩罚模型(SIMP)和移动渐进方法(MMA)求解该优化问题.所提方法可以得到满足不同可靠度要求的一系列最优结构,并用标准算例验证其有效性.
[Abstract]:The actual engineering structure design is usually carried out within the deterministic scope, and there is a great possibility of failure of the resulting structure. Based on this, a dynamic topology optimization method of continuum based on reliability is proposed, in which the structural reliability analysis method is nested into the continuum topology optimization. The uncertainty of structure size and material volume is considered, and the Gao Si distribution is used to measure the uncertainty. It is a quadratic nested optimization problem to use structural reliability as a constraint in continuum topology optimization, but the calculation efficiency is low, so it is not suitable for engineering application. A decoupling strategy is proposed to decouple structural reliability analysis from continuum topology optimization, which makes structural reliability analysis and dynamic topology optimization two independent optimization cycles, which greatly improve the computational efficiency. An optimization problem with the maximum fundamental frequency of the structure as the optimization objective and satisfying certain volume constraints and reliability requirements is established. The problem is solved by using the isotropic material penalty model (SIMP) and the moving asymptotic method (MMA). A series of optimal structures satisfying different reliability requirements can be obtained by the proposed method, and their validity is verified by a standard example.
【作者单位】：湘潭大学土木与力学学院;湖南科技大学信息与电气学院;
【基金】：国家自然科学基金项目资助(51375416) 湖南省教育厅创新平台开放基金资助项目~~
【分类号】：TU318

【相似文献】