基于等效静态载荷法的区间参数结构可靠性拓扑优化

摘要

T his paper aims at investigating reliability-based topology optimization for dynamic problems with interval parameters ,in which equivalent static loads (ESL) method is adopted .The interval static responses from equivalent static loads and interval dynamic responses from dynamic loads are considered to have the same midpoint and deviation .Equivalent static loads are obtained through the Taylor expan-sion and mapping technique .Based upon the equivalent static loads and solids isotropic materials with pe-nalization (SIMP) model ,topology optimization problem is formulated with non-probabilistic reliability constraints .T he adjoint method is adopted to derive the reliability sensitivity ,and the method of moving asymptotes (MMA) is employed to solve the topology optimization problem .Two examples are provided to demonstrate the effectiveness of the proposed method .%研究了用等效静态载荷法，解决动态响应约束下的区间参数结构可靠性拓扑优化问题。对等效静态载荷赋予了新的含义：由等效静态载荷产生的区间静态响应与由动态载荷产生的区间动态响应，其对应的中值与离差均相等。利用泰勒展开计算出区间参数结构动态响应所有可能值组成的集合，再根据集合映射获得包含结构所有不确定信息的等效静态载荷集合，继而建立静态可靠性拓扑优化数学模型。通过集合映射和区间自然扩展，获得静态位移响应区间。基于区间非概率可靠性指标的定义，给出区间非概率可靠性约束的伴随法灵敏度分析算法。采用移动渐近线法完成此优化问题的求解。数值算例验证了模型的正确性和算法的有效性。