基于IPTO算法的连续体结构可靠性拓扑优化

Reliability-based topology optimization of continuum structure with the IPTO algorithm

研究结构几何尺寸、结构材料体积及作用载荷不确定条件下的连续体结构可靠性拓扑优化问题,提出基于改进比例拓扑优化(Improved Proportional Topology Optimization,IPTO)算法的可靠性拓扑优化方法。基于概率方法描述变量的不确定性,建立综合考虑材料体积约束和可靠性约束且使柔度最小的连续体结构可靠性拓扑优化数学模型;为提高计算效率,使用基于解耦思想的混合法将可靠性拓扑优化问题解耦成可靠性分析和当量确定性拓扑优化两个独立子问题。在可靠性分析阶段,遵循一阶可靠度法中可靠性指标的几何意义,获取满足可靠性约束且服从正态分布的随机变量,并通过逆变换对其进行修正;在当量确定性拓扑优化阶段,以修正后的随机变量作为设计参数,使用具有无需获取灵敏度信息功能的IPTO算法对结构执行拓扑优化设计。最后使用MBB梁和悬臂梁两个算例证实了所提方法的有效性。

Aiming at the reliability-based topology optimization problem of continuum structure considering the uncertainties including structural geometrical dimensions,material volume and external load,a reliability-based topology optimization method based on the Improved Proportional Topology Optimization(IPTO)algorithm was proposed.Under the premise of describing the uncertainties of design variables with the probability method,a mathematical model of continuum structure reliability-based topology optimization was constructed,whose objective was to minimize the structural compliance while the material volume constraint and reliability constraint were comprehensively considered.To improve the computational efficiency,the hybrid(or concurrent)method was used to decouple the reliability-based topology optimization problem into two independent sub-problems including reliability analysis and equivalent deterministic topology optimization.In the stage of reliability analysis,the normal random variables satisfying the reliability constraint were obtained according to the geometric meaning of reliability index in the first-order reliability method,and subsequently,the inverse transformation was performed to modify the random variables.In the equivalent deterministic topology optimization stage,the modified random variables were taken as design parameters,and the IPTO algorithm which can avoid obtaining the sensitivity information was employed to perform topology optimization design of the structure.Finally,the effectiveness of the proposed method was verified by two numerical examples.