隐式功能函数结构体可靠性拓扑优化

Reliability-based Topology Optimization of Implicit Performance Function Structure

考虑工程实际中外载荷、材料属性等的随机不确定性对结构安全性的影响,研究了具有结构位移可靠性约束的拓扑优化设计。建立以柔度最小为目标、以单元相对密度为变量、具有材料体积分数约束和结构位移可靠性约束的拓扑优化数学模型;针对运用有限元数值计算方法时结构功能函数为隐式的情况,运用响应面法近似逼近结构真实的功能函数;利用简便高效的一次二阶矩法计算结构位移可靠度;采用内循环为确定性的拓扑优化、外循环控制结构材料体积分数的策略对连续体结构进行可靠性拓扑优化设计。通过两个算例与确定性拓扑优化结果进行比较,结果表明所提设计方法是高效可行的。

Considering the impacts of uncertain factors such as external loading, material property etc. on structural safety in engineering practice, the topology optimization design with the structural displacement reliability constrain was discussed. A mathematical of topology optimization was devel- oped, where the minimization of compliance was taken as objective function, the relative densities of el ements were taken as design variables, the material volume fraction and structural displacement relia-bility were taken as constraints. The response surface method was implemented to approximately ap proach its real performance function, for the situation that the structural performance function was implicit by using finite element numerical method. Then, the simple and efficient first order second moment method was used to obtain the structural displacement reliability. The strategy that inner loop was the deterministic topology optimization and the outer loop was to control the material volume fraction was implemented to carry out the reliability-based topology optimization of continuum structure. Finally, two numerical examples were given to be compared with the results of deterministic topology optimization showing that the design method is efficient and feasible.