考虑外载荷方向不确定性的稳健性拓扑优化

Robust topology optimization considering the uncertainty of load direction

外载荷方向不确定是实际工程中普遍存在的问题。本文研究了考虑外载荷方向不确定性下的稳健性连续体拓扑优化。首先,使用区间变量描述外载荷方向不确定性问题。随后,通过使用旋转矩阵的方式描述名义载荷方向上的扰动,并利用了旋转矩阵导数的特殊性质,通过二阶泰勒展开式以及名义载荷处柔顺度对角度的一阶和二阶导数信息获得不确定性区间内任意角度处的灵敏度。最后运用SIMP模型和优化准则法(OC)对考虑外载荷方向不确定性的连续体结构进行拓扑优化。结果表明,采用该方法得到的优化结果的柔顺度对于载荷方向的变化不敏感,即对于不同方向的外载荷,结构刚度更具稳健性。

Uncertainty of load is a common problem in the engineering field.In this paper,the robust topology optimization of a continuum with uncertain load directions was studied.Firstly,interval variables were used to describe the directional uncertainty.Subsequently,the disturbance in the direction of the nominal load was described by using the rotation matrix,and its sensitivity in any direction was obtained with the second-order Taylor expansion and the first and second derivatives of the compliance with respect to the angle of the nominal load by means A the special property of the derivative of the rotation matrix.Finally,the SIMP model and the optimality criterion method(OC)were used to optimize the topology of the continuum with uncertain load directions.The optimization results obtained by this method showed that the compliances was insensitivity to the change of the load directions that the structural stiffness was more robust to external load in different directions.