基于中心复合实验设计的区间有限元方法

Interval finite element method based on central composite experimental design

区间有限元方法是解决含不确定变量的实际工程问题最为有效的方法之一。对于区间有限元的算法中,区间扩张是其固有问题。区间顶点法能够得到区间线弹性的精确解。然而区间有限元顶点法的计算量大;同时对于实际工程问题,不能确定复杂结构响应在变量区间变化范围内是否为单调的问题。针对上述区间顶点法的两个主要缺点,提出了用中心复合实验设计来降低区间顶点法的计算量,同时检验结构响应函数是否单调,为了区间顶点法的运用提出了理论依据。数值算例表明文中提出方法的有效性以及可行性。

Interval finite element method is one of most effective methods that may solve practical engineering problems involving uncertain variables.Vertex method can obtain the exact solution of interval linear elastic for problems of interval enlarging which is the intrinsic character of interval finite element method.However,because the computation time and cost of vertex method used to solve interval finite element are very high and the monotony of response function for complicated structure can not be decided clearly among the varying range of variable interval for practical engineering problems.In this case,central composite experimental design is proposed to reduce the computation time and cost.Meanwhile the monotony of response function for structure is verified by central composite experimental design,which provides theoretical basis for the application of vertex method.Numerical example demonstrates the effectiveness and feasibility of the presented method.