基于摄动技术的随机无网格点插值法在结构可靠性分析中的应用

Application of stochastic element-free point interpolation method based on perturbation technique to structural reliability analysis

为有效解决点插值法在随机结构可靠性分析中遇到的系数矩阵奇异性问题及提高解的精度问题,将带有多项式的径向基函数点插值法与随机摄动技术相结合引入到随机结构问题计算中。采用径向基函数耦合多项式基函数构造形函数,其插值函数具有Kronecker Delta函数性质,可以很方便地施加本质边界条件。最后用算例验证了此方法不仅在随机结构可靠性分析中有更高的计算精度而且提高了计算效率。

To effectively solve the coefficient matrix singularity problems and calculation accuracy problem in the field of stochastic structure calculation with point interpolation method,the radial basis function（RBF） with polynomial and stochastic perturbation technique is applied to stochastic structural reliability analysis.Using RBF coupling polynomial primary function,the interpolation function has the properties of Kronecker Delta function,easily exerting the essential boundary conditions.Numerical examples show that this method not only has higher calculation accuracy but also improves the computational efficiency in the stochastic structure field.