强非线性梁求解的径向基函数方法

Radial Basis Functions Methods for Strongly Nonlinear Beam

针对强非线性梁提出了一种径向基函数逼近思想结合加权余量配点的求解方法;为减小数值震荡,针对不同问题的边值条件,提出了对应的径向基函数插值表达式,且采用适当的紧支撑正定径向基函数,可获得较好的求解效果。实际算例表明:方法计算精度高,可以达到修正小波伽辽金法、保辛-保能的数值积分法的计算效果;由于配点法相比积分法的计算过程更为简单,方法为强非线性梁的求解提出了一种新途径。

The idea of Radial Basis Functions （RBFs） approximation and the method of weighted residual collocation were combined to solve strongly nonlinear beams. And for different boundary conditions problems, the corresponding RBFs interpolation functions were proposed to decrease the numerical oscillation. By using proper compactness positive definite RBFs, a better solution could be obtained. The actual examples demonstrate that the proposed method has high calculation accuracy that the modified wavelet Galerkin method and the numerical integration algorithm of the sympleetie conservative and energy preserving method can achieve. Therefore, the proposed method provides a new way to solve the strongly nonlinear beam because of the simpler calculation process of collocation method than integration method.