功能梯度梁的无网格分析

Meshless Analysis of Functionally Graded Beam Bending Problems

根据欧拉梁变形理论的特点,本文利用叠加原理,构造出近似位移解形式,其中,齐次解由直接一维积分得到,而特解部分由径向基函数插值得到,这样构造的解形式很容易施加梁边界条件和处理各种横向荷载,最后的数值计算表明该算法形式简单,计算精度高,而且易于程序实现.

The particular solution related to the transverse load is obtained by RBF （radial basis function） interpolation, and then, the homogeneous solution is derived by the standard one-dimensional integration. As a result, the full solution obtained by the superposition of homogeneous and particular solutions is easy to treat various boundary conditions and transverse load. Finally, numerical results show the proposed method has advantages of simple formula, high accuracy and easy implementation.