广义节点无网格法基本原理及其应用

借鉴流形方法思想,引入广义节点的概念,对传统的无网格法进行了改进,建立了可具有任意高阶多项式插值函数的广义节点无网格方法,在阐述这种方法基本原理的同时,针对线弹性力学问题给出了其计算列式.与传统无网格方法相比,这种方法更具有一般性,当选取0阶广义节点位移插值函数时便可得到传统的无网格法;可以通过提高广义节点位移插值函数的阶数降低完备基函数的次数,从而可减少支持域内节点的数目并保证计算精度.最后通过一端承受剪力悬臂梁和中间开口无穷板算例分析,论证了这种方法的合理性.

Fundamentals and application of generalized-node-based meshfree method

A new type of meshfree method is developed by incorporating the generalized node which originated from manifold method with the conventional meshfree method. The proposed method is termed as the generalized-node-based meshfree method.The fundamental theory together with numerical formulations is presented.When the zero-order displacement interpolation function of the generalized node is chosen,the proposed method will be reduced to the conventional meshfree method.And if higher-order displacement interpolation function is utilized,the highest order of complete basis functions can be reduced.Nevertheless,it does not affect the computational accuracy.As numerical examples,a cantilever beam under end shear and an infinite plate with a hole are respectively analyzed by the proposed method and it is shown that the numerical results computed are in good agreement with the theoretical solutions.