广义节点无网格法基本原理及其应用  

Fundamentals and application of generalized-node-based meshfree method

作　　者：叶祥记[1] 栾茂田[1] 黎勇[1] 杨庆[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室

出　　处：《大连理工大学学报》2007年第5期712-717,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(10172022);教育部跨世纪优秀人才培养计划研究基金资助项目(教技函[1998]2号)

摘　　要：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.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.

关 键 词：无网格法 广义节点 广义节点无网格法 

分 类 号：TU311.4[建筑科学—结构工程]