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A novel twice-interpolation finite element method for solid mechanics problems

ISSN号：0567-7718
期刊名称：《力学学报：英文版》
时间：0
分类：O34[理学—固体力学;理学—力学] O241.82[理学—计算数学;理学—数学]
作者机构：[1]State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, 610065 Chengdu, China, [2]State Key Laboratory of Digital Manufacturing and Equipment Technology, Huazhong University of Science and Technology, 430074 Wuhan, China, [3]Department of Mechanical Engineering,Centre for Advanced, Computations in Engineering Science (ACES),National University of Singapore, Singapore 117576, Singapore
相关基金：The project supported by the National Natural Science Foundation of China （50474053, 50475134 and 50675081） and the 863 project （2007AA042142）.

作者： C. Zheng, S. C. Wu, X. H. Tang, J. H. Zhang

关键词：固体力学, 有限元方法, 插值, GALERKIN, 节点应力, 有限元法, 有限元程序, 数值评价, Twice-interpolation finite element method·Stress smoothing · Volumetric locking · Mesh distortion

中文摘要：

明确的表达和新奇两次插值的数字评估有限元素方法(TFEM ) 为稳固的力学问题被介绍。在这个方法，为 Galerkin 弱形式的试用功能通过连续插值的二个阶段被构造。主要插值跟随女性的标准的一模一样的过程并且是进一步的根据两节的价值复制了并且平均从主要插值获得的节的坡度。因此构造的试用功能有连续节的坡度并且没有增加全部的自由，包含更高的顺序多项式。几个基准例子和一个真实水坝问题被用来以精确性和集中检验 TFEM。与标准相比女性， TFEM 能完成显著地更好的精确性，没有任何变光滑的操作，更高的集中率，和连续节的压力能被获得。TFEM 对元素的网孔的质量感觉迟钝，这也被发现。另外，没有任何修正，现在的 TFEM 能对待不可压缩的材料。关键词两次插值有限元素方法 - 应力变光滑 - 容量的锁住 - 工程由中国(50474053， 50475134 和 50675081 ) 和 863 工程(2007AA042142 ) 的国家自然科学基础支持了的网孔失真。

英文摘要：

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

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