期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 103, 期 7, 页码 469-500出版社
WILEY-BLACKWELL
DOI: 10.1002/nme.4899
关键词
finite element; 4-node plane membrane element; unsymmetric formulation; analytical trial function; the second form of quadrilateral area coordinates (QACM-II); MacNeal's theorem
资金
- National Natural Science Foundation of China [11272181]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20120002110080]
- Tsinghua University Initiative Scientific Research Program
Among numerous finite element techniques, few models can perfectly (without any numerical problems) break through MacNeal's theorem: any 4-node, 8-DOF membrane element will either lock in in-plane bending or fail to pass a C-0 patch test when the element's shape is an isosceles trapezoid. In this paper, a 4-node plane quadrilateral membrane element is developed following the unsymmetric formulation concept, which means two different sets of interpolation functions for displacement fields are simultaneously used. The first set employs the shape functions of the traditional 4-node bilinear isoparametric element, while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method, in which the Cartesian coordinates (x,y) and the second form of quadrilateral area coordinates (QACM-II) (S,T) are applied together. The resulting element US-ATFQ4 exhibits amazing performance in rigorous numerical tests. It is insensitive to various serious mesh distortions, free of trapezoidal locking, and can satisfy both the classical first-order patch test and the second-order patch test for pure bending. Furthermore, because of usage of the second form of quadrilateral area coordinates (QACM-II), the new element provides the invariance for the coordinate rotation. It seems that the behaviors of the present model are beyond the well-known contradiction defined by MacNeal's theorem. Copyright (c) 2015 John Wiley & Sons, Ltd.
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