In this paper, the area coordinate method is generalized to formulate quadrilateral elements. The general theory of area coordinate for quadrilateral elements is presented and new quadrilateral elements for membrane and plate bending are formulated by using the area coordinate method.
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References
1.
MertieJ B. Transformation of trilinear and quadriplanar coordinates to and from Cartesian coordinatesThe American Mineralogist, 1964, 49(7/8): 926–936
2.
EisenbergM A and MalvernL E. On finite element integration in natural coordinates. Int. J. Numer. Methods Eng., 1973, 7(4): 574–575
3.
TaigI C. Structural analysis by the matrix displacement method, Engl. Electric Aviation Report, 1961; S017
4.
IronsB M. Engineering application of numerical integration in stiffness method. J. AIAA, 1966, 14: 2035–2037
5.
HuaC. An inverse transformation for quadrilateral isoparametric elements: Analysis and application. Finite Elements in Analysis and Design, 1990, 7: 159–166
6.
LeeN S and BatheK J. Effects of element distortions on the performance of isoparrametric elements. Int.J.Numer.Methods Eng., 1977, 36: 3553–3576
7.
WeissmanS L and TaylorR L. Resultant fields for mixed plate bending elements. Computer Methods in Applied Mechanics and Engineering, 1990, 79: 321–355
8.
BatozJ L and TaharM B. Evaluation of a new quadrilateral thin plate bending element. Int.J.Numer.Methods Eng., 1982, 18: 1655–1677
9.
SohA KZhifeiLong and SongCen. A Mindlin plate triangular element with improved interpolation based on Timoshenko' s beam theory. Communication in Numerical Methods in Engineering, 1999, 15(7):527–532
10.
BatozJ LTaharM B. Evaluation of a new quadrilateral thin plate bending element. J. Num. Meth. Eng., 1982;18:1655–1677
11.
ZienkiewiczO CXuZZengL FSamuelsonA and WibergN E. Linked interpolation for Ressner-Mindlin plate elements: Part I – A simple quadrilateral. Int. J. Num. Meth. Eng., 1993;36:3043–3056
12.
IbrahimbegovicA. Quadrilateral finite elements for analysis of thick and thin plates. Computer Methods in Applied Mechanics and Engineering, 1993;110:195–209
13.
LongYuqiuLiJuxuanLongZhifei and CenSong. Area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering. 1999, 15(8): 533–545
14.
LongZhifeiLiJuxuanCenSong and LongYuqiu. Some basic formulae for area coordinates used in quadrilateral elements. Communications in Numerical Methods in Engineering. 1999, 15(12): 841–852
