三角形REISSNER-MINDLIN板元
Triangular Elements for Reissuer-Mindlin Plate
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摘要: 本文提出构造无自锁现象的Reissuer-Mindlin板元的一个一般性方法.此方法将剪切应变用它的适当的插值多项式代替,当板厚趋于零时这对应于插值点的Kirchhoff条件,因而单元无自锁现象.根据这种方法我们构造两个三角形元──一个3节点元和一个6节点元,并给出数值结果.
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关键词:
- Reissuer-Mindlin板模型 /
- 自锁现象 /
- 三角形元
Abstract: A general method to construct locking free Reissner-Mindlin plate elements is presented. According to this method the shear strain is replaced by its proper interpolation polynomial, which corresponds to the Kirchhoff conditions at the interpolation points as the thickness of plate tends to zero so the element is locking free. We construct two triangular elements by this method——a 3-node elenent and a 6-node element. The numerical results are provided.-
Key words:
- Reissner-Mindlin plate /
- locking /
- triangular element
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[1] Chen Shaochun, Rectangular Reissner-Mindlin plate elements based on Taylor's formula.Chinese J. Num. Math. & Appl., 16, 1 (1994), 98~106. (中文:计算数学,3 (1993), 373-380). [2] F. Brezzi, K. Bathe and M. Fortin, Mixed-interpolated elements for Reissner-Mindlinplates' Int. J. Aum. Meth. Engn., 28 (1989), 1787~1801. [3] D. N. Arnold and R. S. Falk, A uniformly accurate finite element method for theReissner-Mindlin plate-SIAM J. Num. Anal.. 26. 6 (1989). 1276~1290. [4] D. G. Ciarlet, The finite Element Method for Elliptic Problems, North-Holland (1978). [5] K. J. Bath, Finite Element Procedures in Engineering Analysis, Dentice-Hall. EnglewoodCliffs (1982). [6] S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells. 2nd ed.McGraw-Hill. New York (1959).
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