曲梁单元和它的收敛率*
The Curved Beam Element and Its Convergence Rate
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摘要: 本文给出了拟协调曲梁和扁曲梁单元.数值结果表明,用于近似曲梁的拟协调曲梁和扁曲梁单元较直梁单元具有更好的精度.由位移法构造的曲梁单元不能够满足刚体位移条件,为了近似地满足刚体位移条件必须用很多的单元.本文证明了直梁单元、拟协调曲梁和扁曲梁单元,当单元尺寸无限缩小时,具有相同的收敛速度O(l2),当使用均匀网格时,其中l是单元的长度.Abstract: The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam clement. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approxtmately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l2) and when regular elements are used. l is the element length.
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[1] Cook,R.D.and Feng Zhao-hua,Deflection and buckling of ring with straight and curved finite elements,Computers and Structures,15,6(1982).647-651. [2] Tang,Li-min,Lü He-xiang,Chen Wan-ji and Liu Ying-xi,Quasi-conforming element technique for the finite element method.Numerical Method for Engineering,G.A.M.N.1. 2 2nd International Congress DUNOD(1980),565-572. [3] 吕和祥,拟协调元的某些问题和在拱结构中的应用,固体力学学报,4 (1981),11. [4] 吕和祥、刘迎曦,有限元法中的拟协调元和在双曲壳单元上的应用,大连工学院学报,20,1 (1981),3. [5] Timoshenko.S.,Theory of Plates and Shells,second edition.McGraw-Hill Book Company,Inc.(1959),513. [6] Cook,R,D.,Concepts and Application of Finite Element Analysis,John Wiley & Sons,Inc.(1974). -
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