The Curved Beam Element and Its Convergence Rate

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Article Navigation > Applied Mathematics and Mechanics > 1989 > 10(6): 487-498

Lü He-xiang, Tang Li-min, Liu Xiu-lan. The Curved Beam Element and Its Convergence Rate[J]. Applied Mathematics and Mechanics, 1989, 10(6): 487-498.

Citation:

Lü He-xiang, Tang Li-min, Liu Xiu-lan. The Curved Beam Element and Its Convergence Rate[J]. Applied Mathematics and Mechanics, 1989, 10(6): 487-498.

Citation:

Lü He-xiang, Tang Li-min, Liu Xiu-lan. The Curved Beam Element and Its Convergence Rate[J]. Applied Mathematics and Mechanics, 1989, 10(6): 487-498.

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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