关于计入剪切效应的板弯曲杂交模式的若干问题

本文从Reissner变分原理出发,构造一计入剪切效应的9自由度板弯曲杂交元。通过离散型Kirchhoff约束的实施,把厚板公式直接推广于薄板计算而不出现解的“闭锁”现象。文中提出的能量调整原理有效地解决了厚板元素中的弯、剪匹配问题,从而实现了厚薄板分析的统一性。文章最后给出计算实例。

SOME PROBLEMS OF PLATE BENDING HYBRID MODEL WITH SHEAR EFFECT

A triangular plate bending hybrid element is constructed according to Reis-ner's principle. It has 9 degrees of freedom and takes, the shear effect into account. The C0 formulation of the thick plate is extended to the thin plate and the"shear locking"phenomenon can be avoided through imposing the discrete type of Kirchhoff's constraints. It is interesting to note that the kind of discrete constraints can be directly imposed by means of Hermite interpolation. This is one of the features which distinguish the paper from ref. 5 ]and 1 ]. On the other hand, the specific matching between bending and shearing is discussed in the analysis of the thick plate. It is shown that the reasonable matching between bending and shearing complementary energies may be destroyed by inhomogeneous magnification of the discretization errors. Furthermore, a principle of energy regulation is put forward, with the aid of which this matching problem is effectively treated so that the unified analysis of the thick and thin plates is achieved. Finally, numerical examples are given.