板弯曲元列式的一致位移—杂交应力有限元方法

A Consistent Displacement-Hybrid Stress Scheme for the Formulation of Plate Element

本文基于 Reissner-Mindlin 板弯曲理论,并引用一致场的概念,建立了一个四边形杂交应力板元(CDHP)。数值结果表明,在收敛性方面与LH4(Spilker,1980)极为相似,而对歪斜网格模型的敏感程度大大低于 LH4。根据 MIN4(Tessler,1983)和 CDHP 的数值比较研究可见,企图用完全一致的位移插值来克服“自锁”是不易的,试图用替代应变函数的方法达到这一目的也是无效的。在这方面,本文的方法具有优势,且有直接和简单的特点。

Basing on the Reissner-Mindlin plate-bending theory in conjunc- tion with the consistent field concept,a 4-node quadrilateral hy- brid stress plate element(CDHP)is derived.Numerical investiga- tions demonstrate the remarkable characteristic behaviors of CDHP in its convergence rate versus LH 4(Spilker,1980).Specifically favorable is the significantly low sensitivity of CDHP to distorted mesh patterns compared with that of LH4.Doubts about the fea- sibility of invoking perfectly consistent displacement interpolat ions are indicated via numerically comparative studies on element MIN 4 versus CDHP.The ineffectiveness of the substitutive func- tions for such purposes is also noted.In this aspect,the pre- sent scheme is appealing for its simplicity and straightforwardness in use.