关于厚薄板弯曲分析的内位移杂交元法

THE APPROACH TO HYBRID ELEMENTS WITH INNER DISPLACEMENTS IN BENDING ANALYSIS OF THICK-THIN PLATES

本文通过引入单元内位移和优化处理的单元应力场,以计入剪切变形的板弯曲能量泛函为基础,导出适用于厚、薄板分析的四边形杂交应力元。内力场和内位移的合理选择避免了单元零能模式的出现、避免了解的剪切自锁现象。该优化单元显示了较好的通用性和收敛性。对关于剪切自锁的RCI判据提出了反例、说明了它的局限性。

By employing stress optimization condition of hybrid stress element, a quadrangular hybrid stress element HE3 for bending analysis of thick-thin plates is developed based on the energy functional with shear effect and incompatible displacements. The element is free from Shear Locking and Zero Energy Deformation Modes owing to the rational selection of both shear force field and incompatible displacements. Numerical examples show that HE3 element possesses a good performance for thick-thin plates. It is also pointed out by the paper that Spilker's RCI criterion is not sufficient for the absence of the Shear Locking phenomenon in the bending analysis of thick-thin plate elements.