关于C^1类薄板弯曲有限单元的多变量列式方法的探讨

On the Formulative Methodology of C1 Plate-Bending Multi-Variable Elements

本文由修正的Л_R变分原理出发,建立了C^1类薄板弯曲杂交/混合元的一种新列式方法。新法对应的泛函包含域内挠度(W)、域内曲率(К)及边界上的非协调法向转动(φ_λ)三类独立变量,由此还可导致C^1类薄板弯曲杂交应力有限元列式工作中的Л_R和Л_(mc)两类泛函。数值研究表明,采用本文列式法建立的4-节点四边形平板弯曲单元X-1和X-2均不发生“自锁”,所提供的应力解与位移解较已有的同类单元都有所改善。

Basing on the modified Л_R-typed variational principle, a new method is developed for the derivation of C^1 plate-bending elements. Unlike the existing Л_(mc)-based hybrid-stress counter- parts, the present method features three types of independent Variables: the intra-element deflexion W(X), the intra-element curvature K(X), and the non-compatible normal rotation on ele- ments boundary. Among the particularizations, the present vari- ational functional includes the Л_R and Л_(mc) mostly in use for the formulation of hybrid-stress thin plate elements. Numerical stud- ies demonstrate the effectiveness of the present method. Both the 4-node quadrilateral elements X-1 and X-2 presneted in this paper are free from spurious kinematic mode, induciug no shear locking phenomenon, and capable of providing improved stress as well as deflexion results against existing counterparts.