具有附加内转动变量的四边形杂交/混合板元

A Hybrid/Mixed Quadrilateral Element with Additional Internal Rotary Variables for Plate Bending Analysis

本文根据Reissner-Mindlin平板弯曲理论,引用内部转动变量建立了势能-杂交/混合型泛函,并在此基础上推导了四节点四边形平板弯曲单元MP4a。数值研究表明,MP4a不含多余机动模式,对于歪斜网格的敏感性较低,不致引起“自锁”,其挠度以及力矩的收敛性较已有的同型单元皆有改进。本文建立的泛函,可以导致C^1类平板弯曲杂交应力有限元列式工作中的两类泛函。本文建立的势能-杂交/混合有限元联合模式,其特倒包括李胜元—卞学鐄(1978)的势能有限元格式,Prathap(1983)的“一致应变场”列式以及采用减缩积分/选择减缩积分的位移协调模型。

Basing on Reissner-Mindlin plate bending theory, a potential hybrid/mixed type variational functional is developed with the inclusion of independently assumed incompatible rotations in addition to compatible deflexions and rotations, In application, 4-node quadrilateral C° plate bending elements are emphasized. Numerical studies on one such element MP4a demonstrate remarkable behaviour in convergence regarding deflexion and moment responses, and in low sensitiveness to distorted mesh situations. Especially, MP4a exhibits no 'locking' phenomenon in thin plate limits and introduces no spurious kinematic mode. Special cases of the present functional includable are: Lee-Plan's potential mixed finite element scheme, the'consistent strain field' formulation by Prathap, and the RIT/SRIT displacement model.