应用Pian-Sumihara杂交列式的板弯曲模拟元

把典型的平面弹性杂交应力元-Pian-Sumihara 元-转化为板弯曲单元,从而初步探讨了将平面弹性杂交元转化为板弯曲单元的方法。应用板弯曲多类变量变分原理和弯矩函数空间中的Pian-Sumihara 列式,再通过基于平面弹性-板弯曲相似性的单元转化过程,得到一个四节点八自由度板弯曲位移元。该单元为显式单元,计算量少。数值结果表明该单元能通过常曲率分片试验,收敛稳定并具有较好的精度。

A PLATE BENDING ELEMENT AS THE COUNTERPART OF PIAN-SUMIHARA HYBRID ELEMENT

The transformation of the typical hybrid stress element of plane elasticity, Pian-Sumihara element, into a plate bending element is studied. First, a direct counterpart of Pian-Sumihara element is constructed using both the pro-variational principle of plate bending and the Pian-Sumihara formulation in stress function space. Secondly, the direct counterpart with stress function as nodal variables is transformed into a plate bending element with deflection and rotation as unknown discrete variables. The plate bending element, with four nodes and eight-DOF (degree of freedom), has explicit formulation and consequently high efficiency in computation. Numerical results of typical problems show that it passes the constant curvature patch test and possesses stable convergence and high accuracy.