含面内转动自由度的广义协调曲面矩形扁壳元

Generalized conforming curved rectangular shallow shell element with in-plane rotational degrees of freedom

扁壳单元中引入结点转角自由度可以在不增加结点的情况下,增加位移场的阶次,提高计算精度,从而显著地提高单元性能。同时在单元中引入泡状位移场,能有效地扩大了单元位移场的解空间,所构造的单元具有计算精度高、对计算网格畸变不敏感的优良特性。本文利用广义协调薄板单元RGC-12的位移函数作为扁壳元的法向位移,利广义协调矩形膜元的位移函数作为扁壳面的切向位移,通过附加面内转动自由度构造了一个具有24个自由度的4结点广义协调曲面矩形扁壳元GRC-S24。在此基础上再增加一个广义泡状位移,又构造了一个具有更高计算精度的曲面矩形扁壳元GRC-S24M。并通过实例分析对这两个单元的收敛性和精度进行了验证。

The introduction of rotation degrees of freedom in the shallow shell element can increase the order of the interpolation functions for displacement field, improve the calculation accuracy, and thus significantly improve the performance of element without introducing additional nodes. Since generalized displacement field is introduced into the element, the scope of solution is extended significantly. The present element demonstrates attractive merits, such as high precision and less sensitivity to geometric distortion. In this paper a generalized conforming curved rectangular shell element GRC-S24 with twen- ty-four degrees of freedom is presented through adding in-plane rotational degrees of freedom. In the derivation of the stiffness matrix of the shell element, the displacement functions of the generalized con- forming plate bending element RGC-12 and that of the membrane element with vertex rigid rotational freedoms - were used to describe the normal and the tangential displacement,respectively. Furthermore add a generalized bubble displacement on that base, and then construct another generalized conforming curved rectangular shell element GRC-S24M which with higher precise. Numerical analysis was conduc- ted to validate the accuracy and convergence of these two elements.