具有转角自由度的曲面矩形扁壳元

Curved rectangular shallow shell element with 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。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,利用广义协调矩形膜元的位移函数作为扁壳面的切向位移,构造了一个具有转角自由度的4结点广义协调曲面矩形扁壳元。并通过实例分析对该单元的收敛性和精度进行了验证,数值算例的结果表明,该单元收敛稳定迅速,用较少的自由度就获得了很高的精度,是一个性能良好的壳单元。

The introduction of rotation degrees of freedom in the shallow shell element can increase the displacement field, improve the calculation accuracy, thus significantly improve the performance of the elements in the circumstance of no additional nodes. In this paper a four node generalized conforming curved rectangular shell element with rotational degrees of freedom is presented in the derivation of the stiffness matrix of the shell element, in the displacement functions of the generalized conforming plate bending element RGC - 12 and in the membrane element with vertex rigid rotational freedoms. The result of the numerical analysis indicates that this element is a good performance shell element, because of its steady rapid eonstringeney and upper precision with fewer degrees of freedom.