基于五次Hermite插值的时间有限元全域算法求解结构动力响应

A New Universal Time Finite Element Method for Dynamic Response Based on Five-order Her mite Interpolation

提出了一种时间有限元全域算法来计算结构动力响应。基于五次Hermite插值,采用加权残值伽辽金法在时间域离散构造了求解结构动力学2阶线性微分方程组的全域时间有限元算法。该方法稳定性好、正确性和可靠性高,无需复杂中间计算过程。此外,该方法的一个重要特点是建立在整个时间域上来求解结构动力响应,严格按照有限元的基本思想,是真正意义上的时间有限元法。利用本法求解了2个典型的算例,计算结果表明本方法的结果是可靠和精确的。

Based on five-order Hermite interpolation and Galerkin weighted residual method,a new universal time finite element method was proposed to obtain structural dynamic response.This method was characterized as a highly stable,accurate,reliable and no need of complicated middle computational procedure.Besides,the method was a real time finite element method,which acquired structural dynamic response in all time domains according to the basic rules of finite element method.The satisfactory results of two typical examples validated the accuracy and reliability of the method.