Gurtin变分原理及其应用的时间有限元法

动力学Ｇｕｒｔｉｎ变分原理完整地表征了动力学的全部特征。由于在Ｇｕｒｔｉｎ变分原理的泛函中含有双重卷积，给时间域的离散带来很大困难。本文通过在Ｌａｐｌａｃｅ空间构造泛函，获得了几个具有单重卷积的Ｇｕｒｔｉｎ原理。由于卷积降阶，所给出的泛函更加便于应用。本文还通过在时间域采用适当的插值多项式逼近广义节点坐标，进一步讨论了时间有限元法实施的基本原理和步骤。

GURTIN VARIATIONAL PRINCIPLES AND FINITE TIME ELEMENT METHODS FOR DYNAMIC ANALYSIS

It is known that Gurtin variational principles present completely the total characteristics of dynamics. But it is very difficult to develop finite element model by use of Gurtin variational principles because of the two-order convolution in Gurtin functionals. In this paper, several simplified Gurtin variational principles have been derived by use of the convolution theory and functionals in Laplace space. Comparing with existing variational principles of Gurtin type, the derived functionals in this paper are convenient for applications. Further more, the authors take up appropriate polynomials in the time domain to approach the values of the generalized nodal coordinates and give a discussion about the fundamental theory and working steps to realize the Finite Time Element Methods.