Gurtin变分原理在矩形板动力初值问题中的应用

结构动力分析是工程设计中的重要组成部分，传统动力分析方法并不能全面反映动力初值特征，而Ｇｕｒｔｉｎ变分原理则被认为是目前唯一能全面反映动力初值特征的变分原理。本文基于位移型Ｇｕｒｔｉｎ变分原理，对空间和时间同时离散，建立了一种求解板的动力初值问题的时空有限元法，并对两种边界情况板的振动问题进行了编程计算，计算结果表明时空元法精确度很高且稳定收敛。

Application of Gurtin-type Variational Principle in Dynamic Initial-value Problems of Rectangular Plate

Structural dynamic analysis is an important part in engineering. But the traditional dynamic analysis method cannot consider all initial condition in computing. It is believed that Gurtin-type variational principle is the only variational principle which can take into account the initial displacement and velocity by now. In this paper, based on Gurtin-type variational principle of displacement, a new method called the "time-space method" is developed to solve plate-bending dynamic response problems. In this method, finite element discretizations in both space and time are considered. Two examples with different boundary condition and load are programmed and computed. The numerical results show that this method has higher accuracy and better stability and convergence.