采用复合样条有限元方法求解板的动力初值问题

结构动力分析是工程设计中的重要组成部分，传统结构动力分析不能全面反映结构动力的初值特征，而Gurtin变分原理被认为是目前唯一能全面反映结构动力初值特征的变分原理。本文应用以位移为参变量的Gurtin变分原理，采用复合样条有限元的方法，即在时间域及空间域的y方向采用三次B样条函数，而在空间域的x方向采用多项式逼近广义位移，从而建立了精度较高的计算板动力初值问题的样条有限元模型。数值计算结果表明，本文所建立的方法能有效地求解板的动力初值问题，且计算精度高。

Solving dynamic initial value problem of plate by using composite spline finite element method

In this paper,based on Gurtin variation principle,a spline finite element method for the initial value problem of plate is presented by using a cubic B spline function in the time domain and in the y direction of space domain,and a polynomial function in the x direction of space domain. The numerical calculations show that higher accuracy can be obtained by using the proposed method for dynamic responses.