样条状态变量法分析扁球壳的动力响应

基于瞬时变分原理与样条函数理论,建立扁球壳的动力方程,引入样条参数及其对时间的导数作为状态变量,导出状态方程,对空间域,采用样条有限元法,对时间域,采用现代控制论中的状态空间法,此外,建立了一种状态变量的递推计算格式,在计算过程中,不解线性方程组,也不需采用解耦技术,只要作矩阵运算,可直接算出动力响应量,文末给出的数值算例表明本文方法是可靠 与有效的。

Dynamic response analysis spherical shells by spline state variable method

Based on instantaneous potential energy principle and spline interpolate function, the dynamic equation of flat spherical shell is derived. The spline parameters and their derivatives are taken as state variables, the state equation is established. The spline finite element is used for space domain and the state space method is used for time domain respectively. In addition, a state variable recursive scheme is developed. The main advantages of the present method are that one is not necessary to solve linear equations, second is not to be applied to the technique of uncoupling and reduced order and only the matrix operations are required. Some numerical results are presented to demonstrate the effectiveness and reliability of present method.