摘要
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。
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.
出处
《计算力学学报》
CAS
CSCD
北大核心
2001年第2期205-209,共5页
Chinese Journal of Computational Mechanics
基金
安徽省教委自然科学基金资助
关键词
样条函数
状态变量
动力响应
瞬时变分原理
扁球壳
建筑结构
spline function
state variable
dynamic response
instantaneous variational principle
flat spherical shell
