基于状态空间理论的多变量样条元法

THE MULTIVARIABLE SPLINE ELEMENT METHOD BASED ON STATE SPACE THEORY

本文提出一种基于状态空间理论的多变量样条元法。文中根据弹性理论的控制方程和二类变量广义变分原理导出状态方程．应用基样条函数构造二类场变量函数，建立了以样条结点参数为未知量的状态方程组，由现代控制论中的状态空间法来求解．文中给出平面应力问题的数值算例，计算结果表明，与材料力学方法十分接近．本文方法计算量小、精度好、效率高。

his peper prements a multivartable spline element method based on state spacetheory.According to controlled equations of elaSticity and the generalized variational principlewith two kinds of variables, the state space equations are derived. The field function of the displacements and foral are consthected by using the the sPline functions.The state space eguationsof spline node parameters as unhnowns are established and solved by using the state space methodin control theory. A numerical example of plsne stress problem is given, and the results are compared with strength of materials, which shows good agreement. The method in the paper needsless computstions, but has biter efficency and accuracy, and it can be extended to plates andchens.