在三维结构分析问题中合适的离散-连续有限元法

摘要

This paper is devoted to discrete-continual finite element method of structural analysis (DCFEM).Operational and variational formulations are presented.The discrete-continual design model for structures with constant physical and geometrical parameters in one direction is offered on the basis of so-called discrete-continual finite elements.Element coordinate system,approximation of nodal unknowns,construction of element nodal load vector are under consideration.Element system of differential equations is formulated with the use of special generalized block-structured stiffness matrix of discrete-continual finite element.Local differential relations are formulated.Resultant multipoint boundary problem for system of ordinary differential equations is given.Method of analytical solution of multipoint boundary problems in structural analysis is offered as well.Its major peculiarities include universality,computer-oriented algorithm involving theory of distributions,computational stability,optimal conditionality of resultant systems,partial Jordan decomposition of matrix of coefficients,elimination of the necessity of calculation of root vectors.Special iterative method of analysis of structures with unilateral constraints within DCFEM is presented.%对结构分析中的离散-连续有限元法(DCFEM)进行了研究.给出了该方法的运算及变分公式.对于在一个方向物理及几何参数为常量的结构,其离散一连续设计模型是建立在所谓的离散一连续有限元的基础上的.研究了单元坐标的建立、结点未知量的近似表达及单元结点荷载矢量的建立问题.单元的微分方程组是借助于离散一连续有限元特殊广义的块结构刚度矩阵来建立的.建立了局部坐标中的微分关系,形成了常微分方程组多点边值问题的提法,也给出了结构分析中多点边值问题的解析方法.这一方法的主要特点包括其普适性、算法的计算机适应性、计算的稳定性、最终方程组的条件优化特性、系数矩阵的部分Jordan分解特性、计算根矢量必要性的解除.给出了在离散-连续有限元法框架内具有单向约束的结构分析中特殊的迭代法.