桁架结构材料非线性弹性问题的广义逆力法

通过回顾传统位移法和传统力法的思路,比较了两种传统方法,分别指出了它们在计算机求解材料非线性问题中的优缺点。从经典力法的求解思路出发介绍了用于桁架结构材料非线性弹性问题的广义逆力法(AforcemethodbasedonGeneralizedInverseMatrix,GIM),给出了该算法的推导思路及求解过程。特别指出了传统力法用计算机求解材料非线性问题所遇到的困难,对如何解决这些困难作了探讨,从而给出了结构力学计算的一个全新视角,也使得力法在计算机计算领域重新得到发展空间。广义逆力法是一种基于力法和广义逆矩阵理论的新的迭代解法,对于材料非线性问题,由于无需像传统的基于位移法的逐步增量法那样逐步递进计算,所以也称特大增量步算法(LargeIncrementMethod,LIM)。同时也指出了该算法在结构并行计算方面不同于传统的子结构并行计算的新的特点。做为一种新的迭代算法,也给出了该算法求解的唯一性和收敛性证明。

THE LARGE INCREMENT METHOD FOR NONLINEAR ELASTIC PROBLEMS OF TRUSS SYSTEMS

A comparison of the classical displacement method with the classical force method is made. The classical algorithm of material nonlinearity problems, i.e. the step by step process based on the displacement method, is discussed and the unavoidable disadvantages of the step by step process are highlighted. A new method, called Large Increment Method (LIM), is introduced. It is based on the force method and the generalized inverse matrix (GIM) theory for material nonlinearity problems. Unlike the classical force method, the large increment method does not need primary structure any more, so this method imparts new life to the force method in computational mechanics field. The large increment method is different from the Large Time Increment Method (LATIN) presented by Ladeveze of University of Paris. GIM has some natural parallel-calculating characteristics which are different from the classical substructural algorithm. Some difficulties when applying the new method are overcome. The solution uniqueness and convergence of the method are proved. Only nonlinear elastic problem of truss systems is considered in this paper.