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The Finite Element Formulation of Large Increment Method in Material Nonlinear Problems

机译：材料非线性问题中大增量法的有限元表示。

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摘要

In the present paper the finite element formulation of Large Increment Method (LIM) for material nonlinear problems is given. The LIM is a new iteration method, which is based on the force method and the generalized inverse matrix theory for solving material nonlinear problems, so LIM is also called the force method based on Generalized Inverse Matrix (GIM). Unlike the classical force method, LIM does not need to find a basic structure any more, so this method brings the force method a new light in the computer calculation field. LIM doesn't need to solve the material nonlinear problem step by step, as the traditional method based on the displacement method does. The system control equations are divided into a linear group, which includes the equilibrium equation and the compatibility equation, and a nonlinear group, which includes the constitutive equation. The whole iteration procedure can be divided into the global stage and the local stage. With the general finite element formulation, this new method can not only solve the problems of truss system, but also the multi-dimensional problems. As the mathematical background of LIM, the generalized inverse matrix theory is also introduced. Besides, there are very strong parallel-calculating characteristics in LIM, which are different with the traditional sub-structural algorithm. Finally, an example of plane stress problem is given, which shows the efficiency and generality of this new method.
机译：本文给出了材料非线性问题的大增量法（LIM）的有限元公式。 LIM是一种新的迭代方法，它是基于力方法和广义逆矩阵理论来解决材料非线性问题的，因此LIM也称为基于广义逆矩阵（GIM）的力方法。与传统的力方法不同，LIM不再需要查找基本结构，因此该方法在计算机计算领域为力方法带来了新的亮点。 LIM不需要逐步解决材料非线性问题，就像基于位移方法的传统方法一样。系统控制方程分为线性组和非线性组，线性组包括平衡方程和相容性方程，非线性组包括本构方程。整个迭代过程可以分为全局阶段和局部阶段。使用通用的有限元公式，这种新方法不仅可以解决桁架系统的问题，而且可以解决多维问题。作为LIM的数学背景，还介绍了广义逆矩阵理论。此外，LIM具有非常强的并行计算特性，这与传统的子结构算法不同。最后，给出了一个平面应力问题的例子，说明了这种新方法的有效性和普遍性。

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