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Duality preserving discretization of the large time increment methods

机译：大时间增量方法的对偶保留离散化

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The large time increment method is a well established iterative computational method for time-dependent non-linear structural analyses, which has the peculiarity to produce at each iteration an approximation of the complete structural response over the whole considered history of loading. The method establishes a converging iterative sequence by exploiting the specific structure of the equations governing the continuum problem. The relatively large body of literature on the subject has been mostly concerned with assessing conceptual and practical properties of the method by referring to the continuum problem. So far, computer implementations where based on heuristic considerations and standard finite element technology. In the present paper a different approach is followed: a space and time discretization which preserves the duality structure of the continuum problem is introduced first, then the method is reformulated for the discrete problem. It is shown how the so-called 'generalized variable' modelling preserves the fundamental duality structure of the continuum problem. A proof of convergence of the iterative scheme to the solution of the discrete problem is also outlined.
机译：大的时间增量法是用于时间依赖的非线性结构分析的一种完善的迭代计算方法，它具有在每次迭代过程中生成整个结构响应（在整个考虑的载荷历史上）的近似值的特性。该方法通过利用控制连续性问题的方程式的特定结构来建立收敛的迭代序列。关于该主题的相对大量的文献主要涉及通过参考连续性问题来评估该方法的概念和实用特性。到目前为止，基于启发式考虑和标准有限元技术的计算机实现。本文采用一种不同的方法：首先介绍保留连续性问题对偶结构的时空离散化方法，然后针对离散问题重新构造该方法。它显示了所谓的“广义变量”建模如何保留连续性问题的基本对偶结构。还概述了迭代方案对离散问题的解的收敛性证明。

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