Duality preserving discretization of the large time increment methods

Abstract

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.