Duality preserving discretization of the large time increment methods

The large time increment method is a well established iterative computation al method for time-dependent non-linear structural analyses, which has the peculiarity to produce at each iteration an approximation of the complete s tructural response over the whole considered history of loading. The method establishes a converging iterative sequence by exploiting the specific str ucture of the equations governing the continuum problem. The relatively lar ge body of literature on the subject has been mostly concerned with assessi ng conceptual and practical properties of the method by referring to the co ntinuum 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 pr eserves 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 du ality structure of the continuum problem. A proof of convergence of the ite rative scheme to the solution of the discrete problem is also outlined. (C) 2000 Elsevier Science S.A. All rights reserved.