Towards an adaptive ‘semi-implicit’ solution scheme for nonlinear structural dynamic problems

This paper presents considerations regarding the search for improved computational efficiency in the solution of structural dynamic problems. Beginning with an overview of the procedures traditionally employed for the solution of such problems, it proceeds with a critical survey of ‘hybrid’ time integration schemes, that try to combine the advantages of explicit and implicit algorithms. These schemes include: ‘partitioning’ and ‘operator-splitting’ methods, ‘semi-implicit’ methods, and integration schemes employing element-by-element techniques. Next follow some remarks regarding a natural evolution of this line of research, into the study of iterative solvers for the ‘effective’ linear systems of equations that result from the application of implicit methods. An integration scheme for nonlinear dynamic problems is then proposed, based on an iterative solver and with ‘semi-implicit’ characteristics. Its potential is demonstrated by numerical studies on the finite element model of a guyed tower for offshore oil exploration and production. The following aspects are considered: the solver itself and its preconditioner; the strategy for the definition and variation of convergence tolerance values; the computational implementation (whether global or element-by-element); and the incorporation of this scheme into the adaptive time integration strategy presented in Jacob and Ebecken [ Eur.J. Mech., A / Solids 12,277–298 (1993)], by devising adaptive selection criteria for the identification of applications and situations where a direct or an iterative solver is more adequate.