A Variational Framework for Solution Method Developments in Structural Mechanics

Abstract

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variation-ally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.