Some variational formulations for continuum nonlinear dynamics

A modification of a theory developed by Tonti (1984) for obtaining extremal formulations of a generic nonlinear problem is applied to derive several variational formulations for the nonlinear continuum dynamic problem with prescribed initial conditions. Such a problem does not admit "classical" variational statements, owing to its lack of symmetry with respect to "classical" bilinear forms. However, Tonti's theory, with some developments introduced first by Carini, and then in this work, allows the systematic derivation of variational statements which may prove helpful both in understanding theoretical aspects and in devising numerical integration schemes. (C) 1998 Elsevier Science Ltd. All rights reserved.