Finite Elements for Initial Value Problems in Dynamics

Abstract

Abstract : The work of C. D. Bailey amply demonstrates that a variational principle is not a necessary prerequisite for the formulation of variational approximations to initial value problems in dynamics. While Bailey successfully applies global power series approximations to Hamilton's Law of Varying Action, the work herein shows that a straightforward extension to finite element formulations fails to produce a convergent sequence of solutions. The source of the difficulties and their elimination are discussed in some detail and a workable formulation for initial value problems is obtained. The report concludes with a few elementary examples showing the utility of finite elements in the time domain.