Assessment of dynamic response FD algorithms by beam and plate FE computations

Abstract

Improvement in understanding of the process of direct integration of the equations of motion through numerical dissipation parameter interaction is being regarded as one of the significant achievements of structural dynamics research over the past quarter century. The numerical software fraternity has extended one-step integration algorithms, emphasizing controllable approximation characteristics with respect to such factors as period elongation and amplitude decay. These studies have resulted in setting up a class of implicit, second order finite difference (FD) generic models which are unconditionally stable depending on the range of influence of the corporate parameters.

The aim of this paper is to review some of the strategems incorporating the dissipation control, and to provide representative numerical findings in beam and plate applications through a unification algorithm, which streamlines the intervention of alpha modifiers to Newmark's integration formalism by evoking a set of recurrence relations that serves to pool accessible and amendable dissipation parameters. Experience has shown that the beam and plate finite element (FE) response calculations provide considerable impetus to use Bossak's type integrator with large values of the dissipative parameter.