Can a discrete dynamic model ever perfectly simulate a continuum?

摘要

This article elaborates on the seemingly impossible notion that a continuous elastic body subjected to dynamic sources on its outer surface could ever be substituted in all of its essential qualities by a discrete model accomplished with finite elements. This topic is taken up herein and discussed in the context of a very simple two-dimensional model involving the propagation of SH shear waves (or acoustic waves) in a homogeneous elastic half-space. It is shown that there exists at least one discrete solid, referred to here as the Guddati Solid, which from its external surface behaves exactly like the continuum and is able to transmit waves of any frequency and any wavelength. This is a rather surprising finding in that it seems to contradict some well-known elastodynamic representation theorems, not to mention falsify the widespread belief that a discrete system can never behave like the continuum it purports to model. The purpose of this article is thus to present one example which disproves this widely believed postulate.