Computable estimates of the modeling error related to Kirchhoff-Love plate model

Abstract

The Kirchhoff-Love plate model is a widely used in the
analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions
can be viewed as certain limits of displacements and stresses for
elastic plates where the thickness tends to zero. In this paper, we consider
the problem from a different point of view and derive computable
upper bounds of the difference between the exact three-dimensional solution
and a solution computed by using the Kirchhoff-Love hypotheses.
This estimate is valid for any value of the thickness parameter.
In combination with a posteriori error estimates for approximation errors,
this estimate allows the direct measurement of both, approximation
and modeling errors, encompassed in a numerical solution of the
Kirchhoff-Love model. We prove that the upper bound possess necessary
asymptotic properties and, therefore, does not deteriorate as the
thickness tends to zero.