COMPUTABLE ESTIMATES OF THE MODELING ERROR RELATED TO KIRCHHOFF–LOVE PLATE MODEL
Sergey Igorevich Repin, Stefan A Sauter · Analysis and Applications · 2010
The Kirchhoff–Love plate model is 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 note, 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 possesses necessary asymptotic properties and, therefore, does not deteriorate as the thickness tends to zero.