The Korn's type inequality in subspaces and thin elastic structures

Abstract

We present the concept of the Korn's type inequality in subspaces generalized to embrace thin elastic structures of various kinds such as shells, plates, rods, arches and beams of arbitrary geometries which are viewed and analysed as three-dimensional solids. We show that based on this inequality we can eliminate the deterioration of the convergence from which iterative algorithms are known to suffer when applied to thin elastic structures. As a paradigm we consider a class of iterative algorithms and show that a simple modification based on the Korn's type inequality in subspaces yields a radical improvement of their convergence.