A priori modeling error estimates of hierarchical models for elasticity problems for plate- and shell-like structures

Abstract

Here a hierarchical model for thin elastic bodies is presented in which the variations of the displacement field through the thickness can be represented as a sequence of apolynomials. An a priori hierarchical modeling error estimate is derived and it is found that the modeling error decreases monotonically as the order of the thickness-polynomials increases and has a uniform convergence rate with respect to the thickness. Numerical results are given illustrating the theoretical results.