Solving cylindrical shell problems with a non-standard finite element

Abstract

The subject of this work is the numerical analysis of a special finite element for the numerical solution of Naghdi cylindrical shell problems. Its discretization with standard finite elements suffers from the locking phenomenon, i.e., when small thickness shells are solved, the numerical results are affected by a large error. Several solutions to avoid the numerical locking have been proposed: mixed formulations, reduced and/or selective integration. In this paper we present a finite element based on a non-standard formulation of the discrete approximation of the shell problem. The main feature of the element proposed is the introduction of a linear operator that reduces the influence on the numerical solution of both shear and membrane energy terms. The performance of the new element is tested solving a benchmark problem involving very thin shells and severely distorted decompositions. The results show both properties of convergence and robustness.