A REDUCED CONSTRAINT hp FINITE ELEMENT METHOD FOR SHELL PROBLEMS

Abstract. We propose and analyze an hp finite element method for the Nagdhi shell model, based on rectangular elements. We show that for the bending-dominated case, assuming sufficient smoothness on the solution, the method is locking free in terms of both h and p, as the thickness of the shell tends to zero. Our results are established under the assumption that the geometrical coefficients appearing in the model are piecewise polynomial functions. 1