A 14-node brick element, PN5X1, exactly representing linear stress fields

We consider Papcovitch–Neuber (PN) solution to the Navier equation, comprising only the vector potential, and develop a new displacement-based 14-node brick element. We assume PN solution in polynomial form. We impose constraints on unknown coefficients of the polynomials such that the element correctly represents linear stress fields. To validate the performance of the new element which we call PN5X1, we conduct several pathological tests available in the literature. PN5X1 predicts, as anticipated, both stresses and displacements accurately at every point inside the elastic continuum for linear stress fields.