A 14-node brick element, PN5X1, for plates and shells

We use the Papcovitch–Neuber (PN) solution to the Navier equation and develop a new 14-node brick element PN5X1, to represent linear stress fields exactly. We perform patch tests, to assess its ability to converge in plate and shell problems. We also test the new element in rectangular and circular plates with simply supported and clamped edges and subject them to point and uniformly distributed loads. We also use it in locking tests and in low-energy deformation mode tests of rectangular plates. PN5X1 passes the patch tests and predicts, in the limit of discretization, theoretical values in almost all the plate and shell problems.