Eight-node brick, PN340, represents constant stress fields exactly

We develop a new eight-node brick element, PN340, whose interpolation funct ions exactly satisfy the Navier equation. We begin with the Papcovitch-Neub er solutions in polynomial form, to the Navier equation and consider all th e terms necessary to represent cubic displacement fields. We derive constra ints on the unknown polynomial coefficients to make the eight-node brick el ement represent exactly every constant stress field. We provide explanation s for the occurrence of kinematic modes. Based on this understanding, we de velop a systematic procedure to identify the maximum independent degrees of freedom which the cubic displacement field will have while satisfying the Navier equation. Kinematic modes will never occur if the newly identified d of are used. The newly developed element PN340, based on our present proced ure, predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher or der stress fields the element is assured to converge in the limit of discre tisation. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.