A hybrid‐mixed four‐node quadrilateral plate element based on sampling surfaces method for 3D stress analysis

Abstract

SummaryThe hybrid‐mixed assumed natural strain four‐node quadrilateral element using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the plate body N not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree N–1 in the thickness direction permits the presentation of the plate formulation in a very compact form. The SaS are located at Chebyshev polynomial nodes that allow one to minimize uniformly the error due to the Lagrange interpolation. To avoid shear locking and have no spurious zero energy modes, the assumed natural strain concept is employed. The developed hybrid‐mixed four‐node quadrilateral plate element passes patch tests and exhibits a superior performance in the case of coarse distorted mesh configurations. It can be useful for the 3D stress analysis of thin and thick plates because the SaS formulation gives the possibility to obtain solutions with a prescribed accuracy, which asymptotically approach the 3D exact solutions of elasticity as the number of SaS tends to infinity. Copyright © 2016 John Wiley & Sons, Ltd.