A family of ANS four‐node exact geometry shell elements in general convected curvilinear coordinates

Abstract

AbstractThe non‐conventional exact geometry shell elements based on the Timoshenko–Mindlin kinematics with five displacement degrees of freedom are proposed. The term ‘exact geometry (EXG)’ reflects the fact that coefficients of the first and second fundamental forms of the reference surface and Christoffel symbols are taken exactly at every Gauss integration point. The choice of only displacements as fundamental shell unknowns gives an opportunity to derive strain–displacement relationships, which are invariant under rigid‐body shell motions in a convected curvilinear coordinate system. This paper presents a newly developed family consisting of three hybrid and one displacement‐based four‐node EXG shell elements. To avoid shear and membrane locking and have no spurious zero energy modes, the ANS concept is employed. The ANS interpolations satisfy exactly the plate compatibility equation for in‐plane strains. As a result, all EXG shell elements developed pass membrane and bending plate patch tests and exhibit a superior performance in the case of distorted coarse mesh configurations. Copyright © 2010 John Wiley & Sons, Ltd.