A four-node, shear-deformable shell element developed via explicit Kirchhoff constraints

An e cient, four-node quadrilateral shell element is formulated using a linear, rst-order shear deformation theory. The bending part of the formulation is constructed from a cross-diagonal assembly of four three- node anisoparametric triangular plate elements, referred to as MIN3. Closed-form constraint equations, which arise from the Kirchho constraints in the thin-plate limit, are derived and used to eliminate the degrees- of-freedom associated with the `internalʹ node of the cross-diagonal assembly. The membrane displacement eld employs an Allman-type, drilling degrees-of-freedom formulation. The result is a displacement-based, fully integrated, four-node quadrilateral element, MIN4T, possessing six degrees-of-freedom at each node. Results for a set of validation plate problems demonstrate that the four-node MIN4T has similar robustness and accuracy characteristics as the original cross-diagonal assembly of MIN3 elements involving ve nodes. The element performs well in both moderately thick and thin regimes, and it is free of shear locking. Shell validation results demonstrate superior performance of MIN4T over MIN3, possibly as a result of its higher- order interpolation of the membrane displacements. It is also noted that the bending formulation of MIN4T is kinematically compatible with the existing anisoparametric elements of the same order of approximation, which include a two-node Timoshenko beam element and a three-node plate element, MIN3.