An efficient mixed hybrid 4‐node shell element with assumed stresses for membrane, bending and shear parts

A fully mixed hybrid 4‐node shell element for linear analyses is presented and compared to the current state‐of‐the‐art. The specific improvements developed concern the stress assumptions for the transverse shear stresses in the in‐plane directions, such that the element is applicable for arbitrary element geometries without shear locking and satisfies the patch test exactly. Furthermore, in analogy to the membrane and bending part the shear part of the stiffness matrix can be formulated as a one‐point integrated constant part with a rank‐two update representing the linear parts. However, this efficient formulation leads to additional approximations concerning the geometry of arbitrarily curved elements. The latter aspect is discussed with some numerical examples, which demonstrate the capabilities of the developed element.