Derivation of Thin Plate Bending Elements With One Degree of Freedom Per Node: A Simple Three Node Triangle

A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C 0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.