An accurate low order plate bending element with thickness change and enhanced strains

A three-dimensional variational formulation is used to obtain a plate bending element which includes the thickness change of the plate. The nodal degrees of freedom for the four-node element are the deflection w, the rotations θ_x and θ_y, and the thickness change H. Bilinear functions of the in-plane coordinates ξ and η are used for the approximation of the deflection, the rotations and the thickness change. Integration in thickness direction is performed analytically. One key feature of the element is that the three-dimensional constitutive equations for the six stresses have not to be modified. Using eight enhanced strain terms, a well performing plate bending element is obtained.