Linked interpolation for Reissner‐Mindlin plate elements: Part I—A simple quadrilateral

In most plate elements using the Reissner‐Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables. Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed). In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.