Triangular Plate Bending Elements with Enforced Compatibility

A technique for establishing complete normal slope compatibility at the interfaces of triangular plate bending elements is presented. The nodal connections result in a deficiency of one parameter per common boundary for providing automatic conformity. Each deficiency is compensated by a constraint, imposed by the Lagrange multiplier method, which forces compatibility at the midside. The element displacement is described by a complete cubic interpolation polynomial. Nodal freedoms are the displacement tv, slopes wX9 Wy at each corner and w at the centroid. Derivation of the stiffness and other matrices required for the basic element is straightforward. Results presented, including deflections, critical loads and vibration frequencies are in general more accurate than from other available elements of equivalent complexity.