A solution to the C¹ continuity problem in plate bending

A family of high‐order, conforming triangles for the finite element analysis of plate bending problems is developed, using the displacement method of formulation. The development proceeds in two steps. A family of non‐conforming triangles, based on polynomial expansions of order >4 is first generated, and its performance found to be unacceptable. Nodal variables for the non‐conforming family are selected from the set w , w x , w y , w n . The elements are then made to conform, by adding a twist nodal variable w nt at the mid‐side nodes. Rational functions define the three additional degrees‐of‐freedom. Simple and very accurate procedures solve the problems associated with the use of such functions. Numerical results are presented for the conforming triangles of order 4 and 7, following a brief description of the two elements. A listing of the explicit shape functions for the quartic triangle is included. The numerical results are very good. In particular, they are superior per degree‐of‐freedom to the results predicted by the various non‐conforming and conforming, cubic and related elements at present used in computer packages. Together with a similar performance by the quintic member 10 of the family, they validate the proposed theoretical solution.