The Generalized Conforming Element (GCE) — Theory and Applications

The concept of generalized conforming elements and their applications to membrane, plate and shell problems are introduced in this paper. The generalized conforming element method proposed by the first author in 1987 provides a simple and efficient means to deal with structural problems, especially the C1 continuous problems. In the first part of this paper, the theoretical basis of GCE is presented. GCE is a limiting-conforming element which is non-conforming in coarse meshes but tends to be conforming in the limiting case of refined meshes. It is formulated based on the modified potential energy principle and the concept of generalized compatibility conditions. It is a new way to construct the finite elements — combined application of the energy method and the weighted residual method. In the second part of this paper, various models of GCE are illustrated. A series of generalized conforming elements with excellent performance have been constructed, that is, thin and thick plate bending GCE, membrane GCE with drilling freedoms and thin shell GCE.