On evaluating the inf–sup condition for plate bending elements

This paper addresses the evaluation of the inf–sup condition for Reissner–Mindlin plate bending elements. This fundamental condition for stability and optimality of a mixed finite element scheme is, in general, very difficult to evaluate analytically, considering for example distorted meshes. Therefore, we develop a numerical test methodology. To demonstrate the test methodology and to obtain specific results, we apply it to standard displacement-based elements and elements of the MITC family. Whereas the displacement-based elements fail to satisfy the inf–sup condition, we find that the MITC elements pass our numerical test for uniform meshes and a sequence of distorted meshes. © 1997 John Wiley & Sons, Ltd.