On the performance of non-conforming finite elements for the upper bound limit analysis of plates

In this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second-order cone programming for the minimization problem. Three different C¹-discontinuous finite elements are considered: the quadratic six-node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble function at centroid (T6b) and the cubic Hermite triangle (H3). Through numerical examples involving Johansen and von Mises yield criteria, it is shown that cubic elements (H3) give far better results in terms of convergence rate and precision than fully conforming elements found in the literature, especially for problems involving clamped boundaries.