A pseudo-equilibrium finite element for limit analysis of Reissner-Mindlin plates

Abstract A new finite element is developed for the yield design of Reissner-Mindlin plates based on the static theorem of limit analysis. This three-node triangular element satisfies the equilibrium equations and the mechanical boundary conditions on average, and, as such, it is not expected lower bounds on the collapse load from the computed results. The yield criterion is, however, exactly satisfied throughout the element. The relatively small nonlinear convex optimization problem posed here is treated as second-order cone programming and solved with a primal-dual interior-point algorithm implemented in the MOSEK optimization package. The proposed procedure exhibits excellent performance on a series of numerical tests, demonstrating that not satisfying the equilibrium equations and the mechanical boundary conditions rigorously is far from being a handicap. It is also observed that the solution may develop boundary layer along certain types of edges. This real physical phenomenon, likely to be manifested in Reissner-Mindlin plate solutions and that nearly no attention has been paid in the framework of yield design, is a source of convergence delay.