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

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 equi-librium 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 cri-terion 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 optimiza-tion package. The proposed procedure exhibits excellent performance on a series of numer-ical 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 phe-nomenon, 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 de-lay. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

A new finite element is developed for the yield design of Reissner-Mindlin plates based on the static theorem of limit analysis. The proposed procedure demonstrates excellent performance on numerical tests, showing that not strictly satisfying the equilibrium equations and mechanical boundary conditions is not a disadvantage, although the solution may develop boundary layers along certain types of edges.