A Finite Element in Equilibrium in a Weak Sense for the Static Theorem

Eric Luis Barroso Cavalcante¹; Eliseu Lucena Neto¹; Denilson José Ribeiro Sodré²

¹ Instituto Tecnológico de Aeronáutica; ² Faculdade de Engenharia Civil da Universidade Federal do Pará

doi:10.20906/CPS/CILAMCE2015-0393

Resumo

A three-node triangular finite element developed for the static theorem of limit analysis is evaluated considering the von Mises material in plane stress condition. This element satisfies the equilibrium equation and the mechanical boundary condition only in a weak sense. The equilibrium equation, the mechanical boundary condition and the yield criterion, expressed in terms of nodal stresses, are dealt with as constraints of a nonlinear optimization problem whose objective function is defined by the loading. Numerical results of some benchmark tests illustrate that the proposed element can provide reliable lower bound collapse load, and that not satisfying the equilibrium equation and the mechanical boundary condition rigorously is far from being a severe handicap.

Palavras-chave: Finite Element; Nonlinear; Optimization; Numerical analysis