A limit analysis approach for plane stress problem

Resumo

A finite element is developed for plane stress problems based on the static theorem of limit analysis.
This four-node quadrilateral 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.
Numerical tests are carried out using the von Mises criterion, which is exactly satisfied throughout the element.
The 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.