An efficient and reliable steel assembly modelling scheme using second-order cone programming and dual error estimator.

The modelling of steel assemblies under static loading using elastic, elasto-plastic or rigid perfectly plastic material coupled with frictional unilateral contact is discussed within the framework of the second-order cone programming (SOCP). In this article, using a combination of the hard-contact conditions coupled with an associated Coulomb frictional behaviour, the contact conditions are written as second-order cones using a pair of dual kinematic and static variables. The minimizations are then formulated as a pair of dual SOCP problems which are then solved using a state-of-the art primal-dual interior point method (IPM). In comparison with a Newton-Raphson algorithm generally used to solve nonlinear problems, the IPM shows better robustness and efficiency and specially for limit analysis where the Newton-Raphson algorithm cannot be used and allows us to formulate the problem using a dual approach. This yields an optimal pair of dual kinematically and statically admissible fields which allows the user to assess the quality of convergence and to efficiently calculate a discretization error estimator which includes a contact surface error term and plasticity error terms. An efficient remesh scheme, based on the local contributions of the elements to the global error, can then be used to limit the number of elements in the 3D analysis. This article illustrates the whole process in some examples of typical steel assemblies. This will allow structural engineers to evaluate the quality of their results and to produce better and more economical designs.