Summary The objective of this contribution is to present some new recent developments regarding the evaluation of the ultimate bearing capacity of massive three‐dimensional reinforced concrete structures which cannot be modeled as 1D (beams) or 2D (plates) structural members. The approach is based upon the implementation of the lower bound static approach of yield design through a discretization of the three‐dimensional structure into tetrahedral finite elements, on the one hand, the formulation of the corresponding optimization problem in the context of semi‐definite programming techniques, on the other hand. Another key feature of the method lies in the treatment of the concrete‐embedded reinforcing bars not as individual elements, but by resorting to an extension of the yield design homogenization approach. The whole procedure is first validated on the rather simple illustrative problem of a uniformly loaded simply supported beam, then applied to the design of a bridge pier cap taken as an example of more complex and realistic structure.

No abstract

Computation of elastic structures in contact is performed by means of a dual analysis combining displacement-based and equilibrium-based finite elements. Contact conditions are formulated in the framework of second-order cone programmaing (SOCP) and an efficient interior point method (IPM) algorithm is presented for the resolution of the associated optimization problems. The dual approach allows the user to assess the quality of convergence and to efficiently calculate a discretization error estimator which includes a contact error term. An efficient remeshing scheme, based on the local contributions of the elements to the global error, can then be used to efficiently improve the solution accuracy. The whole process is illustrated on some examples and applied to a typical steel assembly. Its efficiency, in particular concerning the IPM solver, is demonstrated in comparison with the industrial finite element code Abaqus.

We investigate the use of a second-order cone programming (SOCP) framework for computing complex 3D steel assemblies in the context of elastoplasticity and limit analysis. Displacement and stress-based variational formulations are considered and appropriate finite-element discretization strategies are chosen, yielding respectively an upper and lower bound estimate of the exact solution. An efficient interior-point algorithm is used to solve the associated optimization problems. The discrete solution convergence is estimated by comparing both static and kinematic solutions, offering a way to perform local mesh adaptation. The proposed framework is illustrated on the design of a moment-transmitting assembly, its performance is assessed by comparison with classical elastoplastic computations using Abaqus and, finally, T-stub resistance and failure mechanisms when assessing the strength of a column base plate are compared with the Eurocodes design rules.

Interior-point methods are well suited for solving convex non-smooth optimization problems which arise for instance in problems involving plasticity or contact conditions. This work attempts at extending their field of application to optimization problems involving either smooth but non-convex or non-smooth but convex objectives or constraints. A typical application for such kind of problems is finite-strain elastoplasticity which we address using a total Lagrangian formulation based on logarithmic strain measures. The proposed interior-point algorithm is implemented and tested on 3D examples involving plastic collapse and geometrical changes. Comparison with classical Newton-Raphson/return mapping methods shows that the interior-point method exhibits good computational performance, especially in terms of convergence robustness. Similarly to what is observed for convex small-strain plasticity, the interior-point method is able to converge for much larger load steps than classical methods.