Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux

Type de document

THESE

Langue

anglais

Auteur

EL BOUSTANI

Résumé / Abstract

This work is the product of a three-year collaboration between Laboratoire Navier and the civil engineering ?rm Strains. It has been shaped by following the needs of the construction industry for a more reliable, e°cient, robust and easy-to-use structural analysis software. Departing from traditional numerical methods used in non-linear ?nite-element analyses, this work aims at adapting and extending the use of optimization-based algorithms to solve a wide range of non-linear mechanical problems. Based on a solid convex-optimization mathematical theory, the primal-dual interior point method is nowadays becoming a reliable technology capable of handling various non-linear and non-smooth problems. Various mechanical behavior such as plasticity or contact conditions can be written using second-order cone complementarity problems which perfectly ?ts in the conic optimization framework. Under the small-strain assumption, the elastoplastic contact problem can be cast as a pair of dual optimization problems. These problems can also be extended to the upper and lower bound theorems of yield design/limit analysis theory. Appropriate displacement and stress-based ?nite-element discretization strategies are chosen and the corresponding minimization problems are then solved using a state-of-the art primal-dual interior-point solver coded from scratch, yielding respectively an upper and a lower bound estimate of the exact solution. The proposed framework is illustrated and validated through various steel structure examples and the results are compared to other ?nite-element commercial software and Eurocode design recommendations. Its e°ciency compared to a standard step-by-step Newton procedure, is proven via important savings in computational time, mainly due to its remarkable robustness with respect to large load steps. The framework has also been extended to a non-convex setting involving ?nite-strain plasticity using a total Lagrangian formulation based on a logarithmic strain measure. The proposed extension of the 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 still exhibits good computational performance, especially in terms of convergence robust-ness. 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. Finally, the potentialities of the proposed framework is illustrated on various complex engineering problems taken from various design studies such as 3D steel assemblies or the second-order analysis of a steel bridge section.