Utilisation de la méthode des éléments finis non-linéaires pour la conception des structures en béton armé: application aux structures massives

Nonlinear finite elements for concrete structures have seen a remarkable advancement in the last half century with more emphasis on constitutive modelling of reinforced and non-reinforced concrete. Applications were restricted to the analysis of simple structures (beams, columns, slabs …etc.), comparisons to experimental tests, and rarely extended to the design of complex structures. Many reasons lie behind this fact. The first is the difficulty to implement such analyses for complex structures: large computation time with respect to conventional linear analyses, and convergence problems generally related to concrete softening. The second important reason is the complexity of the concrete material and the existence of a multitude of models and theories in the literature. Finally, there is a lack in the literature and international codes concerning the reliability framework and the limit state design using nonlinear analyses. The current work presents solutions to these issues and applications in the field of large reinforced concrete structures. To address the first problem, the quasi-static explicit solver algorithm is presented in this work, as an alternative to the conventional static implicit solver. Effectiveness of the explicit solver algorithm compared to the standard implicit one is demonstrated. It is shown through validations that, analysis of complex models with highly non-linear behaviour is being possible without the need for iterations. To address the second and third problems, a methodology that uses nonlinear finite elements analysis for determining a global resistance factor for the design of reinforced concrete structures is suggested.