For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.

Pour les solutions transitoires répétées des structures géométriquement nonlinéaires l’effort numérique présente souvent une contrainte importante. Ainsi, l’introduction d’un modèle d’ordre réduit, qui prend en compte les effets nonlinéaires et qui accélère considérablement les calculs, s’avère souvent nécessaire.Ce travail aboutit à une méthode qui permet des solutions transitoires accélérées, fidèles et paramétrables, à travers d’un modèle réduit de la structure initiale. La structure est discrétisée et son équilibre dynamique décrit par une équation matricielle. La projection sur une base réduite est introduite afin d’obtenir un modèle réduit. Une étude numérique complète sur plusieurs bases communes démontre que la simple introduction d’une base constante ne suffit pas pour prendre en compte le comportement nonlinéaire. Trois exigences sont déduites pour une solution transitoire accélérée, fidèle et paramétrable. L’algorithme de solution doit permettre un suivi de l’évolution nonlinéaire de la solution transitoire, la solution doit être autonome des termes nonlinéaires en éléments finis et la base doit être adaptée à des paramètres externes.Trois approches sont mises en place, chacune répondant à une exigence. Ces approches sont assemblées dans la méthode intégrée. Les approches sont la mise-à-jour et augmentation de la base , la formulation polynomiale des termes nonlinéaires et l’interpolation de la base. Un algorithme de type Newmark forme le cadre de la méthode intégrée. L’application de la méthode intégrée sur des cas test en élément finis géométriquement nonlinéaires confirme qu’elle répond au but initial d’obtenir des solutions transitoires accélérées, fidèles et paramétrables. / For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.