Determination of branches of limit points by an Asymptotic Numerical Method
Résumé
This paper deals with parameter dependence in nonlinear structural stability problems. The main purpose is the study of the influence of imperfections on a structure. This analysis implies the calculation of the so called fold curve connecting the critical points of the equilibrium path when a structural defect varies. This is traditionally achieved by adding a well-chosen constraint equation demanding the criticality of the equilibrium. The crucial feature of the paper lies in the use of the Asymptotic Numerical Method (A.N.M.) for the numerical resolution of the obtained augmented system. The theoretical framework upon which the A.N.M. is based as well as its advantages over incremental-iterative strategies are presented. The numerical isolation of an initial starting limit point is described. The extended system and its resolution with the A.N.M. are discussed. From a numerical point of view, it leads to an efficient treatment which takes the singularity of the tangent stiffness matrix into account. Emphasis is given on a geometrical shape imperfection.
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