A New method to compute perturbed bifurcations: Application to the buckling of imperfect elastic structures

A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

“…Besides, the convergence toward the equilibrium solution is never assured. An alternative is to use an asymptotic numerical method [4] [5]. Such a method principle is, starting from a solution point, to seek the branch of solution as an asymptotic expansion of an arc length measure, leading to a semi-analytical solution.…”

“…The full equilibrium diagram can then be computed iteratively. This method features 3 main advantages : the user does not have any parameter to tune, it requires less computation time than a classical predictor-corrector method and it is not concerned by convergence problems [4]. The main difficulty using this method is to put the system of equations under the quadratic form R(u) = f int (u) − λf ext = C + L(u) + Q(u, u) = 0 (with C, L and Q respectively constant, linear and quadratic operators).…”

Nonlinear elastic buckling and postbuckling analysis of cylindrical panels

“…These methods are typically valid only in the vicinity of critical points. Potier-Ferry and coworkers [16][17][18][19] extended Koiter's idea and developed an asymptoticnumerical method to compute nonlinear postbuckling responses.…”

An asymptotic numerical method for inverse elastic shape design

“…In this paper, we propose to solve the problem of inverse elastic shape design using the Asymptotic Numerical Method (ANM), first introduced in the 1990s [Damil and Potier-Ferry 1990;Cochelin 1994]. ANMs are fundamentally different from traditional Newtontype methods.…”