Reanalysis of Nonlinear Structures using a Reduction Method of Combined Approximations

The aim of reanalysis methods is to approximate the responses of a structure whose parameters have been perturbed or even modified without solving the new equilibrium equation system associated to the updated structure: only the initial solutions and the perturbed data are used. In the particular case of non-linear problems, the re-actualization of the tangent stiffness matrix at each time step of the Newton-Raphson integration algorithm implies many reanalysis leading to a high computational time. To mitigate these difficulties, one proposes a reduction method adapted to non-linear and large size dynamic models. This study especially focuses on geometrical non-linearities, i.e. large displacements. The presented reduction method is based on the combined approximations method (CA method) introduced by Kirsch.