By exploring as much as possible the design parameter space, optimal solutions (displacements, constraints, eigenmodes, etc.) are then calculated. These successive multiple analysis or reanalysis thus imply a large computation cost which often remains prohibitive.

The modifications applied to the structure can be of various types: topological, acting on the form of the structure or its boundary conditions; parametric, acting on the physical parameters of the structure (mass, stiffness, thickness); in a global (whole structure level) or a local way (component level).

Therefore, the aim of reanalysis methods [1] 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.

Moreover, when the problem is non-linear, 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 robust reduction method adapted to non-linear and large sized dynamic models. This study especially focuses on geometrical non-linearities, i.e. large displacements [2].

The presented reduction method is based on the combined approximations method introduced by Kirsch [3,4].

1

G. Masson, B. Ait Brik, S. Cogan, N. Bouhaddi, "Component mode synthesis (CMS) based on an enriched Ritz approach for efficient structural optimization", Journal of Sound and Vibration, 296, 845-860, 2006. doi:10.1016/j.jsv.2006.03.024

2

O.C. Zienkiewicz, R.L. Taylor, "The Finite Element Method, Solid mechanics", 4th edition, vol. 2, McGraw-Hill, New York, 2000.

3

U. Kirsch, M. Bogomolni, I. Sheinman, "Efficient procedures for repeated calculations of the structural response using combined approximations", Structural and Multidisciplinary Optimization, 32, 435-446, 2006. doi:10.1007/s00158-006-0048-4

4

U. Kirsch, "A unified reanalysis approach for structural analysis, design, and optimization", Structural and Multidisciplinary Optimization, 25, 67-85, 2003. doi:10.1007/s00158-002-0269-0

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