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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 93
Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 312

Reanalysis of Nonlinear Structures using a Reduction Method of Combined Approximations

M. Guedri1, T. Weisser2 and N. Bouhaddi2

1Nabeul Preparatory Engineering Institute (IPEIN), M'rezgua, Nabeul, Tunisia
2FEMTO-ST Institute UMR 6174, Applied Mechanics Department, University of Franche-Comté, Besançon, France

Full Bibliographic Reference for this paper
M. Guedri, T. Weisser, N. Bouhaddi, "Reanalysis of Nonlinear Structures using a Reduction Method of Combined Approximations", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 312, 2010. doi:10.4203/ccp.93.312
Keywords: geometrical non-linearities, large displacements, structural reanalysis, combined approximations, robustness.

Complex structure optimization is an important part of the design process where the initial state of the structure is modified, sometimes in a significant way, in order to reach the best possible performance, for a given set of constraints.

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].

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