Keywords: multiscale computational method, domain decomposition, parametric study, contact, friction, parallel processing.

The aim of this work is to develop an efficient strategy for the parametric analysis of problems with multiple contacts in the field of computational mechanics. The applications concern elastic structural assemblies in statics and quasi-statics with local nonlinearities, such as unilateral contact with friction. Our approach is based on a decomposition of an assembly into substructures and interfaces. Within each substructure, the problem is solved using the finite element method and an iterative scheme based on the monoscale or the multiscale LArge Time INcrement (LATIN) method [1]. The LATIN method is a mixed method which deals with both velocities and forces at the interfaces simultaneously. In its multiscale version, it solves a homogenized macroscopic problem in order to accelerate the convergence of the numerical scheme.

Dual substructuring methods could be associated with multispace-multiscale methods: as in [2] or [3], our mixed approach takes different space scales into account.

The LATIN method associated with the mixed domain decomposition method is inherently parallelizable [4]. It is very well adapted to libraries such as MPI (Message Passing Interface) which carry out transfers of information among machines. Such libraries were used in order to be able to use PC cluster types of architectures.

The objective is to calculate a large number of design configurations [5], each of which corresponds to a set of values of all the variable parameters (friction coefficients, prestresses) introduced into the mechanical analysis. Here, using the capabilities of the monoscale and multiscale LATIN method, instead of carrying out a full analysis for each design configuration, we propose to reuse the solution of a particular problem with one set of parameters in order to solve similar problems with other sets of parameters) [6]. Moreover, we interface our software with OpenTURNS (Open source initiative to Treat Uncertainties, RisksN Statistics) [7] to deal with the distribution of the calculation among several processors.

We present the application of this strategy to the analysis of assemblies of elastic structures taking into account contact and friction. For these assemblies, parametric studies have been carried out on the values of the connection parameters (friction coefficient, gaps, ...). The presented examples will show that the algorithm can be very efficient numerically.

[1]

P. Ladevèze, "Nonlinear computational structural mechanics - New approaches and non-incremental methods of calculation", Springer-Verlag, 1999.

[2]

C. Farhat, M. Lesoinne, K. Pierson, "A scalable dual-primal domain decomposition method", Numer. Lin. Alg. Appl., 7, 687-714, 2000. doi:10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S

[3]

I.D. Parsons, J.F. Hall, "The multigrid method in solids mechanics: part I algorithm description and behaviour", Int. J. for Numerical Methods in Engineering, 29, 719-37, 1990.doi:10.1002/nme.1620290404

[4]

L. Champaney, J.Y. Cognard, D. Dureisseix, P. Ladevèze, "Large scale applications on parallel computers of a mixed domain decomposition method", Computational Mechanics, 19, 253-263, 1997. doi:10.1007/s004660050174

[5]

L. Champaney, P.A. Boucard, S. Guinard, "Adaptive multi-analysis strategy for contact problems with friction. Application to aerospace bolted joints", Computational Mechanics, 42(2), 305-316, 2008. doi:10.1007/s00466-007-0213-7

[6]

P.A. Boucard, L. Champaney, "A suitable computational strategy for the parametric analysis of problems with multiple contact", Int. J. for Numerical Methods in Engineering, 57, 1259-1282, 2003. doi:10.1002/nme.724

[7]

G. Andrianov, S. Burriel, S. Cambier, I. Dutfoy, I. Dutka-Malen, E. de Rocquigny, B. Sudret, P. Benjamin, R. Lebrun, F. Mangeant, M. Pendola, "Open TURNS, an open source initiative to Treat Uncertainties, Risks N Statistics in a structured industrial approach", In Proc. ESREL-2007 Safety and Reliability Conference, Stavenger, Norway, 2007.

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