×

zbMATH — the first resource for mathematics

A suitable computational strategy for the parametric analysis of problems with multiple contact. (English) Zbl 1062.74607
Summary: The aim of the present work is to develop an application of the LArge Time INcrement (LATIN) approach for the parametric analysis of static problems with multiple contacts. The methodology adopted was originally introduced to solve viscoplastic and large-transformation problems. Here, the applications concern elastic, quasi-static structural assemblies with local non-linearities such as unilateral contact with friction. Our approach is based on a decomposition of the assembly into substructures and interfaces. The interfaces play the vital role of enabling the local non-linearities, such as contact and friction, to be modelled easily and accurately. The problem on each substructure is solved by the finite element method and an iterative scheme based on the LATIN method is used for the global resolution. More specifically, the objective is to calculate a large number of design configurations. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestress) which are introduced into the mechanical analysis. A full computation is needed for each set of parameters. Here we propose, as an alternative to carrying out these full computations, to use the capability of the LATIN method to re-use the solution to a given problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters).

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Benaroya, Applied Mechanics Reviews 41 pp 201– (1988)
[2] Macias, Application to fracture mechanics. Revue Francaise de Génie Civil 1 (1997)
[3] Basic Perturbation Technique and Computer Implementation. Wiley: NewYork, 1992.
[4] Kim, International Journal of Solids and Structures 37 pp 5529– (2000)
[5] Nonlinear Computational Structural Mechanics?New Approaches and Non-Incremental Methods of Calculation. Springer: Berlin, 1999. · doi:10.1007/978-1-4612-1432-8
[6] Boucard, Revue Européenne des Éléments Finis 8 pp 903– (1999)
[7] Boucard, Journal of Mechanical Engineering 50 pp 317– (1999)
[8] Allix, Computer Methods in Applied Mechanics and Engineering 191 pp 2727– (2002)
[9] (eds). Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM: Philadelphia, 1988. · doi:10.1137/1.9781611970845
[10] Zhong, Engineering Computations 9 pp 3– (1992)
[11] Wriggers, Archives of Computational Methods in Engineering 2 pp 1– (1995)
[12] et al. Penalty and augmented Lagrangian formulations for contact problems. Proceedings of the NUMETA Conference, Swansea, 1985.
[13] Penalty/finite element approximations of a class of unilateral contact problems. In Penalty Method and Finite Element Method. ASME: New York, 1982.
[14] Armero, Computer Methods in Applied Mechanics and Engineering 158 pp 269– (1998)
[15] Alart, Computer Methods in Applied Mechanics and Engineering 92 pp 253– (1991)
[16] Arora, International Journal for Numerical Methods in Engineering 32 pp 1485– (1991)
[17] Mathematical programming and augmented lagrangian methods for frictional contact problems. Proceedings of the Contact Mechanics International Symposium, Curnier A (ed.), Presses Polytechniques et Universitaires Romandes, 1992; 409-422.
[18] Treatment of the frictional contact via a Lagrangian formulation. In Mathematical and Computer Modelling, (eds), vol. 28. Pergamon Press: Oxford, 1998; 407-412.
[19] Various numerical methods for solving unilateral contact problems with friction. In Mathematical and Computer Modelling, (eds), vol. 28. Pergamon Press: Oxford, 1998; 97-108. · Zbl 1002.74592
[20] Studies in Nonlinear Programming. University Press: Stanford, CA, 1958.
[21] Simo, Computers and Structures 42 pp 97– (1992)
[22] Champaney, Computers and Structures 73 pp 249– (1999)
[23] Ballard, International Journal of Engineering Science 37 pp 163– (1999)
[24] Cocu, International Journal of Engineering Science 34 pp 783– (1996)
[25] Hild, International Journal of Applied Mathematics and Computer Science 12 pp 41– (2002)
[26] Wempner, International Journal of Solids and Structures 17 pp 1581– (1971)
[27] Riks, Transactions of the ASME: Journal of Applied Mechanics 39 pp 1060– (1972) · Zbl 0254.73047 · doi:10.1115/1.3422829
[28] Crisfield, Computers and Structures 13 pp 55– (1981)
[29] Blanzé, Engineering Computations 17 pp 136– (2000)
[30] Blanzé, Engineering Computations 13 pp 15– (1995)
[31] On the Schwartz alternating method III: a variant for non-overlapping subdomains. In Proceedings of Domain Decomposition Methods for Partial Differential Equations, (eds), SIAM: Philadelphia, PA, 1990.
[32] Augmented Lagrangian interpretation of the non-overlapping Schwarz alternating method: domain decomposition method. In Chan TF, Glowinski R, Periaux J, Widlund OB (eds). Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1990; 224-231.
[33] Zavarise, Engineering Computations 16 pp 88– (1999)
[34] Method of seismic fragility for complicated systems. Proceedings of the 2nd Specialistic Meeting on Probabilistic Methods in Seismic Risk Assessment for NPP, Committee on Safety of Nuclear Installations (CSNI), Livermore, CA, 1983.
[35] Faravelli, Journal of Engineering Mechanics 115 pp 2673– (1989)
[36] The response surface method, an efficient tool to determine the failure probability of large structural systems. Proceedings of the International Conference on Spacecraft Structures and Mechanical Testing, Noordwijk, The Netherlands, 24-26 April, ESA SP-321, 1991; 247-251.
[37] Application of the LATIN method to the calculation of response surfaces. In Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, Cambridge, USA, 12-15 June, (ed.), Elsevier, vol.1, 2001; 78-81.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.