A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces. (English) Zbl 1392.74068
Summary: The objective of this work is to develop an efficient strategy for the resolution of many configurations of a quasi-static problem with multiple contacts. Our approach is based on the multiscale LATIN method with domain decomposition. Here we propose to take advantage of the capability of the LATIN method to reuse the solution of a given problem in order to solve many similar problems. We firstly introduce the LATIN method and compare our approach to different strategies commonly used to solve contact problems. Then, we illustrate the capabilities of our method through two examples.
MSC:
| 74M15 | Contact in solid mechanics |
| 74M10 | Friction in solid mechanics |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 65Y05 | Parallel numerical computation |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Software:
ABAQUSReferences:
| [1] | Kikuchi, N.; Oden, J. T.: Contact problems in elasticity: a study of variational inequalities and finite element methods, Society for industrial mathematics (1988) · Zbl 0685.73002 |
| [2] | Zhong, Z.; Mackerle, J.: Static contact problems – a review, Eng comput 9, 3-37 (1992) |
| [3] | Wriggers, P.: Finite element algorithms for contact problems, Arch comput methods eng 2, No. 4, 1-49 (1995) |
| [4] | Barboteu, M.; Alart, P.; Vidrascu, M.: A domain decomposition strategy for nonclassical frictional multi-contact problems, Comput methods appl mech eng 190, 4785-4803 (2001) · Zbl 1020.74041 · doi:10.1016/S0045-7825(00)00347-9 |
| [5] | Dostal, Z.; Friedlander, A.; Santos, S.: Solution of coercive and semicoercive contact problems by FETI domain decomposition, Contemp math 218, 82-93 (1998) · Zbl 0962.74056 |
| [6] | Dureisseix, D.; Farhat, C.: A numerically scalable domain decomposition method for the solution of frictionless contact problems, Int J numer methods eng 50, 2643-2666 (2001) · Zbl 0988.74064 · doi:10.1002/nme.140 |
| [7] | Champaney, L.; Cognard, J. Y.; Dureisseix, D.; Ladevèze, P.: Large scale applications on parallel computers of a mixed domain decomposition method, Comput mech 10, 253-263 (1997) · Zbl 0894.73211 · doi:10.1007/s004660050174 |
| [8] | Farhat, C.; Roux, F. X.: An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element systems, SIAM J sci comput 13, 379-396 (1992) · Zbl 0746.65086 · doi:10.1137/0913020 |
| [9] | Ladevèze, P.: Nonlinear computational structural mechanics – new approaches and non-incremental methods of calculation, (1999) · Zbl 0912.73003 |
| [10] | Farhat, C.; Lesoinne, M.; Pierson, K.: A scalable dual – primal domain decomposition method, Numer linear algebra appl 7, 687-714 (2000) · Zbl 1051.65119 · doi:10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S |
| [11] | Farhat, C.; Lesoinne, M.; Letallec, P.; Pierson, K.; Rixen, D.: Feti-DP: a dual – primal unified FETI method. Part I: a faster alternative to the two-level FETI method, Int J numer methods eng 50, 1523-1544 (2000) · Zbl 1008.74076 · doi:10.1002/nme.76 |
| [12] | Avery, P.; Rebel, G.; Lesoinne, M.; Farhat, C.: A numerically scalable dual – primal substructuring method for the solution of contact problems. Part I: The frictionless case, Comput methods appl mech eng 190, 2403-2426 (2004) · Zbl 1067.74572 · doi:10.1016/j.cma.2004.01.016 |
| [13] | Champaney, L.; Cognard, J. Y.; Ladevèze, P.: Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions, Comput struct 73, 249-266 (1999) · Zbl 1049.74562 · doi:10.1016/S0045-7949(98)00285-5 |
| [14] | Ladevèze, P.; Dureisseix, D.: A micro/macro approach for parallel computing of heterogeneous structures, Int J comput civic struct eng 1, 18-28 (2000) |
| [15] | Allix, O.: Damage analysis of delamination around a hole, New adv comput struct mech, 411-421 (1992) |
| [16] | Cognard, J. Y.; Ladevèze, P.: A large time increment approach for cyclic plasticity, Int J plast 9, 114-157 (1993) · Zbl 0772.73028 · doi:10.1016/0749-6419(93)90026-M |
| [17] | Boucard, P. A.; Ladevèze, P.; Poss, M.; Rougee, P.: A non-incremental approach for large displacements problems, Comput struct 64, 499-508 (1997) · Zbl 0919.73167 · doi:10.1016/S0045-7949(96)00165-4 |
| [18] | Ladevèze, P.; Lemoussu, H.; Boucard, P. A.: A modular approach to 3-D impact computation with frictional contact, Comput struct 78, No. 1/3, 45-52 (2000) |
| [19] | Cognard JY, Ladevèze P, Talbot P. A non-incremental and adaptive computational approach in thermo-viscoplasticity. In: Bruhns OT, Stein E, editors. IUTAM symposium on micro- and macrostructural aspects of thermoplasticity; 1999. p. 281 – 91. |
| [20] | Ladevèze, P.; Loiseau, O.; Dureisseix, D.: A micro-macro and parallel computational strategy for highly heterogeneous structures, Int J numer methods eng 52, 121-138 (2001) |
| [21] | Guidault, P. A.; Allix, O.; Champaney, L.; Cornuault, S.: A multiscale extended finite element method for crack propagation, Comput methods appl mech eng 197, No. 5, 391-399 (2008) · Zbl 1169.74604 · doi:10.1016/j.cma.2007.07.023 |
| [22] | Kerfriden P, Allix O, Gosselet P. Multiscale analysis of delamination in composite laminates. In: IASS-IACM 6th international conference on shells and spatial structures ”spanning nano to mega”; 2008. |
| [23] | Alart, P.; Dureisseix, D.: A scalable multiscale Latin method adapted to nonsmooth discrete media, Comput methods appl mech eng 197, 319-331 (2008) · Zbl 1169.74482 · doi:10.1016/j.cma.2007.05.002 |
| [24] | Vergnault E, Allix O, Maison-le-Poec S. Extension of the LATIN framework for multiscale computation of fluid-structure interaction. In: ECT 2008 – 6th international conference on engineering computational technology; 2008. |
| [25] | Boucard, P. A.; Champaney, L.: A suitable computational strategy for the parametric analysis of problems with multiple contact, Int J numer methods eng 57, 1259-1281 (2003) · Zbl 1062.74607 · doi:10.1002/nme.724 |
| [26] | Kim, Y. Y.; Yoon, G. H.: Multi-resolution multi-scale topology optimization: a new paradigm, Int J solids struct 37, No. 39, 5529-5559 (2000) · Zbl 0981.74044 · doi:10.1016/S0020-7683(99)00251-6 |
| [27] | Benaroya, H.; Rehak, M.: Finite element methods in probabilistic structural analysis: a selective review, Appl mech rev (ASME) 41, No. 5, 201-213 (1998) · Zbl 0688.60047 |
| [28] | Macias, O. F.; Lemaire, M.: Stochastic finite elements and fiability. Application to fracture mechanics, Revue fran caise de génie civil 1, No. 2 (1997) |
| [29] | , Basic perturbation technique and computer implementation (1992) |
| [30] | Ladevèze, P.; Nouy, A.: On a multiscale computational strategy with time and space homogenization for structural mechanics, Comput methods appl mech eng 192, 3061-3087 (2003) · Zbl 1054.74701 · doi:10.1016/S0045-7825(03)00341-4 |
| [31] | Ladevèze P, Néron D, Passieux JC. The LATIN multiscale strategy and the time-space approximation. In: Proc of ECCOMAS thematic conference on multi-scale computational methods for solids and fluids; 2007. |
| [32] | Ladevèze, P.; Nouy, A.; Loiseau, O.: A multiscale computational approach for contact problems, Comput methods appl mech eng 191, 4869-4891 (2002) · Zbl 1018.74036 · doi:10.1016/S0045-7825(02)00406-1 |
| [33] | Kikuchi N. Penalty/finite element approximations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York; 1982. · Zbl 0506.73105 |
| [34] | Arora, J. S.; Chahande, A. I.; Paeng, J. K.: Multiplier methods for engineering optimization, Int J numer methods eng 32, 1485-1525 (2001) · Zbl 0752.90061 · doi:10.1002/nme.1620320706 |
| [35] | Simo, J.; Laursen, T. A.: An augmented Lagrangian treatment of contact problem involving friction, Comput struct 42, 97-116 (1992) · Zbl 0755.73085 · doi:10.1016/0045-7949(92)90540-G |
| [36] | Blanzé, C.; Champaney, L.; Cognard, J. Y.; Ladevèze, P.: A modular approach to structure assembly computations. Application to contact problems, Eng comput 13, No. 1, 15-32 (1995) |
| [37] | Blanzé, C.; Champaney, L.; Védrine, P.: Contact problems in the design of a superconducting quadrupole prototype, Eng comput 17, No. 2/3, 136-152 (2000) · Zbl 0952.74539 · doi:10.1108/02644400010313093 |
| [38] | Dostál, Z.; Horák, D.; Kucera, R.; Vondrák, V.; Haslinger, J.; Dobiás, J.: FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction, Comput methods appl mech eng 194, 395-409 (2005) · Zbl 1085.74046 · doi:10.1016/j.cma.2004.05.015 |
| [39] | Ladevèze, P.; Lubineau, G.; Violeau, D.: Computational damage micromodel of laminated composites, Int J fract 137, 139-150 (2006) · Zbl 1197.74087 · doi:10.1007/s10704-005-3077-x |
| [40] | Wriggers, P.; Simo, J. C.; Taylor, R. L.: Penalty and augmented Lagrangian formulations for contact problems, Proc NUMETA conf 85, 97-106 (1985) |
| [41] | Hibbitt K, and others. ABAQUS theory manual. Pub. Hibbitt, Karlsson & Sorensen; 1998. |
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