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Archive of Applied Mechanics
Erschienen in: Archive of Applied Mechanics 11/2018

06.08.2018 | Original

Proper orthogonal decomposition for substructures in nonlinear finite element analysis: coupling by means of tied contact

verfasst von: Lei Zhou, Jaan-Willem Simon, Stefanie Reese

Erschienen in: Archive of Applied Mechanics | Ausgabe 11/2018

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Abstract

The finite element analysis of complex structures involves a high computational effort, since the equation system to be solved includes a large number of degrees of freedom. This holds particularly in nonlinear finite element analysis. In order to reduce the numerical effort, the total system is subdivided into substructures which are analyzed separately from each other. The computing time can be further reduced, if the number of degrees of freedom of the substructures and thereby the dimension of the global equation system are decreased. In the present paper, this is achieved by projection-based model order reduction applied at the level of the substructures. The corresponding modes include internal and boundary nodes. The precomputation is carried out either directly with respect to the global system or only on one representative substructure. For the coupling, a new surface-to-surface tied contact formulation based on the penalty method is presented which couples the reduced and unreduced substructures. This is also possible for non-matching meshes. Several nonlinear numerical examples are performed which show the feasibility of the new approach.
Vorheriger Artikel An implicit representation of phase interface motion with internal variables
Nächster Artikel Symmetric Galerkin boundary element analysis of the interaction between multiple growing cracks in infinite domains

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Literatur
1.
Antoulas, A.C.: An overview of approximation methods for large-scale dynamical systems. Ann. Rev. Control 29(2), 181–190 (2005)CrossRef
2.
Bamer, F., Markert, B.: An efficient response identification strategy for nonlinear structures subject to nonstationary generated seismic excitations. Mech. Based Des. Struct. Mach. 45, 313–330 (2017)CrossRef
3.
Benner, P., Feng, L.: Model order reduction for coupled problems. Int. J. Appl. Comput. Math. 14(1), 3–22 (2015)MathSciNetMATH
4.
Benner, P., Gugercin, S., Willcox, K.: A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev. 57(4), 483–531 (2015)MathSciNetCrossRef
5.
Besselink, B., Tabak, U., Lutowska, A., Van De Wouw, N., Nijmeijer, H., Rixen, D., Hochstenbach, M., Schilders, W.: A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J. Sound Vib. 332(19), 4403–4422 (2013)CrossRef
6.
Blockmans, B., Tamarozzi, T., Naets, F., Desmet, W.: A nonlinear parametric model reduction method for efficient gear contact simulations. Int. J. Numer. Methods Eng. 102(5), 1162–1191 (2015)MathSciNetCrossRef
7.
Bonet, J., Wood, R .D.: Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge (2008)CrossRef
8.
Corigliano, A., Dossi, M., Mariani, S.: Model order reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem. Comput. Methods Appl. Mech. Eng. 290, 127–155 (2015)MathSciNetCrossRef
9.
Craig, R. Jr.: Coupling of substructures for dynamic analyses: an overview. In: 41st Structures, Structural Dynamics, and Materials Conference and Exhibit, pp. 1573–1584 (2000)
10.
Craig, R.R., Bampton, M.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968)CrossRef
11.
Crisfield, M.: An arc-length method including line searches and accelerations. Int. J. Numer. Methods Eng. 19(9), 1269–1289 (1983)MathSciNetCrossRef
12.
Crisfield, M.: Re-visiting the contact patch test. Int. J. Numer. Methods Eng. 48(3), 435–449 (2000)CrossRef
13.
Farah, P., Popp, A., Wall, W.A.: Segment-based vs. element-based integration for mortar methods in computational contact mechanics. Comput. Mech. 55(1), 209–228 (2015)MathSciNetCrossRef
14.
Fehr, J., Eberhard, P.: Simulation process of flexible multibody systems with non-modal model order reduction techniques. Multibody Syst. Dyn. 25(3), 313–334 (2011)CrossRef
15.
Festjens, H., Chevallier, G., Dion, J.: Nonlinear model order reduction of jointed structures for dynamic analysis. J. Sound Vib. 333(7), 2100–2113 (2014)CrossRef
16.
Fox, R., Miura, H.: An approximate analysis technique for design calculations. AIAA J. 9(1), 177–179 (1971)CrossRef
17.
Galland, F., Gravouil, A., Malvesin, E., Rochette, M.: A global model reduction approach for 3D fatigue crack growth with confined plasticity. Comput. Methods Appl. Mech. Eng. 200(5), 699–716 (2011)MathSciNetCrossRef
18.
Gerstmayr, J., Ambrósio, J.: Component mode synthesis with constant mass and stiffness matrices applied to flexible multibody systems. Int. J. Numer. Methods Eng. 73(11), 1518–1546 (2008)CrossRef
19.
Heirman, G.H., Desmet, W.: Interface reduction of flexible bodies for efficient modeling of body flexibility in multibody dynamics. Multibody Syst. Dyn. 24(2), 219–234 (2010)CrossRef
20.
Hesch, C., Betsch, P.: Isogeometric analysis and domain decomposition methods. Comput. Methods Appl. Mech. Eng. 213, 104–112 (2012)MathSciNetCrossRef
21.
Holzwarth, P., Eberhard, P.: Interface reduction for CMS methods and alternative model order reduction. In: 8th Vienna International Conference on Mathematical Modelling MATHMOD IFAC-PapersOnLine, vol. 48, no. 1, pp. 254–259 (2015)CrossRef
22.
Holzwarth, P., Eberhard, P.: SVD-based improvements for component mode synthesis in elastic multibody systems. Eur. J. Mech A Solids 49, 408–418 (2015)MathSciNetCrossRef
23.
Idelsohn, S.R., Cardona, A.: A reduction method for nonlinear structural dynamic analysis. Comput. Methods Appl. Mech. Eng. 49(3), 253–279 (1985)CrossRef
24.
Junge, M., Brunner, D., Becker, J., Gaul, L.: Interface-reduction for the Craig–Bampton and Rubin method applied to FE–BE coupling with a large fluid-structure interface. Int. J. Numer. Methods Eng. 77(12), 1731–1752 (2009)MathSciNetCrossRef
25.
Kalker, J., Van Randen, Y.: A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems. J. Eng. Math. 6(2), 193–206 (1972)MathSciNetCrossRef
26.
Kerfriden, P., Gosselet, P., Adhikari, S., Bordas, S.P.-A.: Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. Comput. Methods Appl. Mech. Eng. 200(5), 850–866 (2011)MathSciNetCrossRef
27.
Kerfriden, P., Goury, O., Rabczuk, T., Bordas, S.P.-A.: A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics. Comput. Methods Appl. Mech. Eng. 256, 169–188 (2013)MathSciNetCrossRef
28.
Kerfriden, P., Passieux, J.-C., Bordas, S.P.-A.: Local/global model order reduction strategy for the simulation of quasi-brittle fracture. Int. J. Numer. Methods Eng. 89(2), 154–179 (2012)MathSciNetCrossRef
29.
Kerschen, G., Golinval, J.-C., Vakakis, A.F., Bergman, L.A.: The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn. 41(1–3), 147–169 (2005)MathSciNetCrossRef
30.
Kim, J.-G., Markovic, D.: High-fidelity flexibility-based Component Mode Synthesis method with interface degrees of freedom reduction. AIAA J. 54, 3619–3631 (2016)CrossRef
31.
Krysl, P., Lall, S., Marsden, J.: Dimensional model reduction in non-linear finite element dynamics of solids and structures. Int. J. Numer. Methods Eng. 51(4), 479–504 (2001)MathSciNetCrossRef
32.
Laursen, T., Simo, J.: A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems. Int. J. Numer. Methods Eng. 36(20), 3451–3485 (1993)MathSciNetCrossRef
33.
Laursen, T.A., Puso, M.A., Sanders, J.: Mortar contact formulations for deformable-deformable contact: past contributions and new extensions for enriched and embedded interface formulations. Comput. Methods Appl. Mech. Eng. 205, 3–15 (2012)MathSciNetCrossRef
34.
Law, M., Phani, A.S., Altintas, Y.: Position-dependent multibody dynamic modeling of machine tools based on improved reduced order models. J. Manuf. Sci. Eng. 135(2), 021008 (2013)CrossRef
35.
MacNeal, R.H.: A hybrid method of component mode synthesis. Comput. Struct. 1(4), 581–601 (1971)CrossRef
36.
Meyer, M., Matthies, H.G.: Efficient model reduction in non-linear dynamics using the Karhunen–Loeve expansion and dual-weighted-residual methods. Comput. Mech. 31(1), 179–191 (2003)CrossRef
37.
Nickell, R.E.: Nonlinear dynamics by mode superposition. Comput. Methods Appl. Mech. Eng. 7(1), 107–129 (1976)MathSciNetCrossRef
38.
Nigro, P.S.B., Anndif, M., Teixeira, Y., Pimenta, P.M., Wriggers, P.: An adaptive model order reduction with Quasi-Newton method for nonlinear dynamical problems. Int. J. Numer. Methods Eng. 106(9), 740–759 (2016)MathSciNetCrossRef
39.
Noor, A.K.: Recent advances in reduction methods for nonlinear problems. Comput. Struct. 13(1), 31–44 (1981)MathSciNetCrossRef
40.
Noor, A.K.: Recent advances and applications of reduction methods. Appl. Mech. Rev. 47(5), 125–146 (1994)CrossRef
41.
Noor, A.K., Peters, J.M.: Reduced basis technique for nonlinear analysis of structures. AIAA J. 18(4), 455–462 (1980)CrossRef
42.
43.
Radermacher, A., Reese, S.: Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring. Comput. Mech. 54(3), 677–687 (2014)MathSciNetCrossRef
44.
Radermacher, A., Reese, S.: Pod-based model reduction with empirical interpolation applied to nonlinear elasticity. Int. J. Numer. Methods Eng. 107, 477–495 (2015)MathSciNetCrossRef
45.
Rubin, S.: Improved component-mode representation for structural dynamic analysis. AIAA J. 13(8), 995–1006 (1975)CrossRef
46.
Ryckelynck, D., Benziane, D.M., Cartel, S., Besson, J.: A robust adaptive model reduction method for damage simulations. Comput. Mater. Sci. 50(5), 1597–1605 (2011)CrossRef
47.
Segalman, D.J.: Model reduction of systems with localized nonlinearities. J. Comput. Nonlinear Dyn. 2(3), 249–266 (2007)CrossRef
48.
Shabana, A.A.: Substructure synthesis methods for dynamic analysis of multi-body systems. Comput. Struct. 20(4), 737–744 (1985)CrossRef
49.
Spanos, J.T., Tsuha, W.S.: Selection of component modes for flexible multibody simulation. J. Guid. Control Dyn. 14(2), 278–286 (1991)CrossRef
50.
51.
Taylor, R.L., Papadopoulos, P.: On a patch test for contact problems in two dimensions. In: Computational Methods in Nonlinear Mechanics, pp. 690–702. Springer, New York (1991)
52.
Wasfy, T.M., Noor, A.K.: Computational strategies for flexible multibody systems. Appl. Mech. Rev. 56(6), 553–613 (2003)CrossRef
53.
Wilson, E.L.: A new method of dynamic analysis for linear and nonlinear systems. Finite Elem. Anal. Des. 1(1), 21–23 (1985)CrossRef
54.
Wriggers, P.: Computational Contact Mechanics. Springer, Berlin (2006)CrossRef
55.
56.
Zavarise, G., De Lorenzis, L.: A modified node-to-segment algorithm passing the contact patch test. Int. J. Numer. Methods Eng. 79(4), 379–416 (2009)CrossRef
57.
Zavarise, G., De Lorenzis, L.: The node-to-segment algorithm for 2D frictionless contact: classical formulation and special cases. Comput. Methods Appl. Mech. Eng. 198(41), 3428–3451 (2009)MathSciNetCrossRef
Metadaten
Titel
Proper orthogonal decomposition for substructures in nonlinear finite element analysis: coupling by means of tied contact
verfasst von
Lei Zhou
Jaan-Willem Simon
Stefanie Reese
Publikationsdatum
06.08.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 11/2018
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-018-1427-1

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