Browse > Article

http://dx.doi.org/10.12989/csm.2014.3.1.001
###

Formulation, solution and CTL software for coupled thermomechanics systems |

Niekamp, R.
(Technical University Braunschweig)
Ibrahimbegovic, A. (Technical University Braunschweig) Matthies, H.G. (Technical University Braunschweig) |

Publication Information

Abstract

In this work, we present the theoretical formulation, operator split solution procedure and partitioned software development for the coupled thermomechanical systems. We consider the general case with nonlinear evolution for each sub-system (either mechanical or thermal) with dedicated time integration scheme for each sub-system. We provide the condition that guarantees the stability of such an operator split solution procedure for fully nonlinear evolution of coupled thermomechanical system. We show that the proposed solution procedure can accommodate different evolution time-scale for different sub-systems, and allow for different time steps for the corresponding integration scheme. We also show that such an approach is perfectly suitable for parallel computations. Several numerical simulations are presented in order to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed-up of parallel computations, which follow from the adequate choice of the time step for each sub-problem. This work confirms that one can make the most appropriate selection of the time step with respect to the characteristic time-scale, carry out the separate computations for each sub-system, and then enforce the coupling to preserve the stability of the operator split computations. The software development strategy of direct linking the (existing) codes for each sub-system via Component Template Library (CTL) is shown to be perfectly suitable for the proposed approach.

Keywords

coupled thermomechanical system; operator split procedure; nonlinear stability analysis; multiscale in time; code-coupling via CTL;

Citations & Related Records

- Reference

1 | Niekamp, R., Krosche, M. and Matthies, H.G. (2003), Platon: A problem solving environment for computational steering of evolutionary optimisation on the grid, (Eds., Bugeda, G. et al.), EUROGEN. |

2 | Matthies, H.G., Niekamp, R. and Steindorf, J. (2006), "Algorithms for strong coupling procedures", Comput. Method. Appl. M., 195(17-18), 2028-2049. DOI |

3 | Matthies, H.G. and Steindorf, J. (2003), "Partitioned strong coupling algorithms for fluid-structure interaction", Comput. Struct., 81(8-11), 805-812. DOI |

4 | Niekamp, R. (2001), Ctl-homepage, http://www.wire.tu-bs.de/ forschung/ projekte/ ctl/e-ctl.html. |

5 | Niekamp, R., Markovic, D., Ibrahimbegovic, A., Matthies, H.G. and Taylor, R.L. (2009), "Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior.part ii: software coupling and implementation aspects", Int. J. Eng. Comput., 26, 6-28. |

6 | Oden, J.T., Belytschko, T., Babuska, I. and Hughes, T.J.R. (2003), "Research directions in computational mechanics", Comput. Method. Appl. M., 192(7-8), 913-922. DOI |

7 | Oden, J.T., Prudhomme, S. and Bauman, P. (2005), "On the extension of goal-oriented error estimation and hierarchical modeling to discrete lattice models", Comput. Method. Appl. M., 194(34-35), 3668-3688. DOI ScienceOn |

8 | Owen, D.R.J. and Hinton, E. (1980), .Finite element method in plasticity, Pineridge Press, Swansea. |

9 | Simo, J.C., Kennedy, J. and Govindjee, S. (1988), "Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms", Int. J. Numer. Meth. Eng., 26(10), 2161-2185. DOI |

10 | Zienkiewicz, O.C. and Taylor, R.L. (2000), The finite element method, Butterworth-Heinemann, Oxford, 5th Ed. |

11 | Ibrahimbegovic, A., Niekamp, R., Kassiotis, C., Markovic, D. and Matthies, H.G. (2014), "Code-coupling strategy for efficient development of computer software in multiscale and multiphysics nonlinear evolution problems in computational mechanics", Adv. Eng. Softw., in press. |

12 | Ibrahimbegovic, A. and Frey, F. (1994), "Stress resultant geometrically nonlinear shell theory with drilling rotations. Part III: Linearized kinematics", Int. J. Numer. Meth. Eng., 37(21), 3659-3683. DOI |

13 | Ibrahimbegovic, A. and Markovic, D. (2003), "Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures", Comput. Method. Appl. M., 192(28-30), 3089-3107. DOI ScienceOn |

14 | Ibrahimbegovic, A. and Matthies, H.G. (2012), "Probabilistic multiscale analysis of inelastic localized failure in solid mechanics", Comput. Assist. Method. Eng. Sci., 19, 277-304. |

15 | Ibrahimbegovic, A., Taylor, R.L. and Wilson, E.L. (1990), "A robust quadrilateral menbrane finite-element with drilling degrees of freedom", Int. J. Numer. Meth. Eng., 30(3), 445-457. DOI |

16 | Krosche, M. and Matthies, H.G. (2008), "Component-based software realisations of Montecarlo and stochastic galerkin methods", PAMM, 8(1), 10765-10766. DOI ScienceOn |

17 | Ibrahimbegovic, A., Taylor, R.L. and Lim, H. (2003), "Non-linear dynamics of flexible multibody systems", Comput. Struct., 81(12), 1113-1132. DOI ScienceOn |

18 | Kassiotis, C., Ibrahimbegovic, A., Niekamp, R. and Matthies, H. (2001a), "Partitioned solution to nonlinear fluid-structure interaction problems.part i: implicit coupling algorithms and stability proof", Comput. Mech., 47, 305-323. |

19 | Kassiotis, C., Ibrahimbegovic, A., Niekamp, R. and Matthies, H. (2011b), "Partitioned solution to nonlinear fluid-structure interaction problems.part ii: Ctl based software implementation with nested parallelization", Comput. Mech., 47, 335-357. |

20 | Ladeveze, P. (2005), Multiscale computational damage modelling of laminate composites, CISM course, (Ed. Sadowski, T.). |

21 | Langtangen, H.P. (2008), Python scripting for computational science, Springer, Berlin. |

22 | Markovic, D., Niekamp, R., Ibrahimbegovic, A., Matthies, H.G. and Taylor, R.L. (2005), "Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior.part i: mathematical and physical aspects", Int. J. Eng. Comput., 22, 664-683. |

23 | Felippa, C.A. and Park, K.C. (2004), Synthesis tools for structural dynamics and partitioned analysis of coupled systems. In Multi-physics and multi-scale computers models in non-linear analysis and optimal design, pages 50-111, Bled, Slovenia, IOS Press (Eds., Ibrahimbegovic, A. and Brank, B.). |

24 | Hughes, T.J.R.(2005), "Multiscale phenomena: Green functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods", Comput. Method. Appl. M., 127, 387-401. |

25 | Feyel, F. and Chaboche, J.L. (2000), "Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials", Comput. Method. Appl. M., 183, 309-330. DOI ScienceOn |

26 | Gear, G.W. (1971), Numerical initial value problems in ordinary differential equations, Prentice-Hall, Englewood Cliffs N.J. |

27 | Hautefeuille, M., Ibrahimbegovic, A., Matthies, H. and Villon, P. (2012), "Multiscale approach to modeling inelastic behavior with softening", Comput. Struct., 94-95, 83-95. DOI |

28 | Ibrahimbegovic, A. (1994), "Stress resultant geometrically nonlinear shell theory with drilling rotations. Part I: a consistent formulation", Appl. Mech. Eng., 114, 311-332. |

29 | Ibrahimbegovic, A. (2006), Nonlinear computational solid mechanics: theoretical formulation and finite element computations, Hermes-Science Publication, Paris, (in French). |

30 | Ibrahimbegovic, A. (2009), Nonlinear solid mechanics: theoretical formulation and finite element solution methods, Springer, Berlin. |

31 | Ibrahimbegovic, A. and Brank, B. (2005), Multi-physics and multi-scale computer models in nonlinear analysis and optimal design of engineering structures under extreme conditions, IOS Press, Amsterdam. |

32 | Ibrahimbegovic, A., Colliat, J.B. and Davenne, L. (2005), "Thermomechanical coupling in folded plates and non-smooth shells", Comput. Method. Appl. M., 194(21-24), 2686-2707. DOI ScienceOn |

33 | Bindel, D. (2011), Matfeap, http://www.cs.cornell.edu/ bindel/sw/matfeap/. |

34 | Birken, P., Quint, K., Hartmann, S. and Meister, A. (2010), "Choosing norms in adaptive fsi calculations", PAMM, 10(1), 555-556. DOI |

35 | Arnold, M. and Gunther, M. (2001), "Preconditioned dynamic iteration for coupled differential-algebraic systems", BIT Numer. Math., 41(1), 1-25. |

36 | Bathe, K.J. (1996), Finite element procedures, Prentice Hall, Englewood Cliffs. |

37 | Chorin, A.J., Hughes, T.J.R., McCracken, M.F. and Marsden, J.E. (1978), "Product formulas and numerical algorithms", Commun. Pur. Appl. Math., 31(2), 205-296. DOI |

38 | Ciarlet, P.G., Miara, B. and Thomas, J.M. (1989), Introduction to numerical lnear algebra and optimisation, Cambridge University Press, Cambridge. |

39 | Colliat, J.B., Ibrahimbegovi, A. and Davenne, L. (2006), "Heat conduction and radiative heat exchange in cellular structures using _at shell elements", Commun. Numer. Meth. En., 22, 167-180. |

40 | Dennis, J.E. and Schnabel, R.B. (1996), Numerical methods for unconstrained optimization and nonlinear equations, SIAM - Society for Industrial and Applied Mathematics, Philadelphia. |

41 | Dubois-Pelerin, Y. and Pegon, P. (1998), "Object-oriented programming in nonlinear finite element analysis", Comput. Struct., 67(4), 225-241. DOI |

42 | Dubois-Pelerin, Y., Zimmerman, T. and Bomme, P. (1992), "Object-oriented finite element programming: II prototype programme in smalltalk", Comput Method. Appl. M., 98(3), 361-397. DOI |

43 | Ibrahimbegovic, A. and Chorfi, L. (2002), "Covariant principal axis formulation of associated coupled thermoplasticity at finite strains and its numerical implementation", Int. J. Solids Struct., 39(2), 499-528. DOI ScienceOn |

44 | Armero, F. and Simo, J.C. (1993), "A priori stability estimates and unconditionally stable product formula algoritms for nonlinear coupled thermoplasticity", Int. J. Plasticity, 9(6), 749-782. DOI ScienceOn |

45 | Golub, G.H. and Van Loan, C. (1983), Matrix computations, Johns Hopkins University Press. |

46 | Eyheramendy, D. and Gudin-Dardun, F. (2008), Object-oriented finite elements: from smalltalk to java, Trends in Eng. Comp. Technology (Eds., Papadrakakis, M. and Topping, B.H.V.). |

47 | Farhat, C., Park, K.C. and Dubois-Pelerin, Y. (1991), "An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problem", Int. J. Numer. Meth. Eng., 85(3), 349-365. |

48 | Armero, F. and Simo, J.C. (1992), "A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems", Int. J. Numer.Meth. Eng., 35(4), 737-766. DOI |

49 | Brenan, K.E., Cambell, S.L. and Petzold, L.R. (1996), Numerical solution of initial-value problem in differential-algebraic equations, SIAM - Society for Industrial and Applied Mathematics, Philadelphia. |