Coupled systems mechanics

  • 제3권1호
  • /
  • Pages.1-25
  • /
  • 2014
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2014.01.12
  • 심사 : 2014.03.30
  • 발행 : 2014.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. 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. https://doi.org/10.1002/nme.1620350408
  2. 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. https://doi.org/10.1016/0749-6419(93)90036-P
  3. Arnold, M. and Gunther, M. (2001), "Preconditioned dynamic iteration for coupled differential-algebraic systems", BIT Numer. Math., 41(1), 1-25.
  4. Bathe, K.J. (1996), Finite element procedures, Prentice Hall, Englewood Cliffs.
  5. Bindel, D. (2011), Matfeap, http://www.cs.cornell.edu/ bindel/sw/matfeap/.
  6. Birken, P., Quint, K., Hartmann, S. and Meister, A. (2010), "Choosing norms in adaptive fsi calculations", PAMM, 10(1), 555-556. https://doi.org/10.1002/pamm.201010270
  7. 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.
  8. 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. https://doi.org/10.1002/cpa.3160310205
  9. Ciarlet, P.G., Miara, B. and Thomas, J.M. (1989), Introduction to numerical lnear algebra and optimisation, Cambridge University Press, Cambridge.
  10. 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.
  11. Dennis, J.E. and Schnabel, R.B. (1996), Numerical methods for unconstrained optimization and nonlinear equations, SIAM - Society for Industrial and Applied Mathematics, Philadelphia.
  12. Dubois-Pelerin, Y. and Pegon, P. (1998), "Object-oriented programming in nonlinear finite element analysis", Comput. Struct., 67(4), 225-241. https://doi.org/10.1016/S0045-7949(98)00054-6
  13. 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. https://doi.org/10.1016/0045-7825(92)90004-4
  14. 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.).
  15. 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.
  16. 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.).
  17. 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. https://doi.org/10.1016/S0045-7825(99)00224-8
  18. Gear, G.W. (1971), Numerical initial value problems in ordinary differential equations, Prentice-Hall, Englewood Cliffs N.J.
  19. Golub, G.H. and Van Loan, C. (1983), Matrix computations, Johns Hopkins University Press.
  20. Hautefeuille, M., Ibrahimbegovic, A., Matthies, H. and Villon, P. (2012), "Multiscale approach to modeling inelastic behavior with softening", Comput. Struct., 94-95, 83-95. https://doi.org/10.1016/j.compstruc.2011.11.007
  21. Hughes, T.J.R.(2005), "Multiscale phenomena: Green$AAA^{TM}s$ functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods", Comput. Method. Appl. M., 127, 387-401.
  22. Ibrahimbegovic, A. (1994), "Stress resultant geometrically nonlinear shell theory with drilling rotations. Part I: a consistent formulation", Appl. Mech. Eng., 114, 311-332.
  23. Ibrahimbegovic, A. (2006), Nonlinear computational solid mechanics: theoretical formulation and finite element computations, Hermes-Science Publication, Paris, (in French).
  24. Ibrahimbegovic, A. (2009), Nonlinear solid mechanics: theoretical formulation and finite element solution methods, Springer, Berlin.
  25. 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.
  26. 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. https://doi.org/10.1016/S0020-7683(01)00221-9
  27. 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. https://doi.org/10.1016/j.cma.2004.07.052
  28. 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. https://doi.org/10.1002/nme.1620372106
  29. 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. https://doi.org/10.1016/S0045-7825(03)00342-6
  30. 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.
  31. 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.
  32. 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. https://doi.org/10.1002/nme.1620300305
  33. Ibrahimbegovic, A., Taylor, R.L. and Lim, H. (2003), "Non-linear dynamics of flexible multibody systems", Comput. Struct., 81(12), 1113-1132. https://doi.org/10.1016/S0045-7949(03)00032-4
  34. 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.
  35. 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.
  36. Krosche, M. and Matthies, H.G. (2008), "Component-based software realisations of Montecarlo and stochastic galerkin methods", PAMM, 8(1), 10765-10766. https://doi.org/10.1002/pamm.200810765
  37. Ladeveze, P. (2005), Multiscale computational damage modelling of laminate composites, CISM course, (Ed. Sadowski, T.).
  38. Langtangen, H.P. (2008), Python scripting for computational science, Springer, Berlin.
  39. 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.
  40. Matthies, H.G., Niekamp, R. and Steindorf, J. (2006), "Algorithms for strong coupling procedures", Comput. Method. Appl. M., 195(17-18), 2028-2049. https://doi.org/10.1016/j.cma.2004.11.032
  41. Matthies, H.G. and Steindorf, J. (2003), "Partitioned strong coupling algorithms for fluid-structure interaction", Comput. Struct., 81(8-11), 805-812. https://doi.org/10.1016/S0045-7949(02)00409-1
  42. Niekamp, R. (2001), Ctl-homepage, http://www.wire.tu-bs.de/ forschung/ projekte/ ctl/e-ctl.html.
  43. 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.
  44. 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.
  45. 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. https://doi.org/10.1016/S0045-7825(02)00616-3
  46. 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. https://doi.org/10.1016/j.cma.2004.08.010
  47. Owen, D.R.J. and Hinton, E. (1980), .Finite element method in plasticity, Pineridge Press, Swansea.
  48. 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. https://doi.org/10.1002/nme.1620261003
  49. Zienkiewicz, O.C. and Taylor, R.L. (2000), The finite element method, Butterworth-Heinemann, Oxford, 5th Ed.

피인용 문헌

  1. Nonlinear instability problems including localized plastic failure and large deformations for extreme thermo-mechanical loads vol.3, pp.1, 2014, https://doi.org/10.12989/csm.2014.3.1.089
  2. Fluid-structure interaction problems solution by operator split methods and efficient software development by code-coupling vol.5, pp.2, 2016, https://doi.org/10.12989/csm.2016.5.2.145
  3. ED-FEM multi-scale computation procedure for localized failure vol.8, pp.2, 2014, https://doi.org/10.12989/csm.2019.8.2.111
  4. Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects vol.7, pp.2, 2014, https://doi.org/10.12989/aas.2020.7.2.169
  5. A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams vol.9, pp.1, 2014, https://doi.org/10.12989/amr.2020.9.1.033
  6. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201