Compression moulding simulations of SMC using a multiobjective surrogate-based inverse modeling approach

  • B. D. Marjavaara
  • S. Ebermark
  • T. S. Lundström

A multiobjective surrogate-based inverse modeling technique to predict the spatial and temporal pressure distribution numerically during the fabrication of sheet moulding compounds (SMCs) is introduced. Specifically, an isotropic temperature-dependent Newtonian viscosity model of a SMC charge is fitted to experimental measurements via numerical simulations in order to mimic the temporal pressure distribution at two spatial locations simultaneously. The simulations are performed by using the commercial computational fluid dynamics (CFD) code ANSYS CFX-10.0, and the multiobjective surrogate-based fitting procedure proposed is carried out with a hybrid formulation of the NSGA-IIa evolutionary algorithm and the response surface methodology in Matlab. The outcome of the analysis shows the ability of the optimization framework to efficiently reduce the total computational load of the problem. Furthermore, the viscosity model assumed seems to be able to re solve the temporal pressure distribution and the advancing flow front accurately, which can not be said of the spatial pressure distribution. Hence, it is recommended to improve the CFD model proposed in order to better capture the true behaviour of the mould flow.


thermo setting resin computational modeling compression moulding resin flow 


  1. 1.
    H. G. Kia, Sheet Moulding Compounds: Science and Technology, Hanser Verlag, Munich (1993).Google Scholar
  2. 2.
    P. T. Odenberger, H. M. Andersson, and T. S. Lundström, ”Experimental flow-front visualization in compression moulding of SMC,” Composites, Pt. A, 35, No. 10, 1125-1134 (2004).CrossRefGoogle Scholar
  3. 3.
    T. S. Lundström, “Bubble transport through constricted capillary tube with application to resin transfer moulding,” Polym. Compos., 17, 770-779 (1996).CrossRefGoogle Scholar
  4. 4.
    T. S. Lundström, “Measurement of void collapse during resin transfer moulding,” Composites, Pt. A, 28, 201-214 (1997).CrossRefGoogle Scholar
  5. 5.
    M. R. Barone and D. A. Caulk, “Kinematics of flow in sheet moulding compounds,” Polym. Compos., 6, No. 2, 105-109 (1985).CrossRefGoogle Scholar
  6. 6.
    T. A. Osswald and C. L. Tucker, “Compression mold filling simulation for non-planar parts,” Int. Polym. Proc., 2, 79-87 (1990).Google Scholar
  7. 7.
    P. K. Mallick, “Compression molding,” in: P. K. Mallick and S. Newman (eds.), Composite Materials Technology —Processes and Properties, Hanser Publishers, Munich–Vienna–New York (1990), pp. 67-102.Google Scholar
  8. 8.
    T. A. Osswald and S.-C. Tseng, ”Compression molding,” in: S. G. Advani (ed.), Flow and Rheology in Polymer Com osites Manufacturing, Composite Materials Series. Vol. 10, Elsevier (1994), pp. 361-413.Google Scholar
  9. 9.
    W. Michaeli, M. Mahlke, T. A. Osswald, and M. N. Nölke, ”Simulation of the flow in SMC,” Kunstst. Germ. Plast., 80, No. 6, 31-33 (1990).Google Scholar
  10. 10.
    P. T. Odenberger and T. S. Lundström, “Inverse modelling of compression moulding of SMC with us age of computational fluid dynamics,” in: Proc. ICCM-15 Conf., Durban, South Africa, June 27-July 1 (2005).Google Scholar
  11. 11.
    B. D. Marjavaara, T. S. Lundström, T. Goel, Y. Mack, and W. Shyy, “Hydraulic turbine diffuser shape optimization by multiple surrogate model approximations of Pareto fronts,” J. Fluids Eng., 129, No. 9, 1228-1240.Google Scholar
  12. 12.
    N. V. Queipo, R. T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, and P. K. Tucker, “Surrogate-based analysis and optimization,” Prog. Aerosp. Sci., 41, No. 1, 1-28 (2005).CrossRefGoogle Scholar
  13. 13.
    H. A. Barnes, J. F. Hutton, and K. Walters, An Introduction to Rheology, Elsevier, Amsterdam (1989).Google Scholar
  14. 14.
    C. C. Lee and C. L. Tucker, “Flow and heat transfer in compression mold filling,” J. Non-New ton. Fluid Mech., 24, No. 3, 245-264 (1987).CrossRefGoogle Scholar
  15. 15.
    A. Tarantola, Inverse Problem Theory, Elsevier, Amsterdam (1987).Google Scholar
  16. 16.
    I. B. Celik and O. Karatekin, “Numerical experiments on application of Richard son extrapolation with non uniform grids,” J. Fluids Eng., 119, No. 3, 584-590 (1997).CrossRefGoogle Scholar
  17. 17.
    Matlab. The Language of Technical Computing, Version 7.0.1. The MathWorks, Inc. Natick, MA (2004).Google Scholar
  18. 18.
    CFX, CFX-5, Version 10.0. ANSYS Europe Ltd., Riseley, UK (2005).Google Scholar
  19. 19.
    T. Goel, R. Vaidyanathan, R. T. Haftka, N. V. Queipo, W. Shyy, and P. K. Tucker, “Response surface approximation of Pareto opt mal front in multi-objective optimization,” Comput. Meth. Appl. Mech., 196, No. 4, 879-893 (2004).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • B. D. Marjavaara
    • 1
  • S. Ebermark
    • 1
  • T. S. Lundström
    • 1
  1. 1.Luleå University of TechnologyLuleåSweden

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