Multiconstraint Optimization of Composite Structures Manufactured by Resin Transfer Molding Process

Abstract

A simultaneous optimization methodology is proposed considering both the structural and the process requirements for the weight minimization of laminated plates manufactured by the Resin Transfer Molding (RTM) process. The coupling between the structural performance and the process cost is considered through the investigation of state parameters in the RTM process. As the structural constraint, maximum allowable displacement or maximum allowable failure index of the structure under load is assigned. For the process constraint, maximum allowable mold filling time is given. A new approach to deal with design constraints without having to concern about the penalty parameters is suggested. The influence of design constraints on the optimal design configuration is investigated through parametric studies. As the optimization scheme, Genetic Algorithm (GA) is employed. To take into account the layer number variation, genetic operators such as the crossover and the mutation are modified.

Keywords

simultaneous optimization weight minimization Resin Transfer Molding (RTM)Multiconstraint Optimization Genetic Algorithm (GA)

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References

Hinrichsen, J. and Bautista, C. (2001). The Challenge of Reducing Both Airframe Weight and Manufacturing Cost , Air & Space Europe, 3(3-4): 119-121 .

Wang, K. , Kelly, D. and Dutton, S. (2002). Multi-objective Optimisation of Composite Aerospace Structures , Composite Structures, 57: 141-148 .

Jacob, A. (2001). Automotive Composites - The Road Ahead , Reinforced Plastics, 45(6): 28-32 .

Marsh, G. (1999). Process Refinement Key to RTM Success , Reinforced Plastics, 43(2): 26-27 .

Harper, A. (1998). MIT Offers Economic Route to High Volume RTM , Reinforced Plastics, 42(5): 28-29 .

Anon . (2001). RTM Process Cuts Fighter Tail Costs , Reinforced Plastics, 45(2): 15 .

Nardari, C. , Ferret, B. and Gay, D. (2002). Simultaneous Engineering in Design and Manufacture using the RTM Process , Composites: Part A, 33: 191-196 .

Manne, P.M. and Tsai, S.W. (1998). Design Optimization of Composite Plates: Part I - Design Criteria for Strength, Stiffness, and Manufacturing Complexity of Composite Materials , Journal of Composite Materials, 32(6): 544-571 .

Manne, P.M. and Tsai, S.W. (1998). Design Optimization of Composite Plates: Part II - Structural Optimization by Ply Drop Targeting , Journal of Composite Materials, 32(6): 572-598 .

10.

Fine, A.S. and Springer, G.S. (1997). Design of Composite Laminates for Strength, Weight, and Manufacturability , Journal of Composite Materials, 31(23): 2330-2390 .

11.

Kassapoglou, C. (1997). Simultaneous Cost and Weight Minimization of Composite-stiffened Panels under Compression and Shear , Composites: Part A, 28A: 419-435 .

12.

Le Riche, R. and Haftka, R.T. (1995). Improved Genetic Algorithm for Minimum Thickness Composite Laminated Design , Composites Engineering, 5(2): 143-162 .

13.

Barlow, D. , Howe, C. , Clayton, G. and Brouwer, S. (2002). Preliminary Study on Cost Optimization of Aircraft Composite Structures Applicable to Liquid Moulding Technologies , Composite Structures, 57: 53-57 .

14.

Young, W.-B. (1994). Gate Location Optimization in Liquid Composite Molding using Genetic Algorithms , Journal of Composite Materials, 28(12): 1098-1113 .

15.

Smith, D.E. , Tortorelli, D.A. and Tucker III, C.L. (1998). Analysis and Sensitivity Analysis for Polymer Injection and Compression Molding , Computer Methods in Applied Mechanics and Engineering, 167: 325-344 .

16.

Marther, R. , Fink, B.K. and Advani, S.G. (1999). Use of Genetic Algorithms to Optimize Gate and Vent Locations for the Resin Transfer Molding Process , Polymer Composites, 20(2): 167-178 .

17.

Lin, M.Y. , Murphy, M.J. and Hahn, H.T. (2000). Resin Transfer Molding Process Optimization , Composites: Part A, 31: 361-371 .

18.

Saravanos, D.A. and Chamis, C.C. (1992). Multi-objective Shape and Material Optimization of Composite Structures including Damping , AIAA Journal, 30(3): 805-813 .

19.

Watkins, R.I. and Morris, A.J. (1987). A Multi-criteria Objective Function Optimization Scheme for Laminated Composites for Use in Multilevel Structural Optimization Schemes , Computer Methods in Applied Mechanics and Engineering, 60: 233-251 .

20.

Fonseca, C.M. and Fleming, P.J. (1998). Multi-objective Optimization and Multiple Constraint Handling with Evolutionary Algorithms - Part I: A Unified Formulation , IEEE Transaction on Systems, Man, and Cybernetics - Part A: Systems and Humans, 28(1): 26-37 .

21.

Koski, J. and Silvennoinen, R. (1987). Norm Methods and Partial Weighting in Multi-criterion Optimization of Structures , International Journal for Numerical Methods in Engineering, 24: 1101-1124 .

22.

Liu, B. , Haftka, R.T. , Akgun, M.A. and Todoroki, A. (2000). Permutation Genetic Algorithm for Stacking Sequence Design of Composite Laminates , Computer Methods in Applied Mechanics and Engineering, 186: 357-372 .

23.

Todoroki, A. and Haftka, R.T. (1998). Stacking Sequence Optimization by a Genetic Algorithm with a New Recessive Gene Like Repair Strategy , Composites: Part B, 29B: 277-285 .

24.

Potgieter, E. and Stander, N. (1998). The Genetic Algorithm Applied to Stiffness Maximization of Laminated Plates: Review and Comparison , Structural Optimization, 15: 221-229 .

25.

Muc, A. and Gurba, W. (2001). Genetic Algorithms and Finite Element Analysis in Optimization of Composite Structures , Composites Structures, 54: 275-281 .

26.

Soremekun, G. , Gurdal, Z. , Haftka, R.T. and Watson, L.T. (2001). Composite Laminate Design Optimization by Genetic Algorithm with Generalized Elitist Selection , Computers and Structures, 79: 131-143 .

27.

Le Riche, R. and Haftka, R.T. (1993). Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm , AIAA Journal, 31(5): 951-956 .

28.

28. Darcy, H. (1856). Les fontaines publiques de la ville de dijon, Delmont, Paris.

29.

29. Kozeny, J. (1927). Sitzungsber. Wiener Akad. Wiss., Abt Ila, 136.

30.

Carman, P.C. (1937). Fluid Flow through Granular Beds , Trans. Inst. Chem. Eng., 15: 157-182 .

31.

Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley .

32.

Chen, C.L. and Chang, M.H. (1993). An Enhanced Genetic Algorithm, European Congress on Fuzzy and Intelligent Technologies, EUFIT (1993), Arhen, Germany, Sep. 7-10, 1993.

33.

De Jong, K.A. (1976). An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Ph.D. Thesis of University of Michigan , USA, Dissertation Abstracts International, 36(10): 5140B (University Microfilms No. 76-9381).

34.

34. Eyraud, G. (1995). Programme par elements finis d’aide a la conception des plaques stratifiees et sandwich base sur une methode de reanalyse, Ph.D. Thesis, L’Universite Claude Bernard - Lyon I, France.

35.

35. Kang, M.K. (1997). A Numerical and Experimental Study on Mold Filling and Void Formation during Resin Transfer Molding, Ph.D. Thesis of Seoul National University, Korea.

36.

Hirt, C.W. and Nichols, B.D. (1981). Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries , Journal of Computational Physics, 39: 201-225 .

37.

Baliga, B.R. and Patankar, S.V. (1998). Handbook of Numerical Heat Transfer, John Wiley & Sons, Inc. , pp. 421-461.

38.

Halpin, J.C. and Tsai, S.W. (1969). Effects of Environmental Factors on Composite Materials, AFML-TR, 67-423.

39.

Tsai, S.W. and Hahn, H.T. (1980). Introduction to Composite Materials, Technomic Publishing Company, Inc.

40.

Jones, R.M. (1975). Mechanics of Composite Materials, McGraw-Hill, New York.

41.

Advani, S.G. (ed.) (1994). Flow and Rheology in Polymer Composites Manufacturing, Elsevier Science .

42.

Scheidegger, A.E. (1974). Physics of Flow through Porous Media, 3rd edn, University of Toronto Press, Toronto .

43.

Boccard, A. , Lee, W.I. and Springer, G.S. (1995). Model for Determining the Vent Locations and the Fill Time of Resin Transfer molds , Journal of Composite Materials, 29(3): 306-333 .

44.

Chan, A.W. , Larive, D.E. and Morgan, R.J. (1993). Anisotropic Permeability of Fiber Preforms: Constant Flow Rate Measurement , Journal of Composite Materials, 27(10): 996-1008 .