Skip to main content

Advertisement

Log in

Multi-objective optimal design of laminated composite skirt using hybrid NSGA

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In this paper a new hybridised version of non-dominated sorting genetic algorithm (NSGA) is proposed to solve combinatorial optimisation problems associated with laminated composite structures. The proposed algorithm is used to optimise the design of hybrid laminated fibre composite skirt of solid rocket motor, subjected to a buckling strength constraint and an overstressing strength constraint under aerodynamic torque and axial thrust. The present investigations involve in determining the best laminate configuration to minimise the weight as well as cost of the skirt through multi-objective optimisation. Buckling strength and overstressing strength of the composite cylindrical skirt are analysed using classical laminate theory. Tsai-Wu failure criterion is employed to assess the first ply failure, and failure strength is described by an overstressing load level factor. The superiority of the proposed hybrid algorithm is demonstrated by comparing with the originally proposed NSGA algorithm. The studies presented in this paper clearly indicate that the proposed modification to the NSGA improves the convergence properties quite appreciably.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Callahan KJ, Weeks GE (1992) Optimum design of composite laminates using genetic algorithms. Composites, Part B, Eng 2:149–160

    Article  ADS  Google Scholar 

  2. Le Riche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximisation by genetic algorithm. AIAA J 31(5):951–956

    Article  ADS  MATH  Google Scholar 

  3. Bert CW (1997) Optimal design of composite material plates to maximise its fundamental frequency. J Sound Vib 50:229–237

    Article  ADS  Google Scholar 

  4. Reiss R, Ramachandran S (1987) Maximum frequency design of symmetric angle-ply laminates. Compos Struct 100:476–487

    Google Scholar 

  5. Adali S (1995) Lay-up optimization of laminated plates under buckling loads. In: Turvey GJ, Marshall IH (eds) Buckling and post buckling of composite plates. Chapman & Hall, London

    Google Scholar 

  6. Venkataraman S, Haftka R (1999) Optimization of composite panels-a review. In: Proceedings of the American Society of Composites—14th annual technical conference, Fairborn, OH, pp 479–488

  7. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  8. Messac A (1996) Physical programming: effective optimization for computational design. AIAA J 34(1):149–158

    Article  ADS  MATH  Google Scholar 

  9. Sen P, Yang JB (1998) Multiple criteria decision support in engineering design. Springer, London

    Book  Google Scholar 

  10. Chankong V, Haimes YY (1983) Multi-objective decision making theory and methodology, vol 4. Elsevier Science, New York

    Google Scholar 

  11. Kumar N, Tauchert TR (1992) Multi-objective desing of symmetrically laminated plates. Journal of Mechanical Design 114(4):620–625

    Article  Google Scholar 

  12. Adali S, Walker M, Verijenko VE (1996) Multi-objective optimization of laminated plates for maximum pre buckling, buckling and post buckling strengths using continuous and discrete ply angles. Composite Structures 35(1):117–130

    Article  Google Scholar 

  13. Walker M, Reiss T, Adali S (1997) Multi-objective design of laminated cylindrical shells for maximum torsional and axial buckling loads. Comput Struct 62:237–242

    Article  MATH  Google Scholar 

  14. Walker M, Smith R (2003) A technique for the multi-objective optimization of laminated composite structures using genetic algorithms and finite element analysis. Compos Struct 62:123–128

    Article  Google Scholar 

  15. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: Improving the strength Pareto evolutionary algorithm. Tech Rep 103, Computer Engineering and Networks Laboratory (TIK). Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

  16. Knowles J, Corne D (1999) The Pareto archived evolution strategy: a new baseline algorithm for multi-objective optimization. In: Proceedings of the 1999 congress on evolutionary computation. IEEE Press, Piscataway, pp 99–105

    Google Scholar 

  17. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  18. James FF (1970) Structural design and analysis of filament wound rocket motor cases. Technical Report, AD876829

  19. Maheshwari M, Grover RL (1983) Development of advanced composite rocket motor case for internal and external load environments. Technical Report, AIAA-Paper-84-1352

  20. Hoffman HJ (1983) Kevlar rocket motor cases. CPIA Report CPTR-83-21

  21. Peters ST, Humphrey WD, Foral RF (1999) Filament windings-composite structure fabrication. SAMPE Press, Covina

    Google Scholar 

  22. Francis M (1993) Design, manufacture and test of composite case for ERINT-1 solid rocket motor. In: AIAA/SAE/ASME/ASEE 19th joint propulsion conference and exhibit

  23. Nshanian YS, Pappas M (1983) Optimal laminated composite shells for buckling and vibration. AIAA J 21:430–437

    Article  ADS  MATH  Google Scholar 

  24. Onoda J (1985) Optimal laminate configurations of cylindrical shells for axial buckling. AIAA J 23:1093–1098

    Article  ADS  Google Scholar 

  25. Sun G, Hansen JS (1988) Optimal design of laminated-composite circular-cylindrical shells subjected to combined loads. J Appl Mech 55:136–142

    Article  MATH  Google Scholar 

  26. Sun G (1989) A practical approach to optimal design of laminated cylindrical shells for buckling. Compos Sci Technol 36:243–253

    Article  Google Scholar 

  27. Zimmermann R (1995) Quick optimum buckling design of axially compressed, fiber composite cylindrical shells. AIAA J 33:1993–1995

    Article  ADS  MATH  Google Scholar 

  28. Xie YJ, Yan HG, Liu ZM (1996) Buckling optimization of hybrid-fiber multilayer-sandwich cylindrical shells under external lateral pressure. Compos Sci Technol 56:1349–1353

    Article  Google Scholar 

  29. Walker M, Reiss T, Adali S (1997) Minimum weight design of composite hybrid shells via symbolic computation. J Franklin Inst 334B:47–56

    Article  MATH  Google Scholar 

  30. Tripathy B, Rao KP (1993) Stiffened composite axisymmetric shells-optimum layup for buckling by ranking. Comput Struct 46:299–309

    Article  ADS  Google Scholar 

  31. Sun G, Hansen JS (1998) Optimal design of laminated composite circular-cylindrical shells subjected to combined load. J Appl Mech 55:136–142

    Article  Google Scholar 

  32. Walker M, Reiss T, Adali S (1997) Multi-objective design of laminated cylindrical shells for maximum torsional and axial buckling loads. Comput Struct 62:237–242

    Article  MATH  Google Scholar 

  33. Smerdov AA (2000) A computational study in optimum formulations of optimization problems on laminated cylindrical shells for buckling I. Shells under axial compression. Compos Sci Technol 60:2057–2066

    Article  Google Scholar 

  34. Smerdov AA (2000) A computational study in optimum formulations of optimization problems on laminated cylindrical shells for buckling II. Shells under external pressure. Compos Sci Technol 60:2067–2076

    Article  Google Scholar 

  35. Adali S, Verijenko VE, Richter A (2001) Minimum sensitivity design of laminated shells under axial load and external pressure. Compos Struct 54:139–142

    Article  Google Scholar 

  36. Rama Mohan Rao A, Lakshmi K (2009) Multi-objective optimal design of hybrid laminated composite structures using scatter search. J Compos Mater 43(20):2157–2181

    Article  Google Scholar 

  37. Rama Mohan Rao A, Lakshmi K (2011) Discrete hybrid PSO algorithm for design of laminate composites with multiple objectives. J Reinf Plast Compos 30(20):1703–1727

    Article  Google Scholar 

  38. Lakshmi K, Rama Mohan Rao A (2012) Multi-objective optimal design of laminate composite shells and stiffened shells. Struct Eng Mech 43(12):771–794

    Article  Google Scholar 

  39. Perera R, Fang SE, Ruiz A (2010) Application of particle swarm optimization and genetic algorithms to multiobjective damage identification inverse problems with modeling errors. Meccanica 45:723–734

    Article  MATH  Google Scholar 

  40. Ghashochi Bargh H, Sadr MH (2012) Stacking sequence optimization of composite plates for maximum fundamental frequency using particle swarm optimization algorithm. Meccanica 47:719–730

    Article  MathSciNet  Google Scholar 

  41. Rama Mohan Rao A, Shyju PP (2011) A new meta-heuristic algorithm for multi-objective optimal design of hybrid laminate composite structures. Comput-Aided Civ Infrastruct Eng 25:149–170

    Google Scholar 

  42. Rama Mohan Rao A, Lakshmi K (2012) Optimal design of stiffened laminate composite cylinder using a hybrid SFLA algorithm. J Compos Mater 46(24):311435674. doi:10.1177/0021998

    Google Scholar 

  43. Rama Mohan Rao A, Arvind N (2005) A scatter search algorithm for stacking sequence optimization of laminated composites. Compos Struct 70(4):383–402

    Article  Google Scholar 

  44. Lahanas M, Baltas D, Zamboglou N (2003) A hybrid evolutionary algorithm for multi-objective anatomy-based dose optimization in high-dose-rate brachytherapy. Phys Med Biol 48:399–415

    Article  Google Scholar 

  45. Gao X, Chen B, He X, Qiu T, Li J, Wang C, Zhang L (2008) Multi-objective optimization for the periodic operation of the naphtha pyrolysis process using a new parallel hybrid algorithm combining NSGA-II with SQP. Comput Chem Eng 32:2801–2811

    Article  Google Scholar 

  46. Deb K (2008) A robust evolutionary framework for multi-objective optimization. In: Proceedings of the 10th annual conference on genetic and evolutionary computation (GECCO’08), 12–16 July, Atlanta, Georgia, USA. ACM, New York, pp 633–640

    Chapter  Google Scholar 

  47. Li M, Zheng J, Wu J (2008) Improving NSGA-II algorithm based on minimum spanning tree. In: Lecture notes in computer science. LNCS, vol 5361. Springer, Berlin, Heidelberg, pp 170–179

    Google Scholar 

  48. Ghomsheh V, Khanehsar MA, Teshnehlab M (2007) Improving the non-dominate sorting genetic algorithm for multi-objective optimization. In: Inter. conf. on computational intelligence and security workshops (CISW 2007), Heilongjiang, China, pp 89–92

  49. Johnson DS, McGeoch LA (1997) The traveling salesman problem: a case study. In: Aarts EH, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 215–310

    Google Scholar 

  50. Jones RM (1975) Mechanics of composite materials. McGraw-Hill, New York

    Google Scholar 

  51. Agarwal BD, Broutman LJ (1990) Analysis and performance of fiber composites, 2nd edn. Wiley, New York

    Google Scholar 

  52. Timoshenko SP, Gere JM (1961) Theory of elastic stability, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  53. Vinson JR (1993) The behaviour of shells composed of isotropic and composite materials. Kluwer, Dordrecht

    Book  Google Scholar 

  54. Grosset L, Venkataraman S, Haftka RT (2001) Genetic optimization of two-material composite laminates. In: Proceedings, 16th ASC technical meeting, Blacksburg, VA, September

  55. Todoroki A, Sasai M (1999) Improvement of design reliability for buckling load maximization of composite cylinder using genetic algorithm with recessive-gene-like repair. JSME Int J Ser A 42(4):530–536

    Article  Google Scholar 

Download references

Acknowledgements

This paper is being published with the permission of the Director, CSIR-SERC, Chennai. This research is supported, in part, by Naval Research Board, New Delhi under the grant DRND/05/4003/NRB/78.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Rama Mohan Rao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lakshmi, K., Rama Mohan Rao, A. Multi-objective optimal design of laminated composite skirt using hybrid NSGA. Meccanica 48, 1431–1450 (2013). https://doi.org/10.1007/s11012-012-9676-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-012-9676-5

Keywords

Navigation