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Structural and Multidisciplinary Optimization

, Volume 60, Issue 5, pp 2131–2156 | Cite as

An investigation on design of signs in composite laminates to control bending-twisting coupling effects using sign optimization algorithm

  • Zhao JingEmail author
  • Jianqiao ChenEmail author
Research Paper
  • 151 Downloads

Abstract

A sign optimization algorithm (SOA) is proposed to design the “±” signs in composite laminates to control the bending-twisting coupling effects. Owing to that the bending-twisting coupling stiffness are cubic on thickness, the innovation is to design the signs of ply orientations from the mid-plane to the outermost sequentially and iteratively. In this manner, the nondimensional anisotropic coefficients are controlled to the target values. Numerical examples are adopted to verify the effectiveness and efficiency of SOA. First, the signs of symmetric laminates [θ32]s are optimized with various boundaries, load ratios, and aspect ratios to show the bending-twisting coupling effects on bending, buckling, and vibration responses of composite plates. Second, the bending-twisting coupling effects are minimized since they may cause large errors in buckling load prediction when using closed-form solution after neglecting them. Third, the optimal sequences obtained from heuristic algorithms are employed for sign optimization. Results show that the bending-twisting coupling effects cannot be neglected; moreover, the buckling and vibration performances can be further improved by redesigning “±” signs in composite laminates. This research aims to provide a design technique to minimize the error induced by bending-twisting coupling and increase the probability to find the global optimum.

Keywords

Sign optimization algorithm Composite laminates Bending-twisting coupling Bending Buckling Vibration 

Notes

Acknowledgments

This work is supported by the Project funded by the National Natural Science Foundation of China (No. 11572134) and the Project funded by China Postdoctoral Science Foundation (No. 2017M612443).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

158_2019_2315_MOESM1_ESM.pdf (264 kb)
ESM 1 (PDF 263 kb)
158_2019_2315_MOESM2_ESM.pdf (788 kb)
ESM 2 (PDF 787 kb)

References

  1. An H, Chen S, Huang H (2015) Laminate stacking sequence optimization with strength constraints using two-level approximations and adaptive genetic algorithm. Struct Multidiscip Optim 51(4):903–918Google Scholar
  2. An H, Chen S, Huang H (2018) Multi-objective optimization of a composite stiffened panel for hybrid design of stiffener layout and laminate stacking sequence. Struct Multidiscip Optim 57:1411–1426 1-16MathSciNetGoogle Scholar
  3. Baucke A, Mittelstedt C (2015) Closed-form analysis of the buckling loads of composite laminates under uniaxial compressive load explicitly accounting for bending–twisting-coupling. Compos Struct 128:437–454Google Scholar
  4. Cho M, Rhee SY (2004) Optimization of laminates with free edges under bounded uncertainty subject to extension, bending and twisting. Int J Solids Struct 41(1):227–245zbMATHGoogle Scholar
  5. Erdal O, Sonmez FO (2005) Optimum design of composite laminates for maximum buckling load capacity using simulated annealing. Compos Struct 71(1):45–52Google Scholar
  6. Ferreira AJM (2008) Matlab codes for finite element analysis: solids and structures. Springer, LondonGoogle Scholar
  7. Fukunaga H (1994) A laminate design for elastic properties of symmetric laminates with extension-shear or bending-twisting coupling. J Compos Mater 28(8):708–731Google Scholar
  8. Fukunaga H, Sekine H, Sato M, Lino A (1995) Buckling design of symmetrically laminated plates using lamination parameters. Comput Struct 57(4):643–649zbMATHGoogle Scholar
  9. Grenestedt JL (1989a) A study on the effect of bending-twisting coupling on buckling strength. Compos Struct 12(4):271–290Google Scholar
  10. Grenestedt JL (1989b) Layup optimization and sensitivity analysis of the fundamental eigenfrequency of composite plates. Compos Struct 12(3):193–209Google Scholar
  11. Grenestedt JL (1990) Composite plate optimization only requires one parameter. Struct Multidiscip Optim 2(1):29–37Google Scholar
  12. Grenestedt JL (1991) Layup optimization against buckling of shear panels. Struct Multidiscip Optim 3(2):115–120Google Scholar
  13. Grenestedt JL, Gudmundson P (1993) Layup optimization of composite material structures. Optimal design with advanced materials. Elsevier Science Publishers, Amsterdam, pp 311–336Google Scholar
  14. Haftka RT, Walsh JL (1992) Stacking-sequence optimization for buckling of laminated plates by integer programming. AIAA J 30(3):814–819Google Scholar
  15. Hao P, Yuan X, Liu H et al (2017) Isogeometric buckling analysis of composite variable-stiffness panels. Compos Struct 165:192–208Google Scholar
  16. Hao P, Yuan X, Liu C, Wang B, Liu H, Li G, Niu F (2018a) An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels. Comput Methods Appl Mech Eng 339:205–238MathSciNetGoogle Scholar
  17. Hao P, Liu C, Liu X, Yuan X, Wang B, Li G, Chen L (2018b) Isogeometric analysis and design of variable-stiffness aircraft panels with multiple cutouts by level set method. Compos Struct 206:888–902Google Scholar
  18. Jensen DW, Lagace PA (1988) Influence of mechanical couplings on the buckling and postbuckling of anisotropic plates. AIAA J 26(10):1269–1277zbMATHGoogle Scholar
  19. Jing Z, Fan XL, Sun Q (2015) Stacking sequence optimization of composite laminates for maximum buckling load using permutation search algorithm. Compos Struct 121(121):225–236Google Scholar
  20. Jing Z, Sun Q, Silberschmidt VV (2016a) Sequential permutation table method for optimization of stacking sequence in composite laminates. Compos Struct 141:240–252Google Scholar
  21. Jing Z, Sun Q, Silberschmidt VV (2016b) A framework for design and optimization of tapered composite structures part I: from individual panel to global blending structure. Compos Struct 154:106–128.26Google Scholar
  22. Jing Z, Sun Q, Chen JQ, Silberschmidt VV (2018) A framework for design and optimization of tapered composite structures part II: enhanced design framework with a global blending model. Compos Struct 188:531–552Google Scholar
  23. Jones RM (1999) Mechanics of composite materials, 2nd ed. Taylor and Francis, PhiladelphiaGoogle Scholar
  24. Kam TY, Chang RR (1993) Design of laminated composite plates for maximum buckling load and vibration frequency. Comput Methods Appl Mech Eng 106:65–81zbMATHGoogle Scholar
  25. Kicher TP, Mandell JF (1971) A study of the buckling of laminated composite plates. AIAA J 9(4):605–613Google Scholar
  26. Le Riche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31(5):951–956zbMATHGoogle Scholar
  27. Liew KM (1996) Solving the vibration of thick symmetric laminates by reissner/mindlin plate theory and the p-ritz method. J Sound Vib 198(3):343–360Google Scholar
  28. Loughlan J (1999) The influence of bend–twist coupling on the shear buckling response of thin laminated composite plates. Thin-Walled Struct 34(2):97–114Google Scholar
  29. Narita Y (2000) Combinations for the free-vibration behaviors of anisotropic rectangular plates under general edge conditions. Am Soc Mech Eng 67(3):568–573MathSciNetzbMATHGoogle Scholar
  30. Narita Y (2003) Layerwise optimization for the maximum fundamental frequency of laminated composite plates. J Sound Vib 263:1005–1016Google Scholar
  31. Nemeth MP (1986) Importance of anisotropy on buckling of compression-loaded symmetric composite plates. AIAA J 24(11):1831–1835Google Scholar
  32. Nemeth MP (1992a) Buckling Behavior of Long Symmetrically Laminated Plates Subjected to Combined Loadings. NASA Technical Paper 3195. NASA, Washington, D.C.Google Scholar
  33. Nemeth MP (1992b) Buckling of symmetrically laminated plates with compression, shear and in-plane bending. AIAA J 30:2959–2965Google Scholar
  34. Sadr MH (2012) Optimization of laminated composite plates for maximum fundamental frequency using elitist-genetic algorithm and finite strip method. J Glob Optim 54(4):707–728MathSciNetzbMATHGoogle Scholar
  35. Selyugin S (2013) On choice of optimal anisotropy of composite plates against buckling, with special attention to bending-twisting coupling. Struct Multidiscip Optim 48(2):279–294MathSciNetGoogle Scholar
  36. Shirk MH, Hertz TJ, Weisshaar TA (1986) Aeroelastic tailoring - theory, practice, and promise. J Aircr 23(1):6–18Google Scholar
  37. Stone MA, Chandler HD (1996) Errors in double sine series solutions for simply supported symmetrically laminated plates. Int J Mech Sci 38(38):517–526zbMATHGoogle Scholar
  38. Thai CH, Nguyen-Xuan H, Nguyen-Thanh N et al (2012) Static, free vibration, and buckling analysis of laminated composite Reissner mindlin plates using NURBS-based isogeometric approach. Int J Numer Methods Eng 91:571–603MathSciNetzbMATHGoogle Scholar
  39. Tiwari N, Hyer MW (2002) Secondary buckling of compression-loaded composite plates. AIAA J 40(10):2120–2126Google Scholar
  40. Walker M, Adali S, Verijenko V (1996) Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling. Comput Struct 58(2):313–319zbMATHGoogle Scholar
  41. Weaver PM, Nemeth MP (2008) Improved design formulas for buckling of orthotropic plates under combined loading. AIAA J 46(9):2391–2396Google Scholar
  42. Weaver PM, Nemeth MP et al (2007) Bounds on flexural properties and buckling response for symmetrically laminated composite plates. J Eng Mech 133(11):1178–1191Google Scholar
  43. York CB (2017) On bending-twisting coupled laminates. Compos Struct 160:887–900Google Scholar
  44. York CB, Almeida SFMD (2018) Effect of bending-twisting coupling on the compression and shear buckling strength of infinitely long plates. Compos Struct 184:18–29Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina

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