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On the thermoelastic coupling of anisotropic laminates

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Abstract

The analysis of the mathematical and mechanical properties of thermoelastic coupling tensors in anisotropic laminates is the topic of this paper. Some theoretical results concerning the compliance tensors are shown and their mechanical consequences analyzed. Moreover, the case of thermally stable laminates, important for practical applications, is also considered. The study is carried out in the framework of the polar method, a mathematical formalism particularly well-suited for the analysis of planar anisotropic problems, introduced by Prof. G. Verchery in 1979.

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Availability of data and materials:All the data generated or analyzed during this study are included in the paper.

References

  1. Cross, R.J., Haynes, R.A., Armanios, E.A.: Families of hygrothermally stable asymmetric laminated composites. J. Compos. Mater. 42, 697–716 (2008)

    Article  Google Scholar 

  2. Haynes, R.A., Armanios, E.A.: New families of hygrothermally stable composite laminates with optimal extension-twist coupling. AIAA J. 48, 2954–2961 (2010)

    Article  Google Scholar 

  3. Haynes, R.A.: Hygrothermally stable laminated composites with optimal coupling. Technical report, Georgia Institut of Technology (2010)

  4. Haynes, R.A., Armanios, E.A.: The challenge of achieving hygrothermal stability in composite laminates with optimal couplings. Int. J. Eng. Sci. 3, 1–9 (2012)

    Google Scholar 

  5. York, C.B.: Unified approach to the characterization of coupled composite laminates: hygrothermally curvature-stable configurations. Int. J. Struct. Integr. 2(4), 406–436 (2011)

    Article  Google Scholar 

  6. Vannucci, P.: On the mechanical and mathematical properties of the stiffness and compliance coupling tensors of composite anisotropic laminates. J. Compos. Mater. 57(26), 4197–4214 (2023)

    Article  Google Scholar 

  7. Verchery, G.: Les Invariants des Tenseurs D’ordre 4 du Type de L’élasticité. In: Proc. of Colloque Euromech 115 (Villard-de-Lans, 1979): Comportement Mécanique des Matériaux Anisotropes, pp. 93–104. Editions du CNRS, Paris (1982)

  8. Vannucci, P.: Plane anisotropy by the polar method. Meccanica 40, 437–454 (2005)

    Article  MathSciNet  Google Scholar 

  9. Vannucci, P.: Anisotropic elasticity. Springer, Berlin (2018)

    Book  Google Scholar 

  10. Jones, R.M.: Mechanics of composite materials, 2nd edn. Taylor & Francis, Philadelphia, PA (1999)

    Google Scholar 

  11. Vannucci, P.: Tensor algebra and analysis for engineers—with applications to differential geometry of curves and surfaces. World Scientific, Singapore (2023)

    Google Scholar 

  12. Kelvin, W.T.-L.: Elements of a mathematical theory of elasticity. Philos. Trans. R. Soc. 146, 481–498 (1856)

    Article  Google Scholar 

  13. Kelvin, W.T.-L.: Mathematical theory of elasticity. Encycl. Br. 7, 819–825 (1878)

    Google Scholar 

  14. Vannucci, P.: A special planar orthotropic material. J. Elast. 67, 81–96 (2002)

    Article  MathSciNet  Google Scholar 

  15. Tsai, S.W., Hahn, T.: Introduction to composite materials. Technomic, Stamford, CT (1980)

    Google Scholar 

  16. Vannucci, P., Desmorat, B.: Plane anisotropic rari-constant materials. Math. Methods Appl. Sci. 39, 3271–3281 (2016)

    Article  MathSciNet  Google Scholar 

  17. Todhunter, I., Pearson, K.: History of the theory of elasticity, vol. 1. Cambridge University Press, Cambridge (1886)

    Google Scholar 

  18. Love, A.E.H.: A treatise on the mathematical theory of elasticity. Dover, New York, NY (1944)

    Google Scholar 

  19. Benvenuto, E.: An introduction to the history of structural mechanics, vol. 2. Springer, Berlin (1991)

    Book  Google Scholar 

  20. Vannucci, P., Verchery, G.: Anisotropy of plane complex elastic bodies. Int. J. Solids Struct. 47, 1154–1166 (2010)

    Article  Google Scholar 

  21. Kandil, N., Verchery, G.: New methods of design for stacking sequences of laminates. In: Proc. of CADCOMP88—computer aided design in composite materials 88, Southampton, UK, pp. 243–257 (1988)

  22. Vannucci, P.: General theory of coupled thermally stable anisotropic laminates. J. Elast. 113, 147–166 (2013)

    Article  MathSciNet  Google Scholar 

  23. Nye, J.F.: Physical properties of crystals. Clarendon, Oxford (1957)

    Google Scholar 

  24. Vannucci, P., Verchery, G.: Stiffness design of laminates using the polar method. Int. J. Solids Struct. 38, 9281–9294 (2001)

    Article  Google Scholar 

  25. Vannucci, P., Verchery, G.: A special class of uncoupled and quasi-homogeneous laminates. Compos. Sci. Technol. 61, 1465–1473 (2001)

    Article  Google Scholar 

  26. Vannucci, P.: On bending-tension coupling of laminates. J. Elast. 64, 13–28 (2001)

    Article  Google Scholar 

  27. Pressley, A.: Elementary differential geometry. Springer, Berlin (2010)

    Book  Google Scholar 

  28. Vannucci, P., Vincenti, A.: The design of laminates with given thermal/hygral ex-pansion coefficients: a general approach based upon the polar-genetic method. Compos. Struct. 79, 454–466 (2007)

    Article  Google Scholar 

  29. Valot, E., Vannucci, P.: Some exact solutions for fully orthotropic laminates. Compos. Struct. 69, 157–166 (2005)

    Article  Google Scholar 

  30. Vannucci, P.: Designing the elastic properties of laminates as an optimisation problem: a unified approach based on polar tensor invariants. Struct. Multidiscip. Optim. 31, 378–387 (2006)

    Article  MathSciNet  Google Scholar 

  31. Vannucci, P.: ALE-PSO : an adaptive swarm algorithm to solve design problems of laminates. Algorithms 2, 710–734 (2009)

    Article  MathSciNet  Google Scholar 

  32. Vincenti, A., Ahmadian, M.R., Vannucci, P.: BIANCA: a genetic algorithm to solve hard combinatorial optimisation problems in engineering. J. Global Optim. 48, 399–421 (2010)

    Article  MathSciNet  Google Scholar 

  33. Montemurro, M., Vincenti, A., Vannucci, P.: A two-level procedure for the global optimum design of composite modular structures—application to the design of an aircraft wing. Part 1: theoretical formulation. J. Optim. Theory Appl. 155, 1–23 (2012)

    Article  MathSciNet  Google Scholar 

  34. Montemurro, M., Koutsawa, Y., Belouettar, S., Vincenti, A., Vannucci, P.: Design of damping properties of hybrid laminates through a global optimization strategy. Compos. Struct. 94, 3309–3320 (2012)

    Article  Google Scholar 

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Vannucci, P. On the thermoelastic coupling of anisotropic laminates. Arch Appl Mech 94, 1121–1149 (2024). https://doi.org/10.1007/s00419-024-02572-y

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