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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures

Abstract

Three-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith we employ a layer-wise approach for multiple (quasi-)homogeneous layers. Every layer is considered separately whereby this disquisition is based on the direct approach for deformable directed surfaces. We limit our considerations to geometrical and physical linearity. In this simple and familiar setting we furnish a layer-wise theory by introducing constraints at interfaces to couple the layers. Hereby we restrict our concern to surfaces where all material points per surface are coplanar and all surfaces are plane parallel. Closed-form solutions of the governing equations enforce a narrow frame since they are strongly restrictive in the context of available boundary conditions. Thus a computational solution approach is introduced using the finite element method. In order to determine the required spatially approximated equation of motion, the principle of virtual work is exploited. The discretization is realized via quadrilateral elements with quadratic shape functions. Hereby we introduce an approach where nine degrees of freedom per node are used. In combination with the numerical solution approach, this layer-wise theory has emerged as a powerful tool to analyze composite structures. In present treatise, we would like to clarify the broad scope of this approach.

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Authors (5)

Details

Category:
Articles
Type:
artykuły w czasopismach
Published in:
Technische Mechanik no. 39, pages 202 - 219,
ISSN: 0232-3869
Language:
English
Publication year:
2019
Bibliographic description:
Aßmus M., Naumenko K., Öchsner A., Eremeev V., Altenbach H.: A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures// Technische Mechanik -Vol. 39,iss. 2 (2019), s.202-219
DOI:
Digital Object Identifier (open in new tab) 10.24352/ub.ovgu-2019-019
Bibliography: test
  1. H. Altenbach and V. Eremeyev. Thin-walled structural elements: Classification, classical and advanced theories, new applications. In H. Altenbach and V. Eremeyev, editors, Shell-like Structures: Advanced Theories and Applications, pages 1-62. 2017. doi: 10.1007/978-3-319-42277-0_1. open in new tab
  2. M. Aßmus. Structural Mechanics of Anti-Sandwiches. An Introduction. SpringerBriefs in Continuum Mechanics. Springer, Cham, 2019. doi: 10.1007/978-3-030-04354-4. open in new tab
  3. M. Aßmus, S. Bergmann, K. Naumenko, and H. Altenbach. Mechanical behaviour of photovoltaic composite structures: A parameter study on the influence of geometric dimensions and material properties under static loading. Composites Communications, 5(-):23-26, 2017a. doi: 10.1016/j.coco.2017.06.003. open in new tab
  4. M. Aßmus, J. Eisenträger, and H. Altenbach. Projector representation of isotropic linear elastic material laws for directed surfaces. Zeitschrift für Angewandte Mathematik und Mechanik, 97(-):1-10, 2017b. doi: 10.1002/zamm.201700122. open in new tab
  5. M. Aßmus, K. Naumenko, and H. Altenbach. Subclasses of mechanical problems arising from the direct approach for homogeneous plates. In H. Altenbach, J. Chróścielewski, V.A. Eremeyev, and K. Wiśniewski, editors, Recent Developments in the Theory of Shells, volume 110 of Advanced Structured Materials, pages 1-20. Springer, Singapore, 2019. doi: 10.1007/978-3-030- 17747-8. open in new tab
  6. E. Carrera. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Archives of Computational Methods in Engineering, 9(2):87-140, 2002. doi: 10.1007/BF02736649. open in new tab
  7. E. Carrera. Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assess- ment and benchmarking. Archives of Computational Methods in Engineering, 10(3):215-296, 2003. doi: 10.1007/BF02736224. open in new tab
  8. A.-L. Cauchy. Recherches sur l'équilibre et le mouvement intérieur des corps solides ou fluides. élastiques ou non élas- tiques, volume 2 of Cambridge Library Collection -Mathematics, pages 300-304. Cambridge University Press, 2009. doi: 10.1017/CBO9780511702518.038. open in new tab
  9. E. Cosserat and F. Cosserat. Théorie des corps déformables. A. Hermann et fils, Paris, 1909. URL http://jhir.library.jhu.edu/ handle/1774.2/34209. open in new tab
  10. J. Eisenträger, K. Naumenko, H. Altenbach, and J. Meenen. A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory. Composite Structures, 133:265-277, 2015. ISSN 0263-8223. doi: 10.1016/j.compstruct.2015.07.049. open in new tab
  11. J.-F. Ganghoffer. Cosserat, Eugène and François, pages 1-6. Springer, Berlin, Heidelberg, 2017. doi: 10.1007/978-3-662- 53605-6_49-1. open in new tab
  12. E. Hinton, D. R. J. Owen, and G. Krause. Finite Elemente Programme für Platten und Schalen. Berlin • Heidelberg, 1990. doi: 10.1007/978-3-642-50182-1. open in new tab
  13. R. Hooke. Lectures de Potentia restitutiva, or of Spring explaining the power of springing bodies. John Martyn, London, 1678. URL http://data.onb.ac.at/rep/103F4578. open in new tab
  14. G. R. Kirchhoff. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik, 40:51-88, 1850. doi: 10.1515/crll.1850.40.51. open in new tab
  15. G. Lamé. Leçons sur la théorie mathématique de l'elasticité des corps solides. Gauthier-Villars, Paris, 1866.
  16. A. Libai and J. G. Simmonds. Nonlinear elastic shell theory. Advances in Applied Mechanics, 23:271-371, 1983. doi: 10.1016/S0065-2156(08)70245-X. open in new tab
  17. R. D. Mindlin. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 18:31-38, 1951. open in new tab
  18. M. Naghdi. The Theory of Shells and Plates. In W. Flügge, editor, Encyclopedia of Physics -Linear Theories of Elasticity and Thermoelasticity, volume VI, a/2 (ed. C. Truesdell), pages 425-640. Springer, Berlin • New York, 1972. doi: 10.1007/978-3- 662-39776-3_5. open in new tab
  19. K. Naumenko and V. A. Eremeyev. A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures, 112: 283-291, 2014. doi: 10.1016/j.compstruct.2014.02.009. open in new tab
  20. W. Noll. A mathematical theory of the mechanical behavior of continuous media. Archive for Rational Mechanics and Analysis, 2(1):197-226, 1958. doi: 10.1007/BF00277929. open in new tab
  21. E. Oñate. Structural Analysis with the Finite Element Method Linear Statics: Volume 2. Beams, Plates and Shells. Springer, Dordrecht, 2013. doi: 10.1007/978-1-4020-8743-1_6. open in new tab
  22. J. Rychlewski. On Hooke's law. Priklat. Mathem. Mekhan., 48(3):303-314, 1984. doi: 10.1016/0021-8928(84)90137-0. open in new tab
  23. J. C. Simo and D. D. Fox. On a stress resultant geometrically exact shell model. part i: Formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering, 72(3):267-304, 1989. doi: 10.1016/0045-7825(89)90002-9. open in new tab
  24. J. C. Simo, D. D. Fox, and M. S. Rifai. On a stress resultant geometrically exact shell model. part ii: The linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering, 73(1):53-92, 1989. doi: 10.1016/0045- 7825(89)90098-4. open in new tab
  25. B. Szabó and I. Babuška. Finite Element Analysis. John Wiley & Sons, Inc., New York • Chichester • Brisbane • Toronto • Singapore, 1991.
  26. S. Vlachoutsis. Shear correction factors for plates and shells. International Journal for Numerical Methods in Engineering, 33 (7):1537-1552, 1992. doi: 10.1002/nme.1620330712. open in new tab
  27. W. Voigt. Über die Beziehung zwischen den beiden Elasticitätskonstanten isotroper Körper. Wiedemann´sche Annalen, 38: 573-587, 1889. doi: 10.1002/andp.18892741206. open in new tab
  28. P. A. Zhilin. Mechanics of deformable directed surfaces. International Journal of Solids and Structures, 12(9):635 -648, 1976. doi: 10.1016/0020-7683(76)90010-X. open in new tab
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