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Nonlinear finite element treatment of unsymmetric laminated composite shells

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Abstract

The concentration of the current contribution is on the geometrically nonlinear analysis of laminated composite shells employing the finite element method. For this purpose, the use is made of a higher-order shell model with extensible directors possessing twelve parameters, then the exact Green–Lagrange strains and the three-dimensional second Piola–Kirchhoff stress tensor are extracted based on the base vectors of the shell mid-surface. The principle of virtual work is adopted to derive the weak form of governing equations. A computationally efficient four-node shell element is designed and to remedy the locking problems involving transverse shear, membrane and curvature–thickness ones, the ANS (assumed natural strain) approach and the assumed strain scheme are used. Finally, standard benchmarks are solved for isotropic materials allowing geometric nonlinearity to examine the performance of the proposed shell element and then results of thin and thick layered composite structures are presented.

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References

  1. Rasdorf WJ, Spainhour LK, Patton EM, Burns BP (1993) A design environment for laminated fiber-reinforced thick composite materials. Eng Comput 9(1):36–48

    Article  Google Scholar 

  2. Dvorkin EN, Bathe KJ (1984) A continuum mechanics based four-node shell element for general non-linear analysis. Eng Comput 1(1):77–88

    Article  Google Scholar 

  3. Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Meth Eng 29(8):1595–1638

    Article  MathSciNet  MATH  Google Scholar 

  4. Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration technique in general analysis of plates and shells. Int J Numer Meth Eng 3(2):275–290

    Article  MATH  Google Scholar 

  5. Areias P, de Sá JMC, Cardoso R (2014) A simple assumed-strain quadrilateral shell element for finite strains and fracture. Eng Comput 31(4):691–709

    Article  Google Scholar 

  6. Laulusa A, Bauchau OA, Choi JY, Tan VBC, Li L (2006) Evaluation of some shear deformable shell elements. Int J Solids Struct 43(17):5033–5054

    Article  MATH  Google Scholar 

  7. Basar Y, Montag U, Ding Y (1993) On an isoparametric finite-element for composite laminates with finite rotations. Comput Mech 12(6):329–348

    Article  MATH  Google Scholar 

  8. Başar Y, Ding Y, Schultz R (1993) Refined shear-deformation models for composite laminates with finite rotations. Int J Solids Struct 30(19):2611–2638

    Article  MATH  Google Scholar 

  9. Basar Y, Ding Y (1995) Interlaminar stress analysis of composites: Layer-wise shell finite elements including transverse strains. Compos Eng 5(5):485–499

    Article  Google Scholar 

  10. Vu-Quoc, L., X.G. Tan, Optimal solid shells for non-linear analyses of multilayer composites. I. Statics. Computer Methods in Applied Mechanics and Engineering, 2003. 192(9–10): p. 975–1016.

  11. Payette GS, Reddy JN (2014) A seven-parameter spectral/hp finite element formulation for isotropic, laminated composite and functionally graded shell structures. Comput Methods Appl Mech Eng 278:664–704

    Article  MathSciNet  MATH  Google Scholar 

  12. Arciniega RA, Reddy JN (2007) Tensor-based finite element formulation for geometrically nonlinear analysis of shell structures. Comput Methods Appl Mech Eng 196(4–6):1048–1073

    Article  MathSciNet  MATH  Google Scholar 

  13. Gutierrez Rivera, M., J.N. Reddy, and M. Amabili, A new twelve-parameter spectral/hp shell finite element for large deformation analysis of composite shells. Composite Structures, 2016. 151: p. 183–196.

  14. Kant T, Manjunatha BS (1988) An unsymmetric FRC laminate C° finite element model with 12 degrees of freedom per node. Eng Comput 5(4):300–308

    Article  Google Scholar 

  15. Chen W, Luo WM, Chen SY, Peng LX (2022) A FSDT meshfree method for free vibration analysis of arbitrary laminated composite shells and spatial structures. Compos Struct 279:114763

    Article  Google Scholar 

  16. Chen W, Yang JS, Wei DY, Yan ST, Peng LX (2022) Buckling analysis of corrugated-core sandwich plates using a FSDT and a meshfree Galerkin method. Thin-Walled Structures 180:109846

    Article  Google Scholar 

  17. Başar Y (1993) Finite-rotation theories for composite laminates. Acta Mech 98(1–4):159–176

    Article  MathSciNet  MATH  Google Scholar 

  18. Choi C-K, Paik J-G (1994) An efficient four node degenerated shell element based on the assumed covariant strain. Struct Eng Mech 2(1):17–34

    Article  Google Scholar 

  19. Ko Y, Lee P-S, Bathe K-J (2016) The MITC4+ shell element and its performance. Comput Struct 169:57–68

    Article  Google Scholar 

  20. Ko Y, Lee P-S, Bathe K-J (2017) A new MITC4+ shell element. Comput Struct 182:404–418

    Article  Google Scholar 

  21. Ko Y, Lee P-S, Bathe K-J (2017) The MITC4+ shell element in geometric nonlinear analysis. Comput Struct 185:1–14

    Article  Google Scholar 

  22. Betsch P, Stein E (1995) An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element. Commun Numer Methods Eng 11(11):899–909

    Article  MATH  Google Scholar 

  23. Stander N, Matzenmiller A, Ramm E (1989) An assessment of assumed strain methods in finite rotation shell analysis. Eng Comput 6(1):58–66

    Article  Google Scholar 

  24. Brank B, Damjanić FB, Perić D (1995) On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells. Comput Mech 16(5):341–359

    Article  MATH  Google Scholar 

  25. Mohan P, Kapania RK (1998) Updated Lagrangian Formulation of a Flat Triangular Element for Thin Laminated Shells. AIAA J 36(2):273–281

    Article  MATH  Google Scholar 

  26. Sansour, C. and F.G. Kollmann, Families of 4-node and 9-node finite elements for a finite deformation shell theory. An assesment of hybrid stress, hybrid strain and enhanced strain elements. Computational Mechanics, 2000. 24(6): p. 435–447.

  27. Hong WI, Kim JH, Kim YH, Lee SW (2001) An assumed strain triangular curved solid shell element formulation for analysis of plates and shells undergoing finite rotations. Int J Numer Meth Eng 52(7):747–761

    Article  MATH  Google Scholar 

  28. Klinkel S, Gruttmann F, Wagner W (1999) A continuum based three-dimensional shell element for laminated structures. Comput Struct 71(1):43–62

    Article  Google Scholar 

  29. Sze KY, Chan WK, Pian THH (2002) An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells. Int J Numer Meth Eng 55(7):853–878

    Article  MATH  Google Scholar 

  30. Kim CH, Sze KY, Kim YH (2003) Curved quadratic triangular degenerated- and solid-shell elements for geometric non-linear analysis. Int J Numer Meth Eng 57(14):2077–2097

    Article  MATH  Google Scholar 

  31. Sze KY, Liu XH, Lo SH (2004) Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elem Anal Des 40(11):1551–1569

    Article  Google Scholar 

  32. Zhang R, Zhong H, Yao X (2018) A weak form quadrature element formulation of geometrically exact shells incorporating drilling degrees of freedom. Comput Mech 63(4):663–679

    Article  MathSciNet  MATH  Google Scholar 

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  1. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    Alireza Beheshti & Reza Ansari

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  1. Alireza Beheshti
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  2. Reza Ansari
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Correspondence to Reza Ansari.

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Beheshti, A., Ansari, R. Nonlinear finite element treatment of unsymmetric laminated composite shells. Engineering with Computers (2023). https://doi.org/10.1007/s00366-023-01863-2

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