Skip to main content
SpringerLink
Log in

Meshless analysis of shear deformable shells: the linear model

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

This work develops a kinematically linear shell model departing from a consistent nonlinear theory. The initial geometry is mapped from a flat reference configuration by a stress-free finite deformation, after which, the actual shell motion takes place. The model maintains the features of a complete stress-resultant theory with Reissner-Mindlin kinematics based on an inextensible director. A hybrid displacement variational formulation is presented, where the domain displacements and kinematic boundary reactions are independently approximated. The resort to a flat reference configuration allows the discretization using 2-D Multiple Fixed Least-Squares (MFLS) on the domain. The consistent definition of stress resultants and consequent plane stress assumption led to a neat formulation for the analysis of shells. The consistent linear approximation, combined with MFLS, made possible efficient computations with a desired continuity degree, leading to smooth results for the displacement, strain and stress fields, as shown by several numerical examples.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  1. Li S, Liu WK (2004) Meshfree particle methods. Springer-Verlag, Berlin Heidelberg

    MATH  Google Scholar 

  2. Liu GR (2003) Mesh free methods: moving beyond the finite element method. CRC Press, Boca Raton

    Google Scholar 

  3. Belytschko T et al (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139 (1–4):3–47

    Google Scholar 

  4. Krysl P, Belytschko T (1996) Analysis of thin shells by the element-free Galerkin Method. Int J Solid Struct 33:3057–3080

    Article  MATH  Google Scholar 

  5. Liu L, Chua LP, Ghista DN (2006) Element-free Galerkin method for static and dynamic analysis of spatial shell structures. J Sound Vib 1–2(295):388–406

    Article  Google Scholar 

  6. Rabczuk T, Areias PMA, Belytschko T (2007) A meshfree thin shell method for non-linear dynamic fracture. Int J Numer Methods Eng 72(5):524–548

    Article  MathSciNet  MATH  Google Scholar 

  7. Noguchi H, Kawashima T, Miyamura T (2000) Element free analyses of shell and spatial structures. Int J Numer Methods Eng 47(6):1215–1240

    Article  MATH  Google Scholar 

  8. Liu L, Liu GR, Tan VBC (2002) Element free method for static and free vibration analysis of spatial thin shell structures. Comput Methods Appl Mech Eng 191(51–52):5923–5942

    Article  MATH  Google Scholar 

  9. Simo JC, Fox DD (1989) On a stress resultant geometrically exact shell model. Part I: formulation and optimal parameterization. Comput Methods Appl Mech Eng 72(3):267–304

    Article  MathSciNet  MATH  Google Scholar 

  10. Li S, Hao W, Liu WK (2000) Numerical simulations of large deformation of thin shell structures using meshfree methods. Comput Mech 25(2–3):102–116

    Article  MATH  Google Scholar 

  11. Pimenta PM, Campello EMB (2009) Shell curvature as an initial deformation: a geometrically exact finite element approach. Int J Numer Methods Eng 78(9):1094–1112

    Google Scholar 

  12. Tiago CM (2007) Meshless methods: extending the linear formulation and its generalization to geometrically exact structural analysis. PhD Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa

  13. Simo JC (1985) A finite strain beam formulation. Part I: the three-dimensional dynamic problem. Comput Methods Appl Mech Eng 49(1):55–70

    Article  MathSciNet  MATH  Google Scholar 

  14. Simo JC, Fox DD, Rifai M (1989) On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects. Comput Methods Appl Mech Eng 73(1):53–92

    Article  MathSciNet  MATH  Google Scholar 

  15. Pimenta PM (1993) On a geometrically-exact finite-strain shell model. In: Proceedings of the 3rd Pan-American Congress on Applied Mechanics, São Paulo.

  16. Pimenta PM, Yojo T (1993) Geometrically-exact analysis of spatial frames. Appl Mech Rev 46(11S):118–128

    Article  Google Scholar 

  17. Campello EMB, Pimenta PM, Wriggers P (2004) A geometrically-exact finite strain shell model for the analysis of initially curved shells. In: Sixth World Congress on Computational Mechanics Second Asian-Pacific Congress on Computational Mechanics, Beijing, China

  18. Tiago CM, Pimenta PM (2005) Geometrically exact analysis of space frames by a meshless method. In: Proceedings of the ECCOMAS Thematic Conference on Meshless Methods, Lisboa, Portugal

  19. Tiago CM, Pimenta PDM (2008) An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations. Eng Anal Boundary Elem 32(6):494–511

    Article  MATH  Google Scholar 

  20. Pimenta PM (1996) Geometrically exact analysis of initially curved rods. In: Topping H (ed) Advances in computational techniques for structural engineering. Civil-Comp, Edinburgh, pp 99–108

    Chapter  Google Scholar 

  21. Campello EMB, Pimenta PM, Wriggers P (2003) A triangular finite shell element based on a fully non-linear shell formulation. Comput Mech 31:505–518

    Article  MATH  Google Scholar 

  22. Teixeira de Freitas JA, Moitinho de Almeida JP, Ribeiro Pereira EMB (1999) Non-conventional formulations for the finite element method. Comput Mech 23(5–6):488–501

    Article  MATH  Google Scholar 

  23. Oñate E, Idelsohn A, Zienkiewicz OC (1996) A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int J Numer Methods Eng 39(22):3839–3866

    Article  MATH  Google Scholar 

  24. Simo JC, Hughes TJR (2000) Computational inelasticity (Interdisciplinary Applied Mathematics), vol 7. Springer, New York

    Google Scholar 

  25. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin Methods. Int J Numer Methods Eng 37(2):229–256

    Article  MathSciNet  MATH  Google Scholar 

  26. Duarte CA (1996) The hp-Cloud Method. PhD Thesis, Faculty of the Graduate School of the University of Texas at Austin, Austin

  27. Campello EM (2005) Modelos não-lineares de casca em elasticidade e elastoplasticidade com grandes deformações: teoria e implementação em elementos finitos. Ph.D. Thesis, Escola Politécnica da Universidade de São Paulo, São Paulo.

  28. MacNeal RH, Harder RL (1985) A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1(1): 3–20

    Google Scholar 

Download references

Acknowledgments

The first author acknowledges his master studies funding by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under grant number 2009/04525-5 and his PhD grant by CNPq (Conselho Nacional de Desenvolvimento Tecnológico). This work is part of the research activity carried out by the second author at ICIST, Instituto de Engenharia de Estruturas, Território e Construção, and has been partially financed by FCT (Fundação para a Ciência e Tecnologia) in the framework of Project ICIST, U0076. The third author acknowledges the support by CNPq (Conselho Nacional de Desenvolvimento Tecnológico) under the grant 301279/2009-8.

Author information

Authors and Affiliations

  1. Polytechnic School at the University of São Paulo, P.O. Box 61548, São Paulo, 05424-970, Brazil

    Jorge C. Costa & Paulo M. Pimenta

  2. Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    Carlos M. Tiago

Authors
  1. Jorge C. Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos M. Tiago
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paulo M. Pimenta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge C. Costa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Costa, J.C., Tiago, C.M. & Pimenta, P.M. Meshless analysis of shear deformable shells: the linear model. Comput Mech 52, 763–778 (2013). https://doi.org/10.1007/s00466-013-0837-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-013-0837-8

Keywords

Search

Navigation