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A coupled peridynamic and finite strip method for analysis of in-plane behaviors of plates with discontinuities

Engineering with Computers (2022)Cite this article

Abstract

In this article, peridynamic and finite strip sub-regions are coupled for the first time. Accordingly, in areas where non-local effects are important, the peridynamic theory is used, while in other areas, the finite strip method, which is an optimal method for solving plate problems, is applied. Static cases with and without crack are investigated using the coupling approach, and the results are compared with those available in the literature. A comprehensive parametric study is performed to investigate the effect of various parameters, such as grid size, the horizon value, the number of strips, and different term functions used in the finite strip. Finally, some examples involving non-uniform load conditions, plate with a hole and crack propagation are studied.

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References

  1. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209

    MathSciNet  MATH  Article  Google Scholar 

  2. Silling SA, Zimmermann M, Abeyaratne R (2003) Deformation of a peridynamic bar. J Elast 73(1):173–190

    MathSciNet  MATH  Article  Google Scholar 

  3. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–1535

    Article  Google Scholar 

  4. Gerstle W, Sau N, Silling S (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237(12–13):1250–1258

    Article  Google Scholar 

  5. Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184

    MathSciNet  MATH  Article  Google Scholar 

  6. Silling SA, Lehoucq RB (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93(1):13

    MathSciNet  MATH  Article  Google Scholar 

  7. O’Grady J, Foster J (2014) Peridynamic beams: a non-ordinary, state-based model. Int J Solids Struct 51(18):3177–3183

    Article  Google Scholar 

  8. Taylor M, Steigmann DJ (2015) A two-dimensional peridynamic model for thin plates. Math Mech Solids 20(8):998–1010

    MathSciNet  MATH  Article  Google Scholar 

  9. O’Grady J, Foster J (2014) Peridynamic plates and flat shells: A non-ordinary, state-based model. Int J Solids Struct 51(25–26):4572–4579

    Article  Google Scholar 

  10. Diyaroglu C, Oterkus E, Oterkus S, Madenci E (2015) Peridynamics for bending of beams and plates with transverse shear deformation. Int J Solids Struct 69:152–168

    Article  Google Scholar 

  11. Cheung Y (1968) The finite strip method in the analysis of elastic plates with two opposite simply supported ends. Proc Am Soc Civ Eng 94:1365–1378

    Google Scholar 

  12. Powell GH, Ogden DW (1969) Analysis of orthotropic steel plate bridge decks. J Struct Div 95(5):909–922

    Article  Google Scholar 

  13. Przemieniecki J (1973) Finite element structural analysis of local instability. AIAA J 11(1):33–39

    MATH  Article  Google Scholar 

  14. Plank R, Wittrick W (1974) Buckling under combined loading of thin, flat-walled structures by a complex finite strip method. Int J Numer Meth Eng 8(2):323–339

    MATH  Article  Google Scholar 

  15. Li W, Cheung Y, Tham L (1986) Spline finite strip analysis of general plates. J Eng Mech 112(1):43–54

    Article  Google Scholar 

  16. Azhari M, Hoshdar S, Bradford MA (2000) On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method. Int J Numer Meth Eng 48(4):583–593

    MATH  Article  Google Scholar 

  17. Cheung YK, Tham L (1997) The finite strip method. CRC Press

    Google Scholar 

  18. Sarrami-Foroushani S, Azhari M (2014) Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects. Physica E 57:83–95

    Article  Google Scholar 

  19. Golmakani M, Rezatalab J (2015) Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory. Compos Struct 119:238–250

    Article  Google Scholar 

  20. Sarrami-Foroushani S, Azhari M, Saadatpour M (2013) Buckling of functionally graded stiffened and unstiffened plates using finite strip method. Comput Methods Civil Eng 4(1):1–24

    Google Scholar 

  21. Beena K, Parvathy U (2014) Linear static analysis of functionally graded plate using spline finite strip method. Compos Struct 117:309–315

    Article  Google Scholar 

  22. Wang Y, Qiao P (2021) Improved buckling analysis of stiffened laminated composite plates by spline finite strip method. Compos Struct 255:112936

    Article  Google Scholar 

  23. Rostamijavanani A, Ebrahimi M, Jahedi S (2020) Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method. J Fail Anal Prev 21(1):20–301

    Google Scholar 

  24. Loja M, Soares CM, Barbosa J (2013) Analysis of functionally graded sandwich plate structures with piezoelectric skins, using B-spline finite strip method. Compos Struct 96:606–615

    Article  Google Scholar 

  25. Chan H, Foo O (1977) Buckling of multi-layer sandwich plates by the finite strip method. Int J Mech Sci 19(8):447–456

    MATH  Article  Google Scholar 

  26. Shimpi RP (2002) Refined plate theory and its variants. AIAA J 40(1):137–146

    Article  Google Scholar 

  27. Dawe D (1978) Finite strip models for vibration of Mindlin plates. J Sound Vib 59(3):441–452

    Article  Google Scholar 

  28. Mousavi H, Azhari M, Saadatpour MM, Sarrami-Foroushani S (2020) Application of improved element-free Galerkin combining with finite strip method for buckling analysis of channel-section beams with openings. Eng Comput 38(1):739–755

    Article  Google Scholar 

  29. Macek RW, Silling SA (2007) Peridynamics via finite element analysis. Finite Elem Anal Des 43(15):1169–1178

    MathSciNet  Article  Google Scholar 

  30. Oterkus E, Madenci E, Weckner O, Silling S, Bogert P, Tessler A (2012) Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot. Compos Struct 94(3):839–850

    Article  Google Scholar 

  31. Lubineau G, Azdoud Y, Han F, Rey C, Askari A (2012) A morphing strategy to couple non-local to local continuum mechanics. J Mech Phys Solids 60(6):1088–1102

    MathSciNet  Article  Google Scholar 

  32. Zaccariotto M, Mudric T, Tomasi D, Shojaei A, Galvanetto U (2018) Coupling of FEM meshes with Peridynamic grids. Comput Methods Appl Mech Eng 330:471–497

    MathSciNet  MATH  Article  Google Scholar 

  33. Shojaei A, Zaccariotto M, Galvanetto U (2017) Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour. Eng Comput 34(5):1334–1366

    Article  Google Scholar 

  34. Galvanetto U, Mudric T, Shojaei A, Zaccariotto M (2016) An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems. Mech Res Commun 76:41–47

    Article  Google Scholar 

  35. Zaccariotto M, Tomasi D, Galvanetto U (2017) An enhanced coupling of PD grids to FE meshes. Mech Res Commun 84:125–135

    Article  Google Scholar 

  36. Silling S, Littlewood D, Seleson P (2015) Variable horizon in a peridynamic medium. J Mech Mater Struct 10(5):591–612

    MathSciNet  Article  Google Scholar 

  37. Seleson P, Beneddine S, Prudhomme S (2013) A force-based coupling scheme for peridynamics and classical elasticity. Comput Mater Sci 66:34–49

    Article  Google Scholar 

  38. Liu W, Hong J-W (2012) A coupling approach of discretized peridynamics with finite element method. Comput Methods Appl Mech Eng 245:163–175

    MathSciNet  MATH  Article  Google Scholar 

  39. Madenci E, Oterkus E (2014) Peridynamic theory. Peridynamic theory and its applications. Springer, pp 19–43

    MATH  Chapter  Google Scholar 

  40. Szilard R (2004) Theories and applications of plate analysis: classical, numerical and engineering methods. Appl Mech Rev 57(6):B32–B33

    Article  Google Scholar 

  41. R. ABAQUS version 6.14.4 (2018) Providence, USA

  42. Scabbia F, Zaccariotto M, Galvanetto U (2021) A novel and effective way to impose boundary conditions and to mitigate the surface effect in state-based Peridynamics. Int J Numer Meth Eng 122(20):5773–5811

    MathSciNet  Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Zahra Shafiei, Saeid Sarrami & Mojtaba Azhari

  2. Department of Industrial Engineering, University of Padova, v. Venezia 1, 35131, Padua, Italy

    Ugo Galvanetto & Mirco Zaccariotto

Authors
  1. Zahra Shafiei
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  2. Saeid Sarrami
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  3. Mojtaba Azhari
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  4. Ugo Galvanetto
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  5. Mirco Zaccariotto
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Correspondence to Saeid Sarrami.

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Shafiei, Z., Sarrami, S., Azhari, M. et al. A coupled peridynamic and finite strip method for analysis of in-plane behaviors of plates with discontinuities. Engineering with Computers (2022). https://doi.org/10.1007/s00366-022-01665-y

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  • DOI: https://doi.org/10.1007/s00366-022-01665-y

Keywords

  • Peridynamic theory
  • Finite strip method
  • Coupling element
  • Crack propagation