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BEM for thick plates on unilateral Winkler springs

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Abstract

A new direct boundary element (BEM) technique is established to analyze plates on tensionless elastic foundation. The soil is modeled as Winkler springs. The considered BEM is based on the formulation of shear deformable plate bending theory according to Reissner. The developed technique is based on coupling a developed plate bending software with iterative process to eliminate tensile stresses underneath the considered plate. Tensile zones are redistributed until the final contact zone of plate is reached. Examples are tested and results are compared to analytical and previously published results to verify the proposed technique.

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References

  1. Katsikadelis JT, Armenakas AE (1984) Plates on elastic foundation by BIE method. J Eng Mech 110:1086–1105

    Article  Google Scholar 

  2. Reissner E (1947) On bending of elastic plates. Q Appl Math 5:55–68

    Article  Google Scholar 

  3. Vander Weeën F (1982) Application of the boundary integral equation method to Reissner’s plate model. Int J Num Methods Eng 18:1–10

    Article  Google Scholar 

  4. Rashed YF, Aliabadi MH, Brebbia CA (1998) The boundary element method for thick plates on a Winkler foundation. Int J Numer Methods Eng 41:1435–1462

    Article  Google Scholar 

  5. Rashed YF, Aliabadi MH (2000) Boundary element analysis of buildings foundation plates. Eng Anal Bound Elem 24:201–206

    Article  Google Scholar 

  6. Rashed YF (2005) A boundary/domain element method for analysis of building raft foundations. Eng Anal Bound Elem 29:859–877

    Article  Google Scholar 

  7. Weitsman Y (1970) On foundations that react on compression only. ASME J Appl Mech 37:1019–1030

    Article  Google Scholar 

  8. Celep Z (1988) Rectangular plates resting on tensionless elastic foundation. J Eng Mech 114:2083–2092

    Article  Google Scholar 

  9. Li H, Dempsey JP (1988) Unbonded contact of a square plate on an elastic half-space or a Winkler foundation. ASME J Appl Mech 55:430–436

    Article  Google Scholar 

  10. Sapountzakis EJ, Katsikadelis JT (1992) Unilaterally supported plates on elastic foundations by the boundary element method. ASME J Appl Mech 59:580–586

    Article  Google Scholar 

  11. Kexin M, Suying F, Xiao J (1999) A BEM solution for plates on elastic half-space with unilateral contact. Eng Anal Bound Elem 23:189–194

    Article  Google Scholar 

  12. Silva ARD, Silveira RAM, GonÇalves PB (2001) Numerical methods for analysis of plates on tensionless elastic foundations. Int J Solids Struct 38:2083–2100

    Article  Google Scholar 

  13. Jirousek J, Zieliński AP, Wróblewski A (2001) T-element analysis of plates on unilateral elastic Winkler-type foundation. Comput Assist Mech Eng Sci 8:343–358

    Google Scholar 

  14. Xiao JR (2001) Boundary element analysis of unilateral supported Reissner plates on elastic foundations. Comput Mech 27:1–10

    Article  Google Scholar 

  15. Shen HS, Yu L (2004) Nonlinear bending behavior of Reissner–Mindlin plates with free edges resting on tensionless elastic foundations. Int J Solids Struct 41:4809–4825

    Article  Google Scholar 

  16. Silveira RAM, Pereira WLA, GonÇalves PB (2008) Nonlinear analysis of structural elements under unilateral contact constrains by a Ritz type approach. Int J Solids Struct 45:2629–2650

    Article  Google Scholar 

  17. Torbacki W (2009) Numerical analysis of beams on unilateral elastic foundation. Arch Mater Sci Eng 29(2):109–112

    Google Scholar 

  18. Buczkowski R, Torbacki W (2009) Finite element analysis of plate on layered tensionless foundations. Arch Civil Eng 56(3):255–274

    Article  Google Scholar 

  19. Kongtong P, Sukawat D (2013) Coupled integral equations for uniformly loaded rectangular plates resting on unilateral supports. Int J Math Anal 7:847–862

    Article  Google Scholar 

Download references

Acknowledgements

This project was supported financially by the Science and Technology Development Fund (STDF), Egypt, Grant no. 14910. The authors would like to acknowledge the support of (STDF).

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Authors and Affiliations

  1. Department of Structural Engineering, Cairo University, Giza, Egypt

    Ahmed Fady Farid & Youssef F. Rashed

  2. Supreme Council of Universities in Egypt, Giza, Egypt

    Youssef F. Rashed

Authors
  1. Ahmed Fady Farid
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  2. Youssef F. Rashed
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Corresponding author

Correspondence to Youssef F. Rashed.

Additional information

This paper was selected from GeoMEast 2017—Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology.

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Farid, A.F., Rashed, Y.F. BEM for thick plates on unilateral Winkler springs. Innov. Infrastruct. Solut. 3, 26 (2018). https://doi.org/10.1007/s41062-018-0128-5

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  • DOI: https://doi.org/10.1007/s41062-018-0128-5

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