Skip to main content

Optimization of a finite element mesh for plates subjected to in-plane patch loading


In designing in-plane stressed thin plates, the loading condition where the uniform distributed edge forces are locally applied along one or more of the plate’s boundaries is often encountered. We investigated the optimal grid pattern that can be used in the analysis of the displacement and stress fields of a simply supported thin plate partially compressed. The plate modelling was created by means of an isoparametric rectangular element. This grid pattern was designed to satisfy good accuracy with low density. A convergence analysis was performed through different sets of meshes locally refined in a judicious way. For each focused field, the critical plate area was searched. Displacement and max stress values were recorded in the respective searched critical zone. Good results were obtained in seeking stress and displacement fields using, respectively, a small and a more expanded local refinement.

This is a preview of subscription content, access via your institution.


  1. M. Farshad, Design and Analysis of Shell Structures, Dordrecht: Kluwer Academic Publishers (1992).

    Book  MATH  Google Scholar 

  2. M. R. Khedmati, M. M. Roshanali and Z. H. M. E. Nouri, Strength of steel plates with both-sides randomly distributed with corrosion wastage under uniaxial compression, Thinwalled Structures, 49 (2011) 325–42

    Google Scholar 

  3. C. Graciano and A. Ayestarán, Steel plate girder webs under combined patch loading, bending and shear, J. of Constructional Steel Research, 80 (2013) 202–212

    Article  Google Scholar 

  4. G. Ikhenazen, M. Saidani and A. Chelghoum, Finite element analysis of linear plates buckling under in-plane patch loading, J. of Constructional Steel Research, 66 (2010) 1112–1117

    Article  Google Scholar 

  5. R. Brighenti, Buckling of cracked thin-plates under tension or compression, Thin-Walled Structures, 43 (2005) 209–24

    Article  Google Scholar 

  6. R. Brighenti, Numerical buckling analysis of compressed or tensioned cracked thin plates, Engineering Structures, 27 (2005) 265–76

    Article  Google Scholar 

  7. M. Kilardj, G. Ikhenazen, T. Messager and T. Kanit, Linear and nonlinear buckling analysis of a locally stretched plate, J. of Mechanical Science and Technology, 30 (8) (2016) 3607–3613.

    Article  Google Scholar 

  8. K. Rockey and D. Bagchi, Buckling of plate girder webs under partial edge loadings, International J. of Mechanics and Science, 12 (1970) 61–76

    Article  Google Scholar 

  9. L. M. Gil-Martín, B. Šcepanovic, E. Hernández-Montes, M. A. Aschheim and D. Lucic, Eccentrically patch-loaded steel Igirders: The influence of patch load length on the ultimate strength, J. of Constructional Steel Research, 66 (2010) 716–722

    Article  Google Scholar 

  10. M. A. Komur and M. Sonmez, Elastic buckling behavior of rectangular plates with holes subjected to partial edge loading, J. of Constructional Steel Research, 112 (2015) 54–60

    Article  Google Scholar 

  11. K. Prajapat, S. Ray-Chaudhuri and A. Kumar, Effect of inplane boundary conditions on elastic buckling behaviour of solid and perforated plates, Thin Walled Structures, 90 (2015) 171–182

    Article  Google Scholar 

  12. Pafec-fe Ltd, Program for Automatic Finite Elements Calculations, Structural finite elements analysis software catering for: Static, dynamic, non-linear, thermal analysis, Nottingham, NG8 6PE.

  13. B. A. Szabo, Estimation and control of error based on pconvergence, Proc. Int. Conf. Accuracy Estimates and Adaptive Refinements in Finite Element Computations (ARFEC) (1984).

    Google Scholar 

  14. J. Huang, N. Nguyen-Thanh and K. Zhou, Extended isogeometric analysis based on Bézier extraction for the buckling analysis of Mindlin–Reissner plates, Acta Mechanica, 28 (9) (2017) 3077–3093.

    Article  MATH  Google Scholar 

  15. O. C. Zienkiewicz, The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, New York (1967).

    MATH  Google Scholar 

  16. O. C. Zienkiewicz, B. M. Irons, J. Ergatoudis, S. Ahmed and F. C. Scott. Isoparametric and associated element families for two and three-dimensional analysis, Proc. Course on Finite Element Methods in Stress Analysis, Holland I and Bell K. Trondheim (Ed.), Tech. Univ. (1969).

    Google Scholar 

  17. O. C. Zienkiewicz and D. V. Philips, An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates, Int. J. Num. Meth. Engin., 3 (1971) 519–28

    MathSciNet  Article  MATH  Google Scholar 

  18. B. Fraeijs de Veubeke, Bending and stretching of plates, Proc. Conf. Matrix Meth. Struc. Mech. Wright Patterson Air Force Base, Dayton, Ohio (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ghania Ikhenazen.

Additional information

Recommended by Associate Editor Yang Zheng

Ghania Ikhenazen received her M.Phil. in Civil Engineering from Heriot Watt University in the United Kingdom; also, her Ph.D. in Structural Engineering from University of Sciences and Technology Houari Boumediene in Algeria, in 2010, where she is currently a Lecturer and an Associate Researcher. Her research interests include buckling and ultimate strength analyses of plate structures.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ikhenazen, G., Saidani, M. & Kilardj, M. Optimization of a finite element mesh for plates subjected to in-plane patch loading. J Mech Sci Technol 33, 1185–1193 (2019).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Displacement curves
  • Finite element analysis
  • Optimal grid pattern
  • Partial compression
  • Stress
  • Thin plates