Computational Mechanics

, Volume 38, Issue 1, pp 61–75 | Cite as

Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory

Article

Abstract

This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results for both trapezoidally and sinusoidally corrugated plates are then reported.

Keywords

Buckling analysis Corrugated plate Equivalent properties First-order shear deformation theory Mesh-free Galerkin method Meshless approach 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Seydel EB (1931) Schubknickversuche mit Wellblechtafeln, Jahrbuch d. Deutsch. Versuchsanstallt für Luftfahrt, E.V. München und Berlin, pp. 233–235Google Scholar
  2. Easley JT and McFarland DE (1969) Buckling of light-gage corrugated metal shear diaphragms. J Struct Div Proc of the ASCE 95:1497–1516Google Scholar
  3. Nilson AH and Ammar AR (1974) Finite element analysis of metal deck shear diaphragms. J Struct Div-ASCE 100 (NST4):711–726Google Scholar
  4. Easley JT (1975) Buckling formulas for corrugated metal shear diaphragms. J Struct Div-ASCE 101(7):1403–1417Google Scholar
  5. Davies JM (1976) Calculation of steel diaphragm behavior. J Struct Div 102: 1411–1430Google Scholar
  6. Lau JH (1981) Stiffness of corrugated plate. J Eng Mech Div-ASCE 107(1):271–275Google Scholar
  7. Briassoulis D (1986) Equivalent orthotropic properties of corrugated sheets. Comput Struct 23(2):129–138CrossRefGoogle Scholar
  8. Shimansky RA and Lele M.M. (1995) Transverse stiffness of a sinusoidally corrugated plate. Mech Struct Mach 23(3):439–451Google Scholar
  9. Luo R and Edlund B.(1996) Shear capacity of plate girders with trapezoidally corrugated webs. Thin-Wall Struct 26(1):19–44Google Scholar
  10. Samanta A and Mukhopadhyay M (1999) Finite element static and dynamic analyses of folded plates. Engi Struct 21:277–287CrossRefGoogle Scholar
  11. Semenyuk NP and Neskhodovskaya NA. (2002) On design models in stability problems for corrugated cylindrical shells. Int Appl Mech 38(10):1245–1252CrossRefMATHMathSciNetGoogle Scholar
  12. Machimdamrong C, Watanabe E and Utsunomiya T (2004) Shear buckling of corrugated plates with edges elastically restrained against rotation. Int J Struct Stab Dyna 4(1):89–104CrossRefGoogle Scholar
  13. Lucy LB. (1977) A numerical approach to the testing of the fission hypothesis. Astronomical Journal 82:1013–1024CrossRefGoogle Scholar
  14. Belytschko T, Lu YY and Gu L (1994) Element-free Galerkin methods. International J Numer Meth Eng 37:229–256CrossRefMATHMathSciNetGoogle Scholar
  15. Ren J. and Liew KM. (2002) Mesh-free method revisited: two new approaches for the treatment of essential boundary conditions. Int J Comput Eng Sci 3(2):219–233CrossRefGoogle Scholar
  16. Liu GR, and Gu YT. (2000) Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Computa Mech 26:166–173CrossRefMATHGoogle Scholar
  17. Gu YT, and Liu GR. (2000) A boundary point interpolation method for stress analysis of solids. Computa Mech 28:47–54CrossRefGoogle Scholar
  18. Wang J, Liew K, Tan MJ and Rajendran, S. (2002) Analysis of rectangular laminated composite plates via FSDT meshless method. Inte J Mech Sci 44:1275–1293CrossRefMATHGoogle Scholar
  19. Liew KM, Lim HK, Tan MJ and He XQ (2002) Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method. Computa Mech 29(6):486–497CrossRefMATHGoogle Scholar
  20. Reddy JN (1999) Theory and Analysis of Elastic Plates. Taylor & Francis, London.Google Scholar
  21. Reddy JN (1999) Analysis of functionally graded plates. Inter J Numer Meth Eng 47:663–684CrossRefGoogle Scholar
  22. Shell63, Element Reference, ANSYS 6.1 DocumentationGoogle Scholar
  23. Shell181, Element Reference, ANSYS 6.1 DocumentationGoogle Scholar
  24. Beam188, Element Reference, ANSYS 6.1 Documentation.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Nanyang Centre for Supercomputing and VisualisationNanyang Technological UniversitySingapore
  2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingapore
  3. 3.Department of Building and ConstructionCity University of Hong KongHong KongChina

Personalised recommendations