COMBINATION OF PATCH AND WHEEL LOADS – ANALYTICAL APPROACH TO PLATE BUCKLING

  • Olga Mijušković Olga Mijušković University of Montenegro, Faculty of Civil Engineering, Podgorica, Montenegro
  • Branislav Ćorić
  • Biljana Šćepanović

Abstract


Past studies on the stability of rectangular plates under the influence of variable loads were based on assumptions of simplified stress distributions, which put the question of the accuracy of results thus obtained. The procedure of applying the exact stress functions in the problem of elastic stability of the plate with different boundary conditions under effects of patch and wheel loading is presented in this paper. Mathieu (1890) obtained the exact solution for the plane-strain state for a rectangular element for certain types of variable stresses on the boundaries. Baker at al (1993), following Mathieu’s results, analyzed the general problem of a rectangular plate loaded by completely arbitrary distributions of (normal and/or shear) stresses along the edges of the plate. Analytical approach used for determination of the critical load is based on well known Ritz energy technique. The strain energy due to bending of the plate is defined in the traditional way. On the other hand, the exact stress distribution of Mathieu’s theory of elasticity is introduced through the potential energy of the plate associated with the work done by external loads. Results for the critical load obtained by presented analytical approach are reaffirmed by numerical finite-element (FE) runs.

References

Mathieu E. (1890): "Theorie de l'elasticite des corps solides", Seconde partie. GauthierVillars, Paris

Baker G., Pavlović M. N., Tahan N. (1993): "An exact solution to the two-dimensional elasticity problem with rectangular boundaries under arbitrary edge forces", Phil. Trans. R. Soc. London, A 393, pp. 307-336

Liu Y. G. (2006): "Buckling of Plates under Non-Uniform Stresses, with Particular Emphasis on Shear", Ph. D Thesis, Imperial College, London

Mijušković O. (2008): "Analiza stabilnosti pravougaonih ploča korišćenjem tačne funkcije napona", Doktorska disertacija, Građevinski fakultet Univerziteta u Beogradu, Beograd

Mijušković O., Ćorić B. (2013): "Patch loading – analytical approach to critical load determination", original scientific paper, Građevinar, Journal of the Croatian Association of Civil Engineers, 65(1), pp. 1-10

Mijušković O., Ćorić B., Šćepanović B. (2014): "Exact stress functions implementation in stability analysis of plates with different boundary conditions under uniaxial and biaxial compression", Thin-Walled Structures, 80, pp. 192-206

Mijušković O., Ćorić B., Šćepanović B. (2015): "Accurate buckling loads of plates with different boundary conditions under arbitrary edge compression", International Journal of Mechanical Sciences, 101-102, pp.309-323

Mijušković O., Ćorić B., Šćepanović B.,Žugić Lj. (2016): " Analytical model for buckling analysis of the plates under patch and concentrated loads ", Thin-Walled Structures, 101, pp.26-42

Published
2016/04/27
Section
Original Scientific Paper