Engineering Transactions, 67, 3, pp. 429–440, 2019
10.24423/EngTrans.979.20190404

Approximate Estimation of Stability of Homogeneous Beam on Elastic Foundation

Iwona Małgorzata WSTAWSKA
Poznan University of Technology
Poland

Krzysztof MAGNUCKI
Institute of Rail Vehicles “TABOR”
Poland

Piotr KĘDZIA
Poznan University of Technology
Poland

The paper deals with a proposition of obtaining an analytical solution for a beam on elastic foundation. The main objective of presented work was stability analysis of the axially compressed beam. The analytical model was proposed. Shape function for inhomogeneous properties of the foundation was assumed. The Galerkin method was used to calculate the values of critical forces. Main conditions have been defined. The critical loads as a function of geometric and mechanical properties of the beam as well as inhomogeneous properties of the elastic foundation have been calculated.
Keywords: analytical model; homogeneous beam; elastic foundation; critical force
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References

Li Z.M., Qiao P., Thermal postbuckling analysis of anisotropic laminated beams with different boundary conditions resting on two-parameter elastic foundations, European Journal of Mechanics – A/Solids, 54: 30–43, 2015, doi: 10.1016/j.euromechsol.2015.06.001.

Hung S.Y., Chen J.S., Snapping of a buckled beam on elastic foundation under a midpoint force, European Journal of Mechanics – A/Solids, 31(1): 90–100, 2012, doi: 10.1016/j.euromechsol.2011.07.006.

Zhang Y., Liu Y., Chen P., Murphy K.D., Buckling loads and eigenfrequencies of a braced beam resting on an elastic foundation, Acta Mechanica Solida Sinica, 24(6): 510–518, 2011, doi: 10.1016/S0894-9166(11)60051-7.

Griffiths D.V., Bee G., Analytical and numerical observations on the Hetenyi solution for buckling of beams on elastic foundations, Journal of Engineering Mechanics, 141(1): 1–5, 2015.

Ghiasian S.E., Kiani Y., Eslami M.R., Dynamic buckling of suddenly heated or compressed FGM beams resting on nonlinear elastic foundation, Composite Structures, 106: 225–234, 2013, doi: 10.1016/j.compstruct.2013.06.001.

Challamel N., On the post-buckling of elastic beams on gradient foundation, Comptes Rendus Mécanique, 339(6): 396–405, 2011, doi: 10.1016/j.crme.2011.04.003.

Kameswara Rao C., Mirza S., Torsional post-buckling of thin-walled open section beams resting on a continuous elastic foundation, Thin Walled Structures, 8(1): 55–62, 198, doi: 10.1016/0263-8231(89)90010-4.

Kounadis A.N., Mallis J., Sbarounis A., Postbuckling analysis of columns resting on an elastic foundation, Archive of Applied Mechanics, 75(6–7): 395–404, 2006.

Mojdehi A.R., Tavakol B., Royston W., Dillard D.A., Holmes D.P., Buckling of elastic beams embedded in granular media, Extreme Mechanics Letters, 9: 237–244, 2016, doi: 10.1016/j.eml.2016.03.022.

Kameswara Rao C., Bhaskara Rao L., Torsional post-buckling of thin-walled open section clamped beam supported on Winkler-Pasternak foundation, Thin Walled Structures, 116: 320–325, 2017, doi: 10.1016/j.tws.2017.03.017.

Wattanasakulpong N., Ungbhakorn V., Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation, Computational Materials Science, 71: 201–208, 2013, doi: 10.1016/j.commatsci.2013.01.028.

Yas M.H., Samadi N., Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation, International Journal of Pressure Vessels and Piping, 98: 119–128, 2012, doi: 10.1016/j.ijpvp.2012.07.012.

Yaghoobi H., Torabi M., Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation, Applied Mathematical Modelling, 37(18–19): 8324–8340, 2013, doi: 10.1016/j.apm.2013.03.037.

Froio D., Rizzi E., Simões F.M.F., Da Costa A.P., Universal analytical solution of the steady-state response of an infinite beam on a Pasternak elastic foundation under moving load, International Journal of Solids and Structures, 132–133: 245–263, 2018, doi: 10.1016/j.ijsolstr.2017.10.005.

Hassan M.T., Doha E.H., Recursive differentiation method: application to the analysis of beams on two parameter foundations, Journal of Theoretical and Applied Mechanics, 53(1): 15–26, 2015.

Yaghoobi H., Torabi M., An analytical approach to large amplitude vibration and post-buckling of functionally graded beams rest on non-linear elastic foundation, Journal of Theoretical and Applied Mechanics, 51(1): 39–52, 2013.




DOI: 10.24423/EngTrans.979.20190404

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