Thermal buckling of uniform columns on nonlinear elastic foundation

Abstract

Elastic foundations, either discrete or continuous, are commonly used in many fields of civil, mechanical, aerospace, automobile and nuclear engineering structures. The commonly used continuous elastic foundation is the linear Winkler foundation that is modelled with a number of parallel elastic springs.The prediction of the structural response like static, dynamic and buckling analyses becomes simpler, if the linear Winkler foundation is used. However, if the structural deflections are high, the nonlinearity involved in the foundation stiffness has to be considered. Two types of nonlinear elastic foundation stiffness models are presented here. The first nonlinear foundation stiffness depends on the deflection and the second one depends on the square of the deflection. Analytical expressions for the thermal buckling loads of the heated hinged-hinged and clamped-clamped uniform columns resting on these nonlinear elastic foundations are derived, by using the Rayleigh-Ritz method. The numerical results presented for the thermal buckling loads, clearly show the contribution of the variousparameters existing in the nonlinear elastic foundations.