Applicability of simple intuitive formulation for predicting thermal post-buckling behaviour of columns resting on hardening nonlinear elastic foundation

The paper demonstrates the applicability of a simple intuitive formulation, the development of which started around a decade ago in obtaining the thermal post-buckling behaviour of uniformly heated slender columns that rest on hardening nonlinear Winkler foundation. This foundation, which is firmly bonded to the column, is idealised by a number of closely spaced hardening nonlinear elastic springs. The nonlinear foundation stiffness of the nonlinear elastic foundation is dependent on the square of the deflection of the columns. Analytical expressions for the thermal post-buckling loads, for the buckled mode shapes with wave number one, by applying the concept of smart structures, of the commonly used columns on hardening nonlinear foundation are derived, by using a simple, intuitive formulation. The numerical results presented are validated, by comparing from those obtained for the limiting cases and non-violation of the physical and logical behaviour, in the absence of any similar results available in literature. These results reveal, the relative contributions of the various parameters existing in the hardening nonlinear Winkler foundation, on the thermal post-buckling behaviour of hinged–hinged and clamped–clamped columns.