Thermal post-buckling analysis of slender columns using the concept of coupled displacement field

Thermal post-buckling analysis of columns with an axially immovable ends is studied using the Rayleigh–Ritz (R–R) method, where the admissible displacement functions are chosen based on the concept of coupled displacement field (CDF) criteria. Geometric non-linearity is considered using the von-Karman strain displacement relations of the beam. Furthermore, the displacement fields derived from CDF criteria are used in an intuitive formulation, where the thermal post-buckling behavior can be predicted by using two parameters namely tension developed in the column and linear buckling load. An exhaustive set of column boundary conditions are considered namely classical such as hinged–hinged, clamped–clamped, clamped–hinged and non-classical such as clamped–guided and hinged–guided. Post-buckling analysis results are presented in the form of closed form expressions, where the ratio of post-buckling load to linear buckling load parameter is expressed as a function of central amplitude of the column for all the boundary conditions considered. The amount of non-linearity predicted using the present formulations (R–R method and intuitive method) based on the concept of coupled displacement field (CDF) criteria shows an excellent agreement with the available literature results for both classical and non-classical boundary conditions.