Use of nonlinear incremental parameters to predict thermal post-buckling and nonlinear vibration behavior of columns and beams on elastic foundation

Abstract

Simple nonlinear incremental formulation is presented, to predict the thermal post-buckling and nonlinear vibration behavior of columns and beams, on the Winkler foundation. This formulation gives simple formulas to evaluate the thermal post-buckling load and the nonlinear frequency parameters. The numerical constant that is required in this formulation is obtained from the tensile and the thermal buckling loads. The tensile load in the columns and beams is induced due to the immovable end axial displacements and large deflections. The compressive mechanical equivalent of the thermal load is developed in the uniformly heated column with the same immovability condition of the end axial displacements. By using these values, the simple analytical formulas of the thermal post-buckling and the nonlinear frequency parameters can be directly obtained. The derivation of these formulas require only the values of the thermal buckling load and linear frequency parameters of the columns and beams on the Winkler foundation. The efficacy of these simple formulas is demonstrated by comparing with those obtained by using the relatively complex continuum and numerical formulations.