Thermomechanical initial post-buckling of Timoshenko's beam on elastic foundations

Abstract

ABSTRACTThe objective of this work is to propose an analytical solution for the thermomechanical initial post-buckling response of a thick beam resting on a linear elastic foundation and subject to a uniform temperature rise throughout its cross-section. The thermal strain is assumed to follow a linear law with the temperature rise and the material properties are considered temperature independent. The beam cross-section geometrical properties are constant along the beam length, and the formulation is consistent with the small strain assumption. The beam ends are assumed pinned and immovable, thermal expansion is not allowed and as a consequence compressive forces arise and the beam may buckle. If the temperature is increased further, the beam continues to deflect laterally, hence the problem is geometrically non-linear. In addition, the model is appropriate to describe the behavior of short beams as it takes into account transverse shear deformations. The governing equations are derived and made non-dimensional, and it is seen that three non-dimensional parameters control the thermomechanical initial post-buckling problem: The elastic foundation stiffness, the beam slenderness ratio and the beam cross-section shear coefficient. A classical perturbation method is applied to the non-linear set of differential governing equations, therefore the critical buckling temperatures (loads) and modes and the initial post-buckling behavior may be analytically determined. The change in length, reaction forces at the supports and geometric configurations are obtained as a function of temperature, the elastic foundation.