Buckling and post-buckling of pinned Euler beams on weakened Winkler foundation under thermal loading

In engineering practice, it is difficult to guarantee that the foundation of a beam is homogeneous along the whole length. This paper presents an investigation on buckling and post-buckling behavior of beams on the elastic foundation under thermal loading. The virtual work method is employed to deduce the buckling governing equation and post-buckling differential equation of equilibrium. The Buckling load of beams on homogeneous foundation is investigated analytically and it is found that the first buckling mode is determined by nondimensional foundation stiffness. The beam will jump to another mode at a certain value of foundation stiffness. This paper investigates the buckling and post-buckling behavior of beams on elastic foundation under thermal loading. The buckling and post-buckling behaviors of beams on weakened foundation are analyzed by using a shooting technique. The results show that the weakening effect has a significant influence on buckling temperature and buckling mode, and post-buckling path is stable in the whole loading process under thermal effects. It is also observed that the weakening effect can give rise to local deformation of the beam, and the location of the weakening effect has an obvious influence on buckling mode and post-buckling deformation.