Thermal buckling and post-buckling behavior of pined-fixed beams on nonlinear elastic foundation

In this article, both thermal buckling and post-buckling of pinned-fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically nonlinear theory for Euler-Bernoulli beams, considering both linear and nonlinear elastic foundation effects, governing equations for large static deformations of the beams subjected to uniformly temperature rise are derived. Due to large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the nonlinear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second and the third buckling mode shapes are plotted. From these figures it can be found that these curves have no intersection point in the range of K-1 <= 3000, which is different from the behaviors of symmetrically supported beams (pinned-pinned and fixed-fixed). However, there still exist mode transition points. As is expected, nonlinear foundation stiffness parameter K-2 has no influence on the critical buckling temperature and also has little effect on the post-buckling temperature comparing with the K-1 linear parameter.