Thermal buckling and postbuckling of Euler-Bernoulli beams supported on nonlinear elastic foundations

Deformations of homogeneous and isotropic pinned-pinned and fixed-fixed Euler-Bernoulli beams supported on nonlinear elastic foundations and heated uniformly into the postbuckling regime have been analyzed numerically. Geometric nonlinearities introduced by finite deflections and curvature of the deformed beams are incorporated in the problem formulation. First buckling due to the uniform temperature rise and buckling mode transitions are investigated analytically by analyzing the linear problem. Subsequently, the nonlinear boundary-value problems for postbuckling of beams are transformed into initial-value problems and analyzed by the shooting method. For different values of the elastic foundation parameters, postbuckled configurations are illustrated.