Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments

This paper deals with the large amplitude vibration, nonlinear bending and thermal postbuckling of functionally graded material (FGM) beams resting on an elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The motion equations are based on a higher order shear deformation beam theory that includes beam–foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The numerical illustrations concern the nonlinear vibration, nonlinear bending and thermal postbuckling of FGM beams resting on Pasternak elastic foundations under different thermal environmental conditions. It is found that the FGM beam with intermediate material properties does not necessarily have intermediate nonlinear frequencies. The thermal postbuckling path of simply supported FGM beams is no longer of the bifurcation type for both uniform and non-uniform temperature fields.