Thermal buckling analysis of functionally graded beam with longitudinal crack

The thermal buckling problem of functionally graded beam with longitudinal crack is presented in the paper. The whole beam is divided into four sub-beams and each one is modeled as a Timoshenko beam. The buckling governing equation of each sub-beam in thermal environment is established by using Hamilton Principle. Combining with the boundary conditions, the continuous conditions of the displacements and the forces, the buckling governing equations are solved by both the analytical and numerical methods. The buckling modes and critical buckling temperatures are obtained, and the effects of the functionally graded index, crack length, crack depth, and crack longitudinal location on the buckling characteristics of beams are discussed in numerical examples.