Thermal buckling analysis of FGM sandwich beams under the action of transverse non-uniform temperature field
The thermal buckling governing equation of functionally gradient materials(FGM)sand-wich beams subjected to transverse non-uniform heating is derived in view of the classical geomet-ric non-linear beam theory.For the end clamped boundary condition beam,the beam undergoes branch buckling as the temperature increases.Considering the small deformation corresponding to the critical state of branch buckling,the problem of nonlinear boundary value is reduced to a linear ei-genvalue problem.The analytical solution of dimensional critical buckling temperature difference of the system is obtained by solving the linear eigenvalue problem.The non-linear boundary value problem is calculated by shooting method.In addition,the thermal post-buckling equilibrium path and equilibrium configuration of the system are obtained as well.The effects of layer thickness ratio,gradient index,temperature field and geometric parameters on the thermal post-buckling equilibrium path and equilibrium configuration of FGM sandwich beams are investigated by examples.The results show that the critical buckling temperature difference of FGM sandwich beam increases when the relative thickness and gradient index of the gradient layer increase.
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