A new model for thermal buckling of an anisotropic elastic composite beam incorporating piezoelectric, flexoelectric and semiconducting effects

A new model for thermal buckling of an anisotropic elastic composite beam consisting of a dielectric core and two thin semiconductor surface layers is developed. The field equations and boundary conditions for the beam are obtained by using the piezoelectricity, flexoelectricity, strain gradient elasticity and semiconductor theories and the kinematic relations for a Timoshenko beam. The current model includes piezoelectric, flexoelectric and semiconducting effects simultaneously, unlike existing models. A variational formulation based on the principle of minimum potential energy is employed for the dielectric core, where the contribution of the two thin semiconductor surface layers is incorporated through the work done by the free charge density. Two simplified models for piezoelectric and flexoelectric composite beams incorporating the semiconducting effect are obtained as two special cases of the new model for the dielectric composite beam. Thermal buckling of a simply supported composite beam with a piezoelectric or flexoelectric core and two thin semiconductor surface layers is analytically studied by directly applying the two simplified models, leading to the determination of the critical buckling temperature and concentration perturbation of free carriers in the composite beam. Numerical results show that the presence of the piezoelectric or flexoelectric effect results in an increased critical buckling temperature, while the inclusion of the semiconducting effect leads to a reduced value in both cases. In addition, it is seen that the redistributions of free carriers in the piezoelectric composite beam are uniform, whereas those in the flexoelectric composite beam are non-uniform along the beam thickness direction.