Thermal buckling of shear deformable temperature dependent circular/annular FGM plates

• Asymmetrical thermal stability of annular FGM plates is analyzed.
• Temperature dependency of the properties is included.
• An exact analytical solution is presented to extract the buckled shape as well as bifurcation temperatures.
• Fundamental bifurcation points of symmetrically heated plates may be asymmetric.

Bifurcation behaviour of moderately thick heated annular plates made of FGMs is discussed in this study. Properties of the graded plate are distributed across the thickness based on the simple power law form. Temperature-dependency of the material properties is also taken into account. Two types of frequently used thermal loading, i.e. uniform temperature rise and heat conduction across the thickness loadings are considered. General nonlinear equilibrium equations based on the first order shear deformation plate theory (FSDT) and the associated boundary conditions are obtained employing the static version of the virtual displacements method. The pre-buckling solution is accomplished and the proper boundary conditions are chosen to assure the occurrence of bifurcation phenomenon. Stability equations are obtained based on the adjacent equilibrium criterion. Five resulted stability equations are decoupled and reduced to new equations in terms of lateral deflection and the edge zone functions. An exact asymmetrical solution is developed to calculate the critical buckling temperature difference of the plate for the above-mentioned cases of thermal loading. It is shown that the fundamental buckled configuration of annular plates may be asymmetric as previously assumed.