Buckling and Post-buckling of Circular/Annular Plates

Abstract

The stability of circular and annular plates under mechanical and thermal loads are presented in this chapter. The chapter begins with the presentation of the strain-displacement relations based on the von Karman and Kirchhoff assumptions employing the classical plate theory. The linear thermoelastic constitutive relations between the stress and strain components are considered and the stress and moment resultants for a plate with general heterogeneous material property, functionally graded, are obtained in terms of the nonlinear displacement components. The nonlinear equilibrium equations are derived basis on the stationary potential energy, and the linear stability equations of an annular plate are obtained by means of the adjacent-equilibrium criterion. Employing these basic governing equations, the chapter continues to present a number of practical stability problems. Thermal buckling of circular and annular plates based on the classical and shear deformable theories, circular plates on elastic foundation, rotating plate under thermal loading, and the buckling and post-buckling of plates with geometric imperfection are discussed in detail and approximate closed form solutions for a number of cases are presented.