Buckling of Circular Cylindrical Shells

Abstract

This chapter is devoted to the stability behavior of thin cylindrical shells. The basic governing equations of thin circular cylindrical shells employing the Donnell theory with the von-Karman geometrical non-linearity are derived. The nonlinear strain-displacement relations, the nonlinear equilibrium equations, and the linear stability equations are derived employing the variational formulations. The cylindrical shell under uniform compressive axial load is considered and the buckling load is obtained and given by closed form solution. Thermal buckling of cylindrical shell made of FGM for the uniform temperature rise, linear radial temperature, and the nonlinear radial temperature are presented and the effect of piezo-control is examined. Buckling and postbuckling of thin cylindrical shells with piezo-control under thermal loads is discussed and the chapter concludes with the stability discussion of cylindrical shells on elastic foundation. The buckling loads of cylindrical shells of isotropic/homogeneous material are derived by simply setting proper values for the power law index of the FG materials.