Simulation of buckling tests using a mixed FEM for pressurized shallow spherical shells and the reduced stiffness analysis

Abstract

This chapter discusses the buckling behavior of clamped shallow spherical shells having a radius of curvature R, thickness t, base radius a, Young's modulus E, and Poisson's ratio v subjected to uniform external pressure q and shown by the diagram in it. Fifty-two experiments are compared to the present mixed-finite-element analytical results on the elastic pre and postbuckling deflection behaviors of clamped thin-walled shallow spherical shells under external pressure. The numerical simulations have been done using the degenerated nine-node shell element with mixed interpolation functions. The nonlinear prebuckling paths have been statically calculated, and then the corresponding postbuckling behaviors have been obtained through nonlinear dynamic analysis. The finite element based reduced stiffness method for imperfection-sensitive shell buckling design has also been developed in this chapter. Apart from discussing the illumination of the specific buckling behavior of the pressurized shallow spherical shells, this chapter suggests that a similar interplay among experimental, nonlinear analytical and reduced stiffness analytical results may be useful in elucidating behavior and providing a design analysis procedure for many other shell-buckling problems.