Effect of geometrical parameters on mode shape and critical buckling load of dished shells under external pressure

A conical shell frustum with flat circular top is called dished shell. These type of shell find application in many aerospace and rocket industries. These type shells undergo a special type of buckling phenomenon similar to arches and spherical caps, which needs to be studied in detail. In the present study, an Eigen value buckling analysis of dished shallow shell is attempted. Two types of dished shallow shells are chosen: with a stiff top, and with a flexible top. Finite element analysis is done to find out the effect of various geometrical parameters such as shell thickness, height, top flat region radius and various boundary conditions on the mode shape and critical buckling load under uniform external pressure. It is found that mode shape and critical buckling pressure changes with variation in geometrical parameters of shells. It is also observed that shells having stiff central flat circular region show different harmonics in conical region for different modes of deformation and the values of critical pressure for different modes are very close to each other. However, for dished shallow shells with flexible top critical buckling pressures are significantly different for various modes except conjugate ones. The numerical analysis results for dished shell with flexible top and fixed boundary condition is compared with analytical solutions of an equivalent spherical cap and for stiff top condition with analytical solutions of an externally pressurized conical frustum. The information obtained from this study, can be used for design improvement and failure mode analysis of dished shells.