Plastic buckling of moderately thick hemispherical shells subjected to concentrated load on top

This study presents the analytical, numerical, and experimental results of moderately thick hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal translation and the load is vertically applied by a rigid cylindrical boss at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for rigid-perfectly plastic shells are formulated on the basis of Drucker–Shield’s limited interaction yield condition. The effect of the radius of the boss, used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Both axisymmmetric and 3D models are implemented in the numerical work to verify the absence of non-symmetric deformation modes in the case of moderately thick shells. In the end, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load–deflection curves obtained using three different approaches.

► An analytical expression has been derived for plastic buckling of hemispherical shell.
► The initial buckling load highly depends on the radius of the loading boss.
► The hemispherical shell deformation can be represented by a simple mathematical model.
► The analytical solution results closely match those of numerical and experimental values.
► This solution is rigorously applicable for shells having smaller values of R/t0.