A reliability-based design against post-buckling load drop in spherical shell cap with stochastic imperfections

Abstract

Elastic buckling is a critical design consideration for deep spherical shell caps. Significant reduction is observed in the experimental critical load from the linearized eigen-buckling analysis, for reasons extensively discussed in the past and relooked recently through the energy barrier concepts. The Knock Down Factors (KDFs) were proposed to account for such a reduction. The highly conservative KDFs constitute the lower bound of a large experimental dataset; that can be reconciled by nonlinear stability analysis of the imperfect shell. This study models the KDFs as Uncertain-but-Bounded (UBB) variables to present a Reliability-Based Design (RBD) for spherical shell caps having random geometric imperfections in radius (R) and thickness (t). The RBD furnishes the pertinent design variables ((R/t) ratio and the dome height-to-base radius (H/r0) ratio) for a target reliability index (β) and the respective KDFs. A metamodelling approach is employed to reduce the computational burden of the proposed RBD for a thin spherical shell cap having zero-mean, stationary, homogeneous, gaussian stochastic geometric imperfections. The Riks algorithm is employed in the commercial code ABAQUS for the finite element-based nonlinear stability analysis of shells. The KDFs and the reliability bounds are presented for varying degrees of imperfections. Remarkably, the margin of conservatism in the KDFs is shown to be narrowed down by incorporating the dependency on (H/r0).