Reliability analysis and design of randomly imperfect thin cylindrical shells against post-critical drops

Abstract

Thin-walled cylindrical shells are employed for high specific bending stiffness and light design. Elastic buckling of shell is a critical design consideration. The Knock Down Factors (KDFs) are stipulated for accounting the markedly reduced experimental critical load by multiplying the linearized critical load by the KDF. Key to such reductions is the nonlinearity induced modal interactions among the closely spaced buckling modes, over which, the geometric imperfections act in synergy. Being the lower bound of an extensive experimental dataset; the stipulated design KDFs are largely over-conservative; which can be relaxed by accounting for imperfections. With this as the eventual goal, this study first demonstrate the feasibility of modeling the KDFs as uniformly distributed Uncertain-but-Bounded (UBB) type variable. The UBB description is employed to obtain the reliability bounds and the design variables (radius-to-thickness R/t and L/R ratio) for achieving a target reliability index through Reliability Based Design (RBD). Repeated computations of KDFs for reliability assessment are bypassed by fitting the KDFs vs. R/t relations for given L/R. The approach is demonstrated on a thin cylindrical shell with a zero-mean, stationary, gaussian, stochastic imperfection fields. The Riks method is employed for the nonlinear finite element analysis of the shell using the code ABAQUS. The KDFs and reliability bounds are provided for varying imperfections and are compared with an existing study on refining the KDFs. Furthermore, the RBD presents the desired R/t for a given L/R for achieving a target reliability index and the respective KDF for a given imperfection level. The L/R dependency is shown to reduce the over-conservatism in the design stipulation.