Verification and optimization of nonlinear shell buckling formula of thin-shell structures

Abstract

Shell is a popular form of structures as it can withstand relative large load with small thickness, which satisfies the aesthetic preference. Due to the curvatures of shell structures, shell can carry the distributed load as membrane forces instead of bending moments. Due to the small thickness, shell structures are highly sensitive to imperfections. As the loads are carried by membrane forces, buckling failure often govern the design of shell structures. The buckling load could be predicted accurately by performing a nonlinear finite element analysis. However, performing a nonlinear finite element analysis is very time-consuming and expensive as a lot of computational efforts required. The currently used design formula of shell structures can lower down the requirement of computation in a great degree while the accuracy is not very satisfying. Different from other types of structures, shell buckling often starts locally, therefore, an assumption is made that shell buckling is a combination of membrane forces and curvatures. Thus, an improved buckling formula is proposed. In this report, the proposed formula is verified and optimized. In addition, the shell behaviour before buckling has been illustrated by a series of figures that show the deformation and stresses at several load steps.