Investigation Of Buckling Load Of Thin Spherical Shells And Single-layer Reticulated Spherical Shells

Thin spherical shells and single-layer reticulated spherical shells are verypopular structures in many different engineering branches such as civil engineering,aeronautics and astronautics. The load capacity of these structures is mainlydependent on their buckling behavior. Large discrepancy between the test results ofthe mean buckling load and the value predicted by classical buckling theory makesit a need to find a reliable way to predict closely the load capacity of thesestructures. In this study, finite element (FE) modeling and experiments, in whicheffect of the geometric nonlinear behavior and initial geometrical imperfections wasconsidered, were conducted on these structures under uniform radial or verticalcompressure using ABAQUS to investigate their load capacity and to derive anempirical formula to predict their buckling load approximately and reliably.It was revealed by FE modeling that there is a nearly-horizontal plateau or aconverging point, corresponding to a nearly-constant post-buckling load, in thepost-bucked load-deflection curves of thin spherical shells and single-layerreticulated spherical shells. Based on this post-buckling behavior and using thework and energy theorem according to the characteristics of the post-bucklingbehavior of the shells, an empirical formula for the buckling load of thin sphericalshells was obtained and validated by FE modeling. Then a large amount ofnumerical analysis was conducted using ABAQUS to prove that the coefficient inthe formula is a constant and to determine the value of the constant. Existingexperimental results were compared with the value predicted by the empiricalformula, showing the reasonability of using the post-buckling load to predict thebuckling capacity of thin spherical shells.Because of the similar post-buckling behavior of thin spherical shells andsingle-layer reticulated spherical shells, the continuum analogy method was used topredict the buckling load of the single-layer reticulated spherical shells, and theformula derived for thin spherical shells was thus extended.Finally, some experiments of three-way grid single-layer reticulated sphericalshells were designed and conducted to investigate the buckling behavior. The resultsalso showed the reasonability to use the post-buckling load to predict the load capacity of single-layer reticulated spherical shells.In general, through both FE modeling and experimental study, in which theeffect of the nonlinear behavior and initial geometrical imperfections wasconsidered, and based on the post-buckling behavior, this study obtains a formula topredict the load capacity of both thin spherical shells and single-layer reticulatedspherical shells approximately and reliably, providing very important reference toengineering design of these structures.