Extended sequential limit analysis: Addressing large deflections and shape changes in strain hardening circular membranes with a moving coordinate system

Abstract

The sequential limit analysis (SLA) approach can trace load–deflection response and the corresponding plastic limit load of the structures accurately and efficiently. However, this method is limited to the structures without large shape changes in the plane stress directions. In this study, an extended SLA established on moving coordinates is proposed to investigate its further extension for strain-hardening circular membranes with large deflections and shape change behaviors. This new method features dividing entire analysis into sequential optimization problems based on moving coordinate systems to deal with the shape change in plane stress direction for the strain-hardening circular membranes subjected to large deflections. The corresponding adaptive geometry update strategy is also presented. Moreover, the elastic–plastic incremental simulations are conducted for the purpose to validate the correctness and feasibility of the simplifications during model construction and the analysis accuracy of this newly proposed method. From the contrastive results between the extended SLA and ABAQUS simulation, the accuracy of this new approach is confirmed. Furthermore, from the parametric analysis results, the fact can be concluded that the accuracy of SLA for load estimation will be improved with the increase of material Young’s modulus, and reduces with the increase of the initial yield strength and the hardening exponent and hardening coefficient. The accuracy of this method is more sensitive towards hardening exponent and initial yield strength while it is less sensitive towards hardening coefficient. In addition, this extended SLA method with the assumptions of zero bending moment can tolerate a high range variation of thickness–radius ratio, particularly in materials with higher Young’s modulus. These characteristics enables this method be adopted in wild practical application fields as a feasible tool to design the membrane structures initially and determine the structure safety factors preliminarily.