Comparative study of shell element formulations as NLFE parameters to forecast structural crashworthiness

Abstract

This work made a comparison of the effects of selected element formulations (EFs) through nonlinear finite element analysis (NLFEA) and physical configurations in scenario design, particularly target locations. The combined results help in quantifying structural performance, focusing on crashworthiness criteria. The analysis involves nonlinear dynamic finite element methods, using an explicit approach applied to an idealized system. This system models ship-to-ship collisions, specifically the interaction between Ro and Ro and cargo reefer vessels, with one striking the other. Summarizing initial NLFEA results reveals that the chosen EF significantly influences the crashworthiness criteria. Notably, differences in formulations lead to different calculation times. The Belytschko–Tsay (BT) EF is the quickest, followed by the Belytschko–Leviathan (BL), with around a 36% difference. Conversely, formulations such as the Hughes–Liu involve much longer processing times, more than twice that of BT. To address the potential impact of shear locking and hourglassing on calculation accuracy during impact, the fully integrated (FI) version of the EF is used. It mitigates these undesired events. For formulations with the same approach, the FI BT formulation suppresses hourglassing effectively, unlike others that show orthogonal hourglassing increments. To ensure reliability, rules were set to assess hourglassing. The criterion is that the ratio of hourglass energy to internal energy should be ≤10%. All formulations meet this criterion and are suitable as geometric models in NLFEA. Regarding reliability and processing time, analyzing the computation time offers insights. Based on calculations, BL is the fastest, followed by Belytschko–Wong–Chiang, while the FI BT formulation takes more time for the same collision case.

Keywords

• structural performance
• ship–ship collision
• nonlinear finite element analysis
• element formulation
• crashworthiness criteria