Nonlinear Finite Element Simulation of Large Deformation in Elastic Structure Shells under Localized Loading

Abstract

This research work does a comprehensive nonlinear finite element simulation of thin elastic shells when subject to a localized loading and explains the role of geometric nonlinearity in large deformation. The researchers analyzed spherical and cylindrical shell models to investigate differences in stiffness, stress concentration, and post-buckling response. The model used the second Piola-Kirchhoff stress and Green-Lagrange strain tensor to account for large strain effects in an updated Lagrangian context. The results showed that the spherical shells exhibit sharp snap through instability, while the cylindrical shells behave with gradual reduction in stiffness with increasing indentation. Load-displacement and strain energy analyses clearly revealed the switch from bending-dominated deformation to membrane-dominated deformation. According to the study, linear theories will not be able to adequately predict the responses of shells to concentrated loads. Thus, nonlinear finite element analysis is necessary. This is essential for assessing the stability and performance of advanced structural applications.