Geometrically non-linear analysis of arbitrary elastic supported plates and shells using an element-based Lagrangian shell element

In the present paper, the ELF (element-based Lagrangian formulation) 9-node ANS (assumed natural strain) shell element was combined with the spring element for geometrically non-linear analysis of plates and shells sustained by arbitrary elastic edge supports that are subjected to variation in loading.This particular spring element serves as tool for modeling an arbitrary elastic edge support with 6 DOF (degrees of freedom). The elastic edge support was modeled by combining different spring models. The ANS method was used to overcome shear and membrane locking problems inherent in some thin plate and shell problems. In the formulation of the ELF characteristic arrays, the expression of element strains was adopted in the framework of the element natural coordinates. The non-linear analysis results of idealized edge supports were validated against the reference solutions available in the literature. As a result of the numerical test, the combination of the ELF 9-node shell element and spring element shows an exceptional performance for non-linear analysis of plates and shells under elastic edge supports.