Nonlinear static analysis of thin shallow and non-shallow shells using tensor formulation

In this study, a large-amplitude nonlinear static analysis of thin shallow and non-shallow shells is performed. Simply supported linear homogeneous elastic spherical panels and parabolic conoidal shells subjected to concentrated and distributed external loads are considered. To model the shells, the non-orthogonal tensor theory is applied and, to describe the strain–displacement relations of the shells, two approximations of Koiter’s theory are employed. To obtain the set of nonlinear equilibrium equations, a large-dimensional model is obtained by expanding the field displacements using Fourier series and a reduced order model is generated by using the Karhunen–Loève method. The proper orthogonal modes (POMs) of Karhunen–Loève method are acquired from a numerical model performed via Finite Element Analysis (FEA). The nonlinear static paths are compared with literature and with results obtained from FEA. The tensor formulation applied in this work has proven to be efficient when dealing with both shallow and non-shallow shells which are described by non-orthogonal curvilinear coordinates on nonlinear regime. •Koiter theory is applied to determine the nonlinear static response of thin shells.•Shallow and non-shallow shells were studied using tensor formulation.•Low-dimensional shell models using Proper Orthogonal Decomposition.•Semi-analytical solution is compared with FEM showing a good agreement.