Geometrically nonlinear analysis of composite plates and shells using a flat triangular shell element

Abstract

An updated Lagrangian formulation of a three node flat triangular shell element is presented for geometrically non-linear analysis of laminated plates and shells. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element that is similar to the Allman element, but a derivative of the Linear Strain Triangular (LST) element. Results are presented for static response analysis (snap-back behavior of a cylindrical panel, large rotation response of a cantilever beam under an end moment, cylindrical shell under pinching and stretching loads and hemispherical shell under pinching and stretching loads); for dynamic response analysis of a cylindrical panel; and for thermal postbuckling analysis of an imperfect square plate and a cylindrical panel. The element will be used in the near future for the analysis of large inflatable structures which are highly flexible and are expected to undergo large deformations and rotations. In order to estimate the accuracy of the present formulation in predicting the nonlinear response of such large flexible structures, static analysis of an apex-loaded circular arch is performed. The arch presented is a building block of a large inflatable structure. The present results are in good agreement with the results available in the existing literature and those obtained using the commercial finite element software ABAQUS, demonstrating the accuracy of the present formulation.