A simple finite element model for the geometrically nonlinear analysis of thin shells

Abstract

A triangular flat finite element for the analysis of thin shells which undergo large displacements is proposed. It is based upon the geometrically nonlinear theory of von Kármán for thin plates and the total Lagrangian approach. It has a total of only twelve degrees of freedom, namely, three translations at each vertex and one rotation at each mid-side. The stiffness matrix and the tangent stiffness matrix are derived explicitly. The element is tested against nonlinear patch test solutions and its performance is evaluated by solving several standard problems. The directional derivatives of the potential energy function required for the stability analysis are also provided.