A consistent triangular thin flat shell finite element with drilling rotation based on the strain approach

Abstract

The paper offers a new flat shell finite element. It results from the combination of a membrane and a bending elements, both founded on the strain based formulation. The used membrane element is the T43_Eq. It is a triangular element with four nodes, three nodes at the vertices and the fourth one at the barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation procedure. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. Then, the plate element used for the construction of the shell element is a triangular four-node thin plate element based on: the deformation approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient. The shell element result of this combination is robust, competitive and efficient.