A hybrid stress flat-shell finite element for the analysis of folded structures

A new quadrilateral 4-node flat shell finite element for the analysis of folded structures has been developed based on the hybrid stress formulation involving, as primary variables, compatible displacements and elementwise equilibrated stress resultants. As regards the membrane behavior, bilinear shape functions for the displacements on the element domain and quadratic shape functions for the displacements along the edges are used, including the in plane rotation as kinematical parameters. A stress resultants interpolation which is a priori equilibrated within each element, co-ordinate invariant, and ruled by the minimum number of parameters for element stability is accurately set up. In regular geometry, this stress approximation specializes in that proposed in. The modeling of the bending part is inspired by that recently proposed by the authors. The displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and the stress resultants approximation is elementwise equilibrated and ruled by the minimum number of parameters. Stress parameters are eliminated at the element level. Therefore, the resultant element equations involve only displacement nodal values (6 dofs per node), as standard finite elements, and the element is readily implementable into existing finite element codes, besides being simple and locking-free. The element performance is tested both in the linear and geometrically non linear cases. In particular, geometrically non linear analyses are performed using the corotational approach. The accuracy in reproducing the nonlinear equilibrium path is shown by comparison with the results obtained using the codes ABAQUS and KASP.