A model-adaptive hanging node concept based on a new non-linear solid-shell formulation

In this contribution we propose an innovative approach to automatically refine shell finite element meshes in thickness direction. The procedure employs a new eight-node solid-shell element formulation based on the concept of reduced integration with hourglass stabilization. Apart from the important advantages of computational efficiency and robustness this element formulation offers the possibility to work with a variable mesh density in thickness direction. In the present paper we suggest an adaptive approach using the hanging node concept to avoid additional mesh distortion. Among different stress- and strain-based error criteria the warping of the cross-section and the residual error in the solution of the strong form of the balance of linear momentum have been proven to be suitable error measures. The former represents the deviation of the realistically non-linear dependence of the characteristic strain coefficient from its corresponding linear distribution. Applications show that the mesh refines, as expected, in loading domains, in the neighbourhood of bearings or regions with strongly accumulating inelastic deformation. On the other hand, the discretization remains rather coarse in uncritical parts of the structure which decreases the computational effort noticeably.