Project Details
Projekt
A computationally efficient virtual solid-shell element for the non-linear analysis of thin structures
Subject Area
Applied Mechanics, Statics and Dynamics
Mechanics
Mechanics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 495926269
The virtual element method (VEM) has established itself in recent years as an alternative to the finite element method (FEM). The main advantage of the method is that general polygonal and polyhedral meshes with irregularly shaped elements are possible. The number of nodes is arbitrary. Non-convex shapes and hanging nodes can be considered in the VEM-based discretization without further special treatment. For these reasons, VEM is considered as a highly promising discretization method for structures with complex geometries or localizing deformation. Since its introduction only a decade ago, several powerful VEM formulations for nonlinear elastic and inelastic problems in solid mechanics have been developed. One research question that is still open is the choice of stabilization, which becomes necessary due to the under-integration of a part of the stress response automatically resulting from the derivation. In the present project, previously unused but now established knowledge from other methods, the finite element method and the discontinuous Galerkin method, is to be generalized for the VEM. It is expected that this will result in a stabilization for the VEM that can be used over a wide range of applications. One long-term goal of the project is to develop a stabilization that also works automatically in industrially used program packages. The second essential aspect of the project is the development of a VEM for shell-like structures. The aim is to develop a VEM for thin-walled structures and to get by with only one element over the thickness. To achieve the latter, the non-linearity of the stress across the thickness has to be taken into account, proceeding in the shell plane analogously to the two-dimensional VEM. Such an approach is new in the literature on VEM. The long-term goal is to be able to efficiently calculate complex shell structures, as they occur in modern architecture and civil engineering, but also in the human body.
DFG Programme
Research Units
