06.12.2018 17:00 Walter Zulehner (JKU Linz):
On a New Mixed Formulation of Kirchhoff-Love and Reissner-Mindlin Plates and ShellsGebäude 33, Raum 1431 (Werner-Heisenberg-Weg 39, 85577 Neubiberg)

In 2D linear elasticity it is well-known that a stress tensor field satisfying the homogeneous equilibrium equation can be expressed in terms of the Airy stress function provided the domain is topologically simple. There is a similar result for the bending moment tensor field in plate models, if the mid-surface of the plate is simply connected. While the stress tensor field in 2D inear elasticity can be written as a second-order differential operator applied to the Airy stress function, the bending moment tensor field in plate models is only a first-order differential operator applied to some 2D vector field. We will show how this result can be used to reformulate the Kirchhoff-Love and the Reissner-Mindlin plate and shell models as well-posed second-order systems. The reformulation of the plate and shell models as second-order systems allows for discretization methods in approximation spaces with continuous functions. This includes standard continuous Lagrangian finite element methods and spline spaces from isogeometric analysis on multi-patch domains with continuous patching only.