On a new mixed formulation of Kirchhoff plates on curvilinear polygonal domains
For researchers in computational mechanics, this provides a method to handle more complex domain geometries, though it is an incremental extension of prior work.
The paper extends a mixed formulation for Kirchhoff plate bending problems from polygonal to curvilinear polygonal domains by introducing a Lagrange multiplier approach, enabling the solution via three consecutive second-order elliptic problems.
For Kirchhoff plate bending problems on domains whose boundaries are curvilinear polygons a discretization method based on the consecutive solution of three second-order problems is presented. In Rafetseder and Zulehner (preprint, arXiv:1703.07962) a new mixed variational formulation of this problem is introduced using a nonstandard Sobolev space (and an associated regular decomposition) for the bending moments. In case of a polygonal domain the coupling condition for the two components in the decomposition can be interpreted as standard boundary conditions, which allows for an equivalent reformulation as a system of three (consecutively to solve) second-order elliptic problems. The extension of this approach to curvilinear polygonal domains poses severe difficulties. Therefore, we propose in this paper an alternative approach based on Lagrange multipliers.