MESH GENERATION FOR hp TYPE FINITE ELEMENT ANALYSIS OF REISSNER-MINDLIN PLATES

Efficient finite element (FE) analyses of Reissner-Mindlin (RM) plate bending problems require a combination of high-order polynomial trial functions (p-extension) and locally refined meshes, or, in short, an hp-extension of the FE method. In the optimal case, exponential rates in the convergence of the error in energy norm can be obtained by such a discretization. This contribution discusses strategies for the fully automatic generation of finite element meshes that fulfill all the a priori requirements on mesh design for hp-type approximations of RM plate bending problems on general domains. At the same time, the resulting meshes are required to be "as coarse as possible" and consists purely of quadrilaterals. Numerical examples show that the meshes generated by our approach are indeed suitable for achieving very fast convergence on practical examples. Also, we present numerical investigations on the effects of mesh design on convergence in the presence of boundary layer effects, point singularities, and both combined. key words: mesh generation, coarse meshing, hp finite elements, Reissner-Mindlin plate theory, boundary layer effect.