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Description
Recent developments in digitalization and digital fabrication have enforced an increasing complexity of the structural components for the analysis. A promising way to discretize components is to rely on polygonal meshes, as they provide advantages such as simplified mesh generation and highly localized mesh refinement, for example, Voronoi tessellation and quadtree meshes. This calls for finite element formulations that can handle an arbitrary number of edges, such as the scaled boundary finite element method that allows the use of both convex and concave elements. A particular focus is placed on thin-walled structures, widely used in different domains of engineering. This encouraged the development of various thin plate and shell theories. Among these, Reissner-Mindlin theory has gained prominence due to its C$^{\circ}$-continuity requirement, simplifying the selection of interpolation functions in comparison to other plate theories. Despite being computationally more efficient, low-order Reissner-Mindlin plate elements face a significant disadvantage. They are prone to locking effects known as shear locking in the thin plate limit. Further, the plate formulation addresses a specific consideration of constitutive laws that restricts the plate’s application. Accounting additional thickness stretches on element level yields the computation with a full three-dimensional material description. However, it comes with an additional locking phenomenon, called Poisson’s thickness locking.
The presented work focuses on the reduction of shear locking in polygonal Reissner-Mindlin plate elements. It follows a formulation for a scaled boundary finite element that employs mixed interpolation techniques for the bending and shear components. An assumed natural strain method is derived to interpolate the shear strains at the section level of a scaled boundary element. It reduces transversal shear locking significantly for the polygonal scaled boundary finite plate element. Additionally, three-dimensional material laws are incorporated by enhanced thickness strains with a linear interpolation along the thickness direction, effectively addressing Poisson’s thickness locking.
