An αARS-poly formulation on trimmed quadrilateral-dominant meshes for Reissner–Mindlin plate analysis with complex geometries

Abstract

This work introduces an α-assumed rotations and shear strains polygonal formulation (αARS-Poly) embedded within a trimmed quadrilateral-dominant mesh for Reissner–Mindlin plate analysis. The method combines the numerical robustness of α-scaled assumed rotation fields with the geometric adaptability of level-set-based trimmed meshes. Regular quadrilateral elements are retained in the interior domain, while boundary-intersected cells are automatically converted into convex polygonal elements without re-meshing. The proposed approach applies a consistent α-scaled tangential rotation reconstruction to both regular and trimmed elements, preserving a unified stiffness formulation for arbitrary polygonal topologies. The formulation eliminates shear locking, satisfies isotropy and zero-energy mode requirements, and maintains stability under mesh distortion. Numerical investigations confirm optimal convergence in displacement and energy norms for thin and moderately thick plates, demonstrating improved stiffness prediction and robustness compared with fully polygonal discretizations. The resulting framework provides a simple, accurate, and automation-friendly solution for plate problems involving complex geometries and internal cutouts.