Polygonal Cell-based Smoothed Finite Element Using Quadrilateral Smoothing Domains for 2D Plane Stress Problem
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Abstract
This study investigated the polygonal cell-based smoothed finite element divided to quadrilateral smoothing domains. Problem domain, discretized to n-sided polygonal elements, is constructed by transformation of triangular or quadrilateral elements. For smoothing cells, quadrilateral elements are equally created according to number of polygonal element sides. Cantilever two-dimensional plane stress beam subjected to parabolic shear traction at free end is utilized as a benchmark problem to validate the capability of this method. Beam’s responses including displacements and stresses obtained from numerical analysis are compared to both FEM and analytical solutions. Despite the fact that the results obtained from this method arranged between the results from T3 and Q4 finite element method as coarse mesh, more accuracy than finite element results and closed to analytical solutions can be achieved at the finest 48 × 12 mesh. Since there is no mapping between physical and parent element, the flexibility of using polygonal cell-based smoothed finite element can be employed to complex regions/shapes or non-meshing areas efficiently, in author’s perspective.
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