Novel quadtree algorithm for adaptive analysis based on cell-based smoothed finite element method

For finite element analysis of structures with irregular geometry, unsatisfactory meshing quality could be the major concern. Adaptive meshing technique is usually applied to modulate the mesh to approach the geometry. The stress solution from triangular elements is understood less accurate than that of quadrilateral elements. Therefore, adaptive technique for quadrilateral elements is desirable for more proficient analysis of complex geometry. This paper develops a novel adaptive technique that combines a newly developed quadtree algorithm with the cell-based smoothed finite element method (CS-FEM) for automatic mesh adaptation using quadrilateral elements. Since the quadtree algorithm generates a grid with different sizes of quadrilaterals, a number of new CS-FEM elements of n-sided polygon are concomitantly constituted. In the adaptation process, the energy error norm and the geometrical feature are applied as the calibrations for the adaptive refinement. The elements on curved boundaries are either cut or merged with the surrounding elements automatically. It is found that the present new quadtree algorithm works very effectively with the CS-FEM formulation in view of stability and convergence. The results by the current S-FEM are found generally more accurate than those of the general finite element method (FEM) counterpart, especially in terms of strain energy solutions.