Adaptive meshing and analysis using transitional quadrilateral and hexahedral elements

摘要

In adaptive finite element analysis, h-type refinement can be achieved basically in two ways: (ⅰ) small elements are connected directly to large elements with full compatibility at element interfaces and (ⅱ) transitional elements are employed to link up elements of different sizes. While there is no difficulty in generating gradation triangular and tetrahedral meshes, generation of quadrilateral and hexahedral meshes of varying element sizes without severe element distortion proved to be a formidable task. The use of transitional elements allows meshes to be refined without element distortion, and the price that we have to pay is to develop general and efficient transitional elements in two and three dimensions. Transition elements, which satisfy the patch test, can be formulated by means of the enhanced assumed strain (EAS) method, which are in general more efficient than the incompatible elements. Alternatively, in this paper, we try to develop a series of versatile transition elements based on the hybrid stress approach. Direct designing stress fields for transition elements is just too complicated and especially impractical for 3D transition hexahedral elements. However, we found that the same stress field could be used for transition elements with variable number of nodes. By means of elimination and through numerical studies on some benchmark problems, 7- and 24-mode stress fields are adopted, respectively for 2D quadrilateral and 3D hexahedral hybrid stress transition elements. Strategy for generating refinement transition element meshes will be discussed, and the size of elements generated by the 1-irregular mesh restriction is compared with the predicted element size. The comparison shows that the meshing strategy employed in this study can effectively lead to an optimal mesh whose solution error is smaller than the prescribed one.