The main aim of this paper is to develop an automated three-dimensional adaptive h-refinement strategy with the special emphasis on the use of the transition elements. To establish this strategy, the following issues are mainly studied in this paper :
First, a new three-dimensional transition solid element was established by adding variable nodes to basic eight-node for an effective connection between the refined region and the coarse region with minimum degree of freedom possible. To be consistent with eight-node solid element in the accuracy of results during adaptation process, this new transition element was improved through the addition of the appropriate nonconforming modes. It was verified that the proposed elements passed patch tests and there are no zero energy mechanisms identified by the eigenvalue analysis in the elements.
Second, to obtain a better stress field for the error estimation, the superconvergent patch recovery which is proposed for one- or two-dimensional problems by Zienkiewicz and Zhu is extended to recover 3D continuous nodal stresses in this study. The extension of the technique to three-dimensional problems is explained in detail and one typical example is presented to show that this can be effectively used for 3D problems. The results show that the superconvergent patch recovery procedure gives better solution in comparison with others irrespective of mesh regularity and can provide good value at the domain boundary.
Third, a new scheme for three-dimensional adaptive h-refinement strategy by transition elements is presented. This scheme is entirely modular and has a special advantage of carrying out the independent refinement of any element from its neighboring elements. Thus the complicated manipulations in conjunction with the accomodation of irregular nodes due to the refinement can be avoided and only a simple data lists is needed for the complicated refinement process. And some locking problems associated with imposing displacement constraints to enforce compatibility in the conventional adaptive h-refinement are easily overcome.
Finally, in order to demonstrate the performance of the three-dimensional adaptive mesh refinement using the transition elements, some typical examples with a junction, discontinuities or a crack are presented. It is noted that the proposed algorithm is very useful in a wide range of practical engineering problems since the meshes are constructed based on the simple and efficient solid element.
