| In this thesis an h-adaptive strategy is developed based on a subdivision refinement technique for three-dimensional domain problems that allows to obtain more reliable results when the finite elements method is applied. In this sense, three procedures with their respective formulations are developed in order to carry out error estimating using the Zienkiewicz-Zhu ( Z2) estimator, considering the presence, or not, of nonconforming nodes in hexahedrons elements. For considering the presence of these nodes, fictitious elements are used, which are generated dividing the adjacent elements to those divided by the subdivision refinement technique.; For evaluating the Z2 estimator, stress recovery procedures SPR and REP are applied, adapting them to the refinement type developed. Additionally, improvements are implemented that allow to obtain good results when the SPR technique is applied in the contour region. Simultaneously, similar improvements are developed in the REP technique.; For applying the h-adaptive procedure with subdivision refinement, two procedures are developed that allow to approach the number of good elements in the analyzed domain. These procedures assure that the numbers of divisions for element are carried out with a positive integer magnitude, also guaranteeing that the imposed division grade in the interface region between the divided and no-divided elements. The developed h-adaptive procedure with equivalent divisions was found to be the most effective and can be controlled starting from a reduction factor element, which can be introduced by the user. This offers the advantage of obtaining, with a smaller number of mesh steps, better solutions of finite elements according to the user's requirements.; Finally, it is demonstrated that the developed refinement procedure for subdivision presents excellent convergence rate for problems with soft solution and in that cases where the solution is singular. Using this procedure the convergence rate is improved until reached values are similar to those obtained for problems with soft solution.; The developed programs are validated using well-known problems. |
