In the framework of the Jacobi-weighted Sobolev space, we design the a-posterior error estimators and error indicators associated with residuals and jumps of normal derivatives on internal edges with appropriate Jacobi weights for the p-version of the finite element method. With the help of quasi Jacobi projection operators, the upper bounds and the lower bounds of indicators and estimators are analyzed, which shows that such a-posteriori error estimation is quasi optimal. The indicators and estimators are computed for some model problems and programmed in C++. The numerical results show the reliability of our indicators and estimators.

In the framework of the Jacobi-weighted Sobolev space, we design the a-posterior error estimators and error indicators associated with residuals and jumps of normal derivatives on internal edges with appropriate Jacobi weights for the p-version of the finite element method. With the help of quasi Jacobi projection operators, the upper bounds and the lower bounds of indicators and estimators are analyzed, which shows that such a-posteriori error estimation is quasi optimal. The indicators and estimators are computed for some model problems and programmed in C++. The numerical results show the reliability of our indicators and estimators.

Determination of the stress distributions in post-core restored endodontically treated teeth is challenging due to the fact that the post and core systems, the root and its canal, and the bony structures supporting the root have small dimensions and are structurally complex. In this research, a 3D finite element model was developed to evaluate the stress distributions in a post-core restored endodontically treated maxillary incisor under various static loads. The physical model includes dentin, PDL, bone, post, core, gutta percha and crown. All materials are assumed to be homogenous, isotropic, and linear elastic. The effects of various factors on the stress distributions are investigated through simulations. These factors include post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters. It has been found that the horizontal loading is the most dangerous, which causes the highest stresses in dentin and posts, followed by the oblique loading and the vertical loading. The above listed factors, such as post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters, do not change the stress distributions and magnitudes significantly under horizontal and oblique loading. However, the stresses are sensitive to the above factors under the vertical loading, and it has been found that the stress distributions in both dentin and the post are the most uniform without stress concentrations when the elastic modules of the post and the core are similar to that of dentin. Regarding the effects of the gaps at the cervical region on the stress distributions in dentin, the high stresses at the apical portion of the root and the bottom of the gaps decrease as the increase of the depth of the gap under vertical loading. Overall, the sharp angle and notch of the gap at the coronal entrance of the canal should be avoided in tooth restoration since they can cause stress concentrations. On the effects of the ferrule heights, the changes of the stress distributions in dentin and the post are insignificant except that higher ferrule shows lower stresses at the top of the ferrule. Regarding the effects of the diameters of the posts, the results show that although the posts with large diameters support more loads, they cause high stress concentrations at the apical portion of the root, which is not desirable.

No description available.

Determination of the stress distributions in post-core restored endodontically treated teeth is challenging due to the fact that the post and core systems, the root and its canal, and the bony structures supporting the root have small dimensions and are structurally complex. In this research, a 3D finite element model was developed to evaluate the stress distributions in a post-core restored endodontically treated maxillary incisor under various static loads. The physical model includes dentin, PDL, bone, post, core, gutta percha and crown. All materials are assumed to be homogenous, isotropic, and linear elastic. The effects of various factors on the stress distributions are investigated through simulations. These factors include post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters. It has been found that the horizontal loading is the most dangerous, which causes the highest stresses in dentin and posts, followed by the oblique loading and the vertical loading. The above listed factors, such as post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters, do not change the stress distributions and magnitudes significantly under horizontal and oblique loading. However, the stresses are sensitive to the above factors under the vertical loading, and it has been found that the stress distributions in both dentin and the post are the most uniform without stress concentrations when the elastic modules of the post and the core are similar to that of dentin. Regarding the effects of the gaps at the cervical region on the stress distributions in dentin, the high stresses at the apical portion of the root and the bottom of the gaps decrease as the increase of the depth of the gap under vertical loading. Overall, the sharp angle and notch of the gap at the coronal entrance of the canal should be avoided in tooth restoration since they can cause stress concentrations. On the effects of the ferrule heights, the changes of the stress distributions in dentin and the post are insignificant except that higher ferrule shows lower stresses at the top of the ferrule. Regarding the effects of the diameters of the posts, the results show that although the posts with large diameters support more loads, they cause high stress concentrations at the apical portion of the root, which is not desirable.

Typescript (photocopy) / xiii, 363 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Civil Engineering, 1981

Thesis (M.S.)--Rochester Institute of Technology, 1989. / Includes bibliographical references (leaves 88-89).

Thesis (Ph.D. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references (leaves 241-249).

Thesis (M.S.)--Ohio University, June, 1985. / Title from PDF t.p.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Civil Engineering, 1981. / Typescript (photocopy).