近年來為了降低牙橋製作的成本，對橋體金屬部分使用空心設計來節省材料，然而顯少有研究去對改變後的牙橋強度進行分析與討論，本研究目的為評估臼齒區內不同金屬陶瓷牙橋空心設計，在不同受力情況下，對於牙橋結構的力學行為影響。
本研究使用有限元素法建立三維金屬陶瓷牙橋模型作為力學分析。建構的模型包括牙橋最外層的陶瓷材料、牙橋內部不同空心設計之金屬支架與將空心部分填滿的陶瓷材料，施以不同大小的負載，並分成橋體受力與整個金屬陶瓷牙橋受力兩種受力情況來進行模擬分析，以了解牙橋在受力之後，其應力分布以及形變等情況。
本文模擬結果發現在牙橋連接體的位置應力值會較高，牙橋外部陶瓷部分的應力會大於內部金屬支架的應力，牙橋不同的空心設計對於牙橋結構之影響較小。由內部金屬應力的結果來觀察，陶瓷與金屬兩種材料在連接體的位置可能產生剝離，使得牙橋結構已經損壞。

In recent years, in order to reduce the cost of dental bridge produced using hollow design, the metal part of the dental bridge to save material. However, the research about the change dental bridge is seldom seen. The purpose of this study was to investigate the stresses and deformations in porcelain-fused-to-metal bridge by using finite element method(FEM), The parameters under consideration were loading modes and metal frame shapes.
The dental bridge model consists of the outermost layer of the ceramic materials, metal frame design of the bridge and ceramic materials filled in the hollow part of metal. Two different loading models, in which loadings are applied on the pontic and the entire metal-ceramic dental bridge, respectively, are simulated and analyzed. And then the 3-D stress and deformation are performed by using the finite element code ANSYS.
The results show that the stress will be higher at the location of the dental bridge connecting the body and dental bridge. Moreover, external ceramic part of the stress will be greater than the internal stress of the metal frame. The hollow design of the pontic has no significant effect on the strength of the dental bridge structure. In addition, phenomenon of interface debonding between the ceramic and metal may be happened as the loading is higher than 1000N.

[1] M. Ash, "Wheeler's Dental anatomy, physiology, and occlusion (7th edition)," Publisher: W.В. Sаunders 1993.
[2] 王妙先, "牙齒解剖與形態學," 合記圖書出版社, 1992.
[3] 洪純成, "牙科陶瓷技術學," 合記圖書出版社, 2010.
[4] R. W. Clough, "The finite element method in plane stress analysis," Proceedings of American Society of Civil Engineers, 2nd Conference on Electronic Computation,Pittsburgh,PA,pp.345-378, Sept.1960.
[5] A. Hrennikoff, "Solution of Problems of Elasticity by the Frame-Work Method," American Society of Mechanical Engineers vol. A8, pp. 169-175, 1941.
[6] R. Courant, "Variational methods for the solution of problems of equilibrium and vibrations," Bulletin of the American Mathematical Society, vol. 49, pp. 1-23, 1943.
[7] S. M., "Finite Element Analysis-Theory and Application with ANSYS.( 林政仁、陳新郁譯，有限元素分析-理論與應用ANSYS。)," 高立圖書有限公司, 2001.
[8] 劉晉奇、禇晴輝, "Engineering Applications of Finite ElementAnalysis with ANSYS.有限元素分析與ANSYS的工程應用," 滄海書局, 2006.
[9] H. F. K. a. M. Krah, " Keramiken - eine Übersicht," Quintessenz Zahntechnik 27, pp. 668-704, 2001.
[10] G. D. Quinn, A. R. Studart, C. Hebert, J. R. VerHoef, and D. Arola, "Fatigue of zirconia and dental bridge geometry: Design implications," Dental Materials, vol. 26, pp. 1133-1136, Dec 2010.
[11] A. R. Studart, F. Filser, P. Kocher, and L. J. Gauckler, "In vitro lifetime of dental ceramics under cyclic loading in water," Biomaterials, vol. 28, pp. 2695-2705, Jun 2007.
[12] S. IE, "Replacement of a tooth with a fiber-reinforced direct bonded restoration," General Dentistry vol. 48, pp. 314-318, 2000.
[13] H. Fischer, M. Weber, M. Eck, A. Erdrich, and R. Marx, "Finite element and experimental analyses of polymer-based dental bridges reinforced by ceramic bars," Journal of Biomechanics, vol. 37, pp. 289-294, Mar 2004.
[14] M. P. R. Luc Rutten, MDT, "審美インプラントにおける新しい視界QDTT," p. P.14~16, 2008.
[15] P. Christel, A. Meunier, M. Heller, J. P. Torre, and C. N. Peille, "Mechanical properties and short-term in-vivo evaluation of yttrium-oxide-partially-stabilized zirconia," Journal of Biomedical Materials Research, vol. 23, pp. 45-61, Jan 1989.
[16] L. B. Dion, F. Lefebvre, R. Bareille, Ch. Baquey, J.-R. Monties and P. Havlik, "Physico-chemistry and cytotoxicity of ceramics " Journal of Materials Science: Materials in Medicine vol. 5, pp. 18-24, 1994.
[17] A. R. Studart, F. Filser, P. Kocher, and L. J. Gauckler, "Fatigue of zirconia under cyclic loading in water and its implications for the design of dental bridges," Dental Materials, vol. 23, pp. 106-114, Jan 2007.
[18] B.-S. L. Lewinstein I, Eliasi R., "Finite element analysis of a new system (IL) for supporting an implant-retained cantilever prosthesis," The International journal of oral maxillofacial implants vol. 10, pp. 355-366, 1995.
[19] 田村勝美、森博史、妹尾輝明, "Ceramo-metal Bridge," 医齒藥出版株式會社, pp. P.6~22,59~74, 1989.
[20] 川原春幸、武田昭二, "齒科理工學," 医齒藥出版株式會社, p. P.34~36, 1986.
[21] 李輝煌, "ANSYS工程分析基礎與觀念," 高立圖書有限公司, 2005.
[22] S. S. Suzana Varga, Marina Lapter Varga, Sandra Anic Milosevic, Senka Mestrovic, Mladen Slaj "Maximum voluntary molar bite force in subjects with normal occlusion," European Journal Of Orthodontics vol. 33, pp. 427-433, 2011.
[23] A. B. Motta, L. C. Pereira, A. da Cunha, and F. P. Duda, "The influence of the loading mode on the stress distribution on the connector region of metal-ceramic and all-ceramic fixed partial denture," Artificial Organs, vol. 32, pp. 283-291, Apr 2008.
[24] H. Fischer, M. Weber, and R. Marx, "Lifetime prediction of all-ceramic bridges by computational methods," Journal of Dental Research, vol. 82, pp. 238-242, Mar 2003.
[25] O. Eraslan, M. Sevimay, A. Usumez, and G. Eskitascioglu, "Effects of cantilever design and material on stress distribution in fixed partial dentures - a finite element analysis," Journal of Oral Rehabilitation, vol. 32, pp. 273-278, Apr 2005.
[26] S. A. Romeed, S. L. Fok, and N. H. F. Wilson, "Finite element analysis of fixed partial denture replacement," Journal of Oral Rehabilitation, vol. 31, pp. 1208-1217, Dec 2004.
[27] H. S. Yang, L. A. Lang, and D. A. Felton, "Finite element stress analysis on the effect of splinting in fixed partial dentures," Journal of Prosthetic Dentistry, vol. 81, pp. 721-728, Jun 1999.
[28] M. F. L. D. M. Stephen F. Rosenstiel BDS MSD, Junhei Fujimoto DDS MSD DDSc, "Contemporary Fixed Prosthodontics, 4th," 合記圖書出版公司, 2006.