
系統識別號 
U00262408201723034300 
論文名稱(中文) 
三單位陶瓷燒付至氧化鋯固定局部義齒之結構優化 
論文名稱(英文) 
Substructural improvement in 3unit porcelainfusedtozirconia fixed partial denture 
校院名稱 
成功大學 
系所名稱(中) 
生物醫學工程學系 
系所名稱(英) 
Department of BioMedical Engineering 
學年度 
105 
學期 
2 
出版年 
106 
研究生(中文) 
賴融暘 
研究生(英文) 
RongYang Lai 
學號 
P86041061 
學位類別 
碩士 
語文別 
中文 
論文頁數 
58頁 
口試委員 
指導教授張志涵 共同指導教授陳永崇 口試委員莊淑芬 口試委員藍鼎勛

中文關鍵字 
固定式局部義齒
有限元素法
最佳化雙向演進法

英文關鍵字 
fixed partial denture
structural optimization
finite element method

學科別分類 

中文摘要 
固定式局部義齒為臨床上常見的治療缺牙方式之一，隨著醫療科技發展，平均壽命上升，固定式局部義齒的結構強度與使用年限需提升。本研究之目的探討固定式局部義齒之氧化鋯支架幾何設計上是否有改善空間。透過有限元素法與結構優化的結合，重新進行固定式局部義齒支架的設計，並增強結構強度。
研究中使用之數位模型以電腦掃描斷層掃描影像為基礎，利用逆向工程原理建立了三單元式固定式局部義齒所需兩顆支撐牙，包含牙本質與牙髓。而固定式局部義齒模型的建立是由牙科設計軟體進行設計。透過有限元素軟體程序與結構最佳化雙向演進法結合，進行牙橋支架幾何的設計優化。
在結構優化過程，以搜尋固定式局部義齒其結構中瓷鑲面陶瓷和氧化鋯材料的最佳分佈。考慮了不同的氧化鋯支架設計。結果顯示固定式局部義齒透過結構優化演算法改善設計後，各項力學指標均有受到改善。包括本研究欲改善的瓷鑲面陶瓷碎裂，與此破壞模式相對應的最大主應力，也降低了9.7%與19.2%。就生物力學觀點上，獲得了改善。
與初始設計相比，這種新方法能夠通過最小化燒付陶瓷最大主應力來改進固定式局部義齒設計。它為牙科技術人員提供了一種新的設計工具，用於開發更高強度的固定部分假牙，用於更複雜的臨床情況。

英文摘要 
Extended Abstract
Substructural improvement in 3unit porcelainfusedtozirconia fixed partial denture
RongYang Lai
ChihHan Chang
YungChung Chen
Department of Biomedical Engineering, National Cheng Kung University
Summary
Fixed partial denture is one of the most common methods for restoring missing teeth. With the development of medical technology, the average life span of human being was prolonged. Therefore, the structural strength of fixed partial denture needs to be improved for longer use. The purpose of this study was to seek an optimal geometrical design of framework of zirconiabased fixed partial dentures which would improve its strength. Through the combination of finite element method and the bidirectional evolutionary optimization algorithm (BESO), the framework of fixed partial denture framework was optimized to enhance its structural strength.
The numerical model of the present study was based on the images from micro computerized tomography, and the contours of two abutment teeth were constructed via reverse engineering. The contour of fixed partial denture model was sketched using the software exocad.
The process of structural optimization was to search for the optimal material distribution of porcelain and zirconia in the structure of the fixed partial denture by altering a different zirconia framework design. The results showed that the structural optimization improved the design of the fixed partial denture. The maximum principal stress at the both sides of connector decreased by 9.7% and 19.2% respectively, From the biomechanical point of view, the structural optimization improved the framework design of fixed partial denture.
Compared with the traditional design, the optimized fixed partial denture design was expected to extend its life span by minimizing the maximum principal stress within the porcelain layer. It also provides a new design reference for dental professionals to develop fixed partial dentures with higher strength for more complex clinical conditions.
Key words: fixed partial denture, structural optimization, finite element method
Introduction
Fixed partial dentures and single implant are common methods of treating missing tooth clinically. Compared to dental implant, fixed partial dentures have been widely used because of its cost efficiency .The structure of the fixed partial denture usually consists of a framework and veneering porcelain. The framework played an important role for the strength of the fixed denture structure. The zirconiabased fixed partial dentures became mainstream because of the high mechanical strength, biocompatibility and aesthetic characteristics.
Clinical literatures recorded failures of fixed partial dentures that includes framework fracture, chipping, loss of retention, abutment tooth fracture, secondary caries. This present study discussed the failure situations from the mechanical aspect including framework fracture, chipping, and loss of retention.
This study aimed to reduce the occurrence of porcelain chipping through the framework design rather than the fracture resistance of the framework. The objective of this study was to reduce the maximum principal stress of porcelain by altering framework geometry in fixed partial denture.
Materials and Methods
Finite element modeling
The second premolar and the second molar were scanned by micro computerized tomography and the image was used to construct a digital model. The tooth model was imported into the software exoCAD to sketch a fixed partial denture, and the digital model was imported into the finite element software. After setting material properties, boundary conditions, and loading, the model of traditional design was completed. This model was also used to compare the mechanical performance with optimized model.
Description of topology improvement method
BESO was based on python and can be ran parallelly with the finite element software. In this study, the objective of optimization was to prevent the veneering porcelain from chipping by altering framework configuration of the fixed partial denture.
The BESO is an approach which changes the geometry of structure by progressively replacing material to where it is most needed. The BESO calculated the weighting factor of changing each element according the filtering radius. The maximum principal stress of each element within design domain was extracted and multiplied with weighting factor. According to the stress after weighting, the BESO ranked the elements and assigned the highly stress concentrated element with hard material property.
The BESO found the peak maximum principal stress of the design domain. After the assigned volume fraction was reached, the program checked the condition of convergence, when it was reached, the altering process was completed. Because remeshing was not incorporated in the optimization process, the edge of optimized model presented jagged, after smoothing the edge of the model, the optimized design was finished.
Result and Discussion
Stress distribution and improvement of fixed partial denture
The location of the peak value of maximum principal stress was the same as the clinical situation that occurred in the porcelain within the connector. According to the results of finite element analysis, the maximum principal stress at both sides of the connector decreased by 9.7% and 19.2% respectively.
The shear stress and tensile stress at the fusedinterface and the maximum principal stress of the porcelain were improved by 9% or more, it was expected that porcelain chipping can be reduced.
Framework variation after optimization
The objective function of optimization was to reduce the maximum principal stress of the porcelain, and that framework was not considered during optimization. Framework fracture may occur due to concentration of high maximum principal stress. However, the maximum principal stress of the framework was increased from 57.500 MPa to 57.619 MPa, implying that structural strength of the framework remained at a similar level after optimization.
It can be seen from the cross sectional view of the fixed denture, the connector of framework has a greater cross sectional area and smooth curvature after optimization. This results in the maximum principal stress of the porcelain, which had better mechanical performance with less normal stress and shear stress of the fusedinterface
Conclusion
1.The values of maximum principal stress, normal stress, and shear stress were found reduced after optimization.
2.From biomechanic a standpoint point, this suggests that the improvement of traditional framework design is neccessary.
3.The approach of optimized design reduced maximum principal stress and interfacial stress and provided a better reference of framework.

論文目次 
中文摘要 I
Extend Abstract II
致謝 VIII
目錄 IX
表目錄 XI
圖目錄 XII
第一章 緒論 1
1.1研究背景 1
1.1.1前言 1
1.1.2缺牙的影響與固定式局部義齒於臨床上的治療方式 2
1.1.3全瓷固定式局部義齒介紹 4
1.2文獻回顧 6
1.2.1固定式局部義齒於臨床上的失敗 6
1.2.2固定式義齒結構優化 9
1.3有限元素法 10
1.3.1簡介 10
1.4結構優化與演算法 11
1.4.1結構優化簡介 11
1.4.2結構優化簡介 12
1.4.3結構最佳化雙向演進法簡介 12
1.5研究目的 14
第二章 材料與方法 15
2.1研究流程 15
2.1.1研究流程 15
2.2模型建立 17
2.2.1牙齒與固定式局部義齒模型建立 17
2.2.2固定式局部義齒與牙齒有限元素模型建立 22
2.3材料與邊界條件 24
2.3.1材料特性 24
2.3.2邊界條件與負載設定 24
2.4結構優化與程序 26
2.4.1結構最佳化雙向演進法與有限元素法的結合 26
2.4.2 程序與結構最佳化雙向演進法 27
第三章 結果 31
3.1優化後設計組與傳統設計組力學表現 31
3.1.1力學表現與臨床關聯 31
3.1.2瓷鑲面陶瓷最大主應力分布 33
3.1.3燒付介面正向應力探討 35
3.1.4燒付介面剪應力探討 36
3.1.5固定式局部義齒形變探討 37
3.1.6固定式局部義齒黏著介面應力 38
3.2結構最佳化雙向演進法優化參數影響 39
3.2.1優化參數的設定 39
3.2.2映射半徑 40
3.2.3演進率與其影響 42
3.3陶瓷材料機械性質變異與力學表現 43
第四章 討論 45
4.1固定式局部義齒支架設計效果 45
4.2陶瓷材料楊氏係數變換與力學表現 49
4.3優化過程、缺陷與未來應用 51
第五章 結論 54
參考文獻 55

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