臺灣博碩士論文加值系統

固態氧化物燃料電池片是由多層、複合材料、結構所組成（陽極、陰極、連接板、流道等），並藉由電化學反應來達到產電的目的。在正常工作狀態下，燃料電池片會操作在600~1000 °C且不均勻的高溫環境中，不均勻的溫度分佈以及各層材料間不匹配的熱膨脹係數會導致電池片產生熱應力，進而影響電池片壽命。本研究欲結合其他研究來探討燃料電池系統在不同操作策略下，對於燃料電池片壽命的影響。為此，本研究在MATLAB開發平台中撰寫有限元素法模型進行電池片熱應力分析，方便研究成果與其他研究在MATLAB開發平台中進行整合。
由於MATLAB開發平台的計算能力有限，我們必須選擇合適的元件模型來降低計算量且保有一定準確度。為了建立此模型，我們先以商用軟體ANSYS做數個模型的應力分析並相互比較。最後我們選定殼元素（Kirchhoff-Love 板元素、平面應力元素）來模擬燃料電池片，以固體元素來模擬燃料電池的外框。最後我們在MATLAB開發環境中撰寫程式，完成相關的應力分析。
模擬結果顯示：當電池片具有800~1000 °C線性分佈時，若僅模擬電池片與界面條件時，自行撰寫的應力分析軟體與商用軟體ANSYS結果相近，最大差異在2.97%以內。若考慮電池片與外框結合時，自行撰寫程式的結果與ANSYS差異頗大。差異可能來自於我們採用的殼元素與固體元素二者之間的結合方式。

Solid oxide fuel cell (SOFC) is a composite material that consists of multiple layers and structures, which includes anode, cathode, connector, channels, and so on. SOFC uses electro-chemical reactions to generate electricity, which would normally take place at the temperature 600~1000 °C. Due to the high temperature, temperature gradient, and large mismatched thermal-expansion coefficients in each layer, the SOFC experiences lots of stress which deteriorate its lifecycles. The aim of this research is to investigate on the relationship between the operation strategy of the SOFC-CHP system and the lifetime of the SOFC. To this end, we develop a FEM stress analysis tool using the platform MATLAB in this work. This simulation tool will be integrated with other SOFC-CHP simulators that have been developed in the MATLAB platform.
However, limited by the computing power of the MATLAB, we needed to research suitable element models that can reduce the computation power with acceptable computation accuracy. In order to do that, we first various element model using the commercial package ANSYS. And then, we decide to use the shell element (Kirchhoff-Love plate element integrated with the plane stress element) to model the SOFC cell, and the solid element to model the connector. Finally, we develop this FEM stress analysis tool in MATLAB.
In a case study, the SOFC is operated at the temperature with a linear distribution from 800 to 1000 °C. The simulation results indicate that, the in-house developed simulation tool and the commercial package ANSYS have the similar responses when the SOFC model consists of the SOFC cell only. The difference between these two approaches is less than 2.97%. However, there exists large difference when the model consists SOFC cell and the metal connectors. The preliminary study indicates that this large error may originate from our method of integrating shell element and solid element together for the boundary condition setup.

摘要 i
目錄 iii
表目錄 v
圖目錄 vi
一、 緒論 1
1.1 研究動機與目的 2
1.2 文獻回顧 2
1.2.1 固態氧化物燃料電池 2
1.2.2 燃料電池片熱膨脹係數不同導致的熱應力 5
1.2.3 固態氧化物燃料電池使用之材料 6
1.2.4 有限元素法 7
1.2.5 燃料電池片應力計算作法 7
1.3 結語 14
1.4 論文架構 14
二、 FEM應用於燃料電池模型 16
2.1 固態氧化物燃料電池模型 16
2.2 最低總位能原理(The principle of Minimum Potential Energy) 18
2.3 平面應力元素(plane stress element) 19
2.3.1 高斯積分法(Gaussian quadrature) 24
2.4 殼元素(Shell element)理論 27
2.4.1 Plate元素理論 27
2.4.2 合併平面應力元素與殼元素 30
2.5 固體元素(Solid element)理論 32
2.5.1 使用自然座標表示形狀函數 34
2.6 組合全域矩陣 37
2.7 ANSYS使用的元素介紹 40
2.7.1 SOLID185元素 40
2.7.2 SOLID187元素 41
2.7.3 SOLSH190元素 41
2.7.4 SHELL181元素 42
三、 ANSYS模擬 43
3.1 殼元素模擬 43
3.2 電池片固體元素模型與含外框的固體元素模型 46
3.2.1 使用SOLSH190元素模擬電池片模型 55
3.3 簡化之外框模型 59
3.3.1 使用SOLID185元素模擬結果 59
3.3.2 使用SOLSH190、SHELL181元素模擬電池片之結果 63
四、 MATLAB模擬 70
4.1 MATLAB程式架構 70
4.1.1 剛度矩陣及受力矩陣 70
4.2 固體元素結合殼元素之電池模型模擬結果 71
五、 模擬結果討論 82
六、 結論與未來工作 83
七、 參考文獻 84

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