積層陶瓷電容器在繁複的製程中可能會造成內部缺陷，進而影響其功能，故本研究主要目的是針對經由近百層的鈦酸鋇與鎳電極薄膜所交錯堆疊而成的積層陶瓷電容積層板(multi-layered ceramic capacitors green sheet)在承受高溫均壓製程中所產生的變形進行分析與討論。
本文著重理論推導及數值驗證，理論推導採用古典平板理論、線彈性基本假設及平衡方程式，並參考Timoshenko著作中提及有關平板在各種邊界條件及負荷條件下所求得平板之變形方程式，依據實際製程的狀況，假設三種邊界條件分別為四邊皆為簡支(simple-supported)、兩對邊為簡支，另兩對邊為自由邊(free edge)及四邊皆為自由邊等狀況。文中只於四個角點視為固定，並於底部假設為一彈性基座(elastic foundation)支撐，其四邊如上述三種邊界條件之狀況進行理論分析。另外在數值解析方面，利用有限元素法中有限元素模擬分析軟體ANSYS來進行實體模型之建構，將單一積層陶瓷電容器依其分佈位置不同分為九大區塊，並依不同區塊所在之不同邊界條件來進行求解。
經由理論分析與數值解析結果比較得知，當邊界條件中四邊皆為自由邊時，只於四個角點固定之狀況下最符合實際製程，亦即所獲致之理論解與數值解析結果非常相近，誤差約為0.1% ~ 6.2%，其他兩種邊界條件之結果中兩對邊為簡支，另兩對邊為自由邊時其誤差約為0.13% ~ 6.15%，亦可接受，而四邊皆為簡支時因其誤差極大，在此不予討論。因此在不採用數值模擬之軟體運算之情況下，本研究之理論解仍可提供積層陶瓷電容積層板在承受高溫均壓作用時，此九大區塊各個位置之變形量，俾便作為實際製程改進的參考依據。

The complicated process may cause the internal defects of multi-layered ceramic capacitors (MLCCs) and result in the malfunctions. This work aims to investigate the deformations of MLCCs that composed of nearly a hundred of BaTiO3 and Ni electrode films interleaved and stacked due to high pressure at elevated temperature.
This study focuses on theoretical and numerical analyses. Classical laminated plate theory, linear elastic assumptions and equilibrium equations were adopted. Associated with the texts by Timoshenko and practical manufacturing process, three types of boundary conditions were considered, such as all edges simple-supported, two opposite edges simple-supported and the other two free, and four edges free. Also, two more conditions need be added, including four fixed points at corners and the elastic foundation at bottom. The numerical simulation by finite element method (FEM) incorporated with software ANSYS was used to obtain the displacement field of MLCCs due to high pressure at elevated temperature. The MLCCs were divided into nine regions with suitably different boundary conditions.
Compared with the numerical results the analytical solutions of nine regions were found satisfactorily acceptable, i.e., the errors were about 0.1% - 6.2% for the boundary conditions of four edges free and four corners fixed. The errors about 0.13% - 6.15% were also acceptable for the boundary conditions of two opposite edges simple-supported and the others free. However, the analytical solutions did not agree with the numerical results for the case of all the boundary conditions simple-supported. Finally the proposed theoretical methodology provides an analytical method alternatively, instead of FEM and ANSYS, to analyze a nearly hundred layered MLCCs.

中文摘要………………………………………………….…………………i
ABSTRACT……………………………………………….………………………ii
目次.........................................................................................iii
圖目錄……………………………………………………………………….v
表目錄……………………………………………………….……………..vii
第一章 緒論……………………………………………………………………….…1
1-1 前言………………………………………………………………………….1
1-2 研究動機與目的……………………………………………………2
1-3 文獻回顧……………………………………………………………4
1-4 組織與章節………………………………………………………….5
第二章 實驗工作…………………………………………………………………..8
2-1 材料簡介…………………………………...............................……8
2-1-1 鈦酸鋇…………………………………………………………8
2-1-2 鎳金屬………………………………………………………....9
2-2 儀器設備………………………………………….……………........9
2-3 實驗方法……………………………………………...………………9
2-4掃描式電子顯微鏡(SEM)………………………………………………..9
2-5 結果與討論……………………………………………………..……..10
第三章 理論基礎…………………………………………………………..……17
3-1 古典平板理論…………………………………………………………17
3-2 簡支矩形板之Navier解……………………………………………25
第四章 理論推導……………………………………………………………...28
4-1 推導變形方程式:方法一……………………………………………..….28
4-2 推導變形方程式:方法二……………………………………………...…34
4-3 推導變形方程式:方法三………………………………………..…..37
4-4 彈力強度k值……………………………………………………….42
4-5結論………………………………………………………………….42
第五章 分析結果與討論……………………………………………………..46
5-1數值解析………………………………………………………….46
5-1-1分析過程……………………………………………………..46
5-1-2分析結果……………………………………………………..47
5-2理論解析……...…………………………………………………49
5-2-1理論公式說明………………………………………….49
5-2-2理論推導結果……………………………………..….51
5-3 分析與討論…………..…………………………………………52
第六章 結論與建議.………………………………………………………95
6-1 結論………………………………………………………………..95
6-2 建議………………………………………………………………95
參考文獻……………………………………………………………………96

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