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研究生: 賴金鴻
Lau, Chin-Hung
論文名稱: 非對稱C型複合材料樑之等效剛性分析
Analysis of Equivalent Stiffness in Asymmetric C-Shaped Laminated Composite Beam
指導教授: 梁育瑞
Liang, Yu-Jui
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系碩士在職專班
Department of Aeronautics & Astronautics (on the job class)
論文出版年: 2024
畢業學年度: 112
語文別: 中文
論文頁數: 126
中文關鍵詞: 複合材料非對稱C型結構梁加強筋等效剛性非對稱疊層有限元素模型Ansys Workbench
外文關鍵詞: laminated composites beam, asymmetric C shape, equivalent stiffness, asymmetric stacking sequences, finite element method
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  • 本研究提出一種新穎的方法,用於分析非對稱C型複合材料梁,無論是在對稱或非對稱的疊層順序情況下。該方法利用經典層合理論(Classical Lamination Theory)來修改,結合重心和剪切中心概念,推導出非對稱C型複合材料梁之截面性質的明確表達式,包括軸向(Axial)、彎曲(Bending)、扭轉(Torsional)和翹曲剛性(Warping Stiffness)。過程中進行一連串的假設與優化,其中最重要的假設莫過於考慮在結構梁中觀察到獨特的變形行為,而這些假設都建立在彈性變形之下。為了驗證該解析解的準確性,將此結果與三維有限元分析進行比較。在驗證軸向和彎曲剛性之後,搭配驗證軸向應力確認建模正確後,再驗證扭轉和翹曲剛性。這項研究還將參數進行調整,包括各種斷面尺寸、梁的長度和疊層角度,探討與驗證在各種變化之下,等效剛性的影響與準確性。另外,在極端疊層順序情況下,探討此方法與不考慮結構斷面效應之間的比較。同時,比較優化前與優化後的差異。這個新穎的方法能夠加速對非對稱C型複合材料梁的等效剛性評估,與初步設計階段的實際應用具有重要的相關性。

    A novel methodology for the analysis of asymmetric C-shaped laminated composite beams is proposed in this work. Moreover, the proposed approach leverages an adapted Classical Lamination Theory (CLT) with centroid and shear center concepts to derive explicit expressions for the evaluation of crucial sectional properties, including axial, bending, torsional, and warping stiffness. The analytical formulations account for the distinctive deformation characteristics observed in structural beams. To validate the accuracy of the proposed analytical expressions, three-dimensional finite element analyses are performed for comparisons between analytical and numerical results. The solutions for axial and bending stiffness are examined, along with torsional and warping stiffness. Parametric studies are conducted, including various cross-sectional dimensions, the length of the beam, and the stacking sequences of the composite laminates. This study investigates the comparisons between the proposed methodology and the methodology that does not consider the effect of the structural cross-section. Additionally, a comprehensive analysis of the methodology is conducted for both symmetric and asymmetric stacking sequences in this research. This novel approach expedites the assessment of the behavior of laminated composite beams and holds significant relevance for practical applications in the preliminary design phase.

    摘要 I Abstract II 致謝 X 目錄 XI 圖目錄 XIV 表目錄 XVII 符號說明 XVIII 一、 緒論 1 1.1 研究動機 1 1.2 文獻回顧 2 1.3 研究流程 3 二、 研究方法 5 2.1 複合材料力學 5 2.1.1 均質材料 5 2.1.2 橫向各向同性材料 6 2.1.3 異向性材料 8 2.1.4 單層單向纖維 θ°的應力應變關係式 9 2.1.5 經典層合理論 10 2.1.6 層壓板 ABD 矩陣的平移 16 2.2 座標、負載以及C型梁各斷面名稱的定義 18 2.3 正向力與力矩下非對稱C型複合材料梁的本構方程式 20 2.3.1 一般複合材料梁、C型複合材料梁各斷面的矩陣 20 2.3.2 質心的特性與矩陣 22 2.3.3 軸向剛性 27 2.3.4 彎曲剛性 28 2.4 剪切力與扭矩下非對稱C型複合材料梁的本構方程式 32 2.4.1 一般複合材料梁、C型複合材料梁各斷面的矩陣 32 2.4.2 剪切中心的特性與矩陣 35 2.4.3 扭轉剛性 42 2.4.4 一端固定時扭矩與扭轉角的關係式 45 2.4.5 翹曲剛性 49 三、 有限元素分析 56 3.1 材料參數 56 3.2 有限元素模型尺寸 57 3.3 元素類型 57 3.4 結合條件 58 3.5 疊層順序 58 3.6 邊界條件 59 3.6.1 軸向與彎曲剛性 60 3.6.2 扭轉剛性 61 3.6.3 翹曲剛性 63 四、 結果與討論 64 4.1 數值結果探討 64 4.1.1 軸向剛性 64 4.1.2 彎曲剛性 65 4.1.3 扭轉剛性 69 4.1.4 翹曲剛性 70 4.2 收斂性分析 71 4.3 等效剛性於有限元素分析和解析解的比較 76 4.4 參數研究 77 4.4.1 下翼寬的參數研究 77 4.4.2 腹寬的參數研究 81 4.4.3 整體梁長度的參數研究 85 4.4.4 整體梁厚度的參數研究 88 4.4.5 疊層角度的參數研究 92 4.5 一般複合材料梁與C型複合材料梁的假設比較 97 五、 結論與未來展望 101 六、 參考文獻 102

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