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研究生:洪宗彬
研究生(外文):Hung Tsung-Pin
論文名稱:疊層複合材料樑之有限元素分析
論文名稱(外文):Finite Element Analysis for Laminated Composite Beam
指導教授:江毅成
指導教授(外文):Chiang Yih-Cherng
學位類別:碩士
校院名稱:中國文化大學
系所名稱:材料科學與製造研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:86
中文關鍵詞:有限元素分析疊層複材I型樑疊層複材T型樑複材樑理論古典積層板理論彎曲應力撓度
外文關鍵詞:finite element analysislaminated composite I beamlaminated composite T beamcomposite beam theoryclassical laminated theorybending stressdeflection
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本研究以現有的疊層I型複材樑之分析為基礎,依據複材樑理論與複材積層板理論,進一步分析疊層T型複材樑。理論公式的推導將T型複材樑假設為一維或二維之結構,一維之分析在Kirchoff-Love之變形假設下只考慮軸向之應變,導出應變─位移之關係;二維之分析將T型樑視為二片複材薄板之組合。經由應力─應變與力矩─曲率間的關係,推導樑的有效剛性,之後,樑的撓度與各個疊層的應力也可算出。
本研究之有限元素分析軟體為MSC/NASTRAN,取一材料為AS4/3501-6 carbon/epoxy,長20 in,翼緣寬為0.5 in,腹板高為0.75in,對稱翼緣疊層為 ,非對稱翼緣疊層為 ,腹板疊層為 之T型樑與I型樑,疊層厚度皆為0.0052 in,受一分佈負載之簡支樑。經有限元素分析比較後,本研究討論結果如下:
1.理論公式的精確度與其使用的限制,經由有限元素分析得以獲
得驗證。
2.I型樑之有限元素分析,取1200 element/in以上時;T型樑之有
限元素分析,取800 element/in以上時,分析值會趨近於一收斂值。
3.隨複材樑長度/高度比值在15以上,理論值的精確度亦增高。
因此,所推導的公式較適用於細、長型樑。
4.以一維與二維的觀點分析疊層T型複材樑,並推導對稱與非對
稱T型樑之形心位置。由於一維理論分析在推導過程中以只樑理論為基礎,假設中只考慮軸向應變 ,以至於誤差較大。
5.0度疊層承受大部分彎曲應力,因此在不改變材料的情況下,將
0度疊層移至翼緣最外層;或著增加0度疊層,皆能增加樑的彎曲剛性。
Based on the analysis of the laminated I beam, the laminated T beam has been analyzed by using composite beam theory and lamination theory. One-dimensional and two-dimensional approaches are applied to derive the theoretical formulas of the bending stiffness and the bending stress of the laminated T beam. Under the Kirchoff-Love deformation assumption, the one-dimensional approach only considers the uniaxial strain, while the two-dimensional approach takes into account 2-D plane stress state. Furthermore, the laminated T beam has been treated as the combination of two thin laminate plates of the web and the flange for the two-dimensional approach. Then, the neutral axis is determined by the condition of the zero axial force and the effective stiffness can be deduced from the moment-curvature relation. Finally, the stress and strain in each ply can be calculated.
The MSC/NASTRAN for window is applied to perform the finite element analysis. The AS4/3501-6 carbon/epoxy I and T beam with a length of 20in and the web height of 0.75in as well as the flange width of 0.5in are simply supported and subjected to a uniformly distributed load. Two cases of the symmetric flange lay-up of and the nonsymmetric flange lay-up of with the web layup of are used for case studies. The comparisons of the theoretical and FEM results have shown that:
1.The accuracy of and the limitation of the usage of the theoretical formulas have been verified by the finite element analysis.
2.FEA results will convergence as I beam elements greater than 1200 elements/in, while T beam elements greater than 800 elements/in.
3.As the aspect ratio (length/height) is greater than 15, the formulas can provide the acceptable accuracy.
4.As the one-dimensional approach only considers the uniaxial strain, the accuracy of the one-dimensional approach is much less than the two-dimensional approach as compared to the FEM results.
5.Because 0°plies sustain most bending stress and placing them to the outer surface of the flange, the bending stiffness will increase without changing materials.
摘要I
ABSTRACTIII
圖 目 錄V
表 目 錄VIII
第一章序論1
1前言1
1-1文獻回顧2
1-2研究方法與目的4
第二章疊層I型複材樑之理論分析6
2推導步驟6
2-1對稱疊層I型複材樑理論分析7
2-1-1腹板(WEB)9
2-1-2窄翼緣(NARROW FLANGE)11
2-1-3寬翼緣(WIDE FLANGE)12
2-2非對稱I型複材樑理論分析13
2-2-1窄翼緣13
2-2-2寬翼緣14
第三章疊層T型複材樑之理論分析17
3理論分析流程圖17
3-1一維理論分析19
3-1-1位移與應變的關係19
3-1-2應力與應變的關係與形心推導20
3-2二維理論分析23
3-2-1形心推導23
3-2-1-1對稱疊層T型複材樑形心位置23
3-2-1-1-1窄翼緣23
3-2-1-1-2寬翼緣24
3-2-1-2非對稱疊層T型複材樑形心位置25
3-2-1-2-1窄翼緣25
3-2-1-2-2寬翼緣27
3-2-2對稱疊層T型複材樑理論分析29
3-2-2-1窄翼緣29
3-2-2-2寬翼緣30
3-2-3非對稱T型複材樑理論分析31
3-2-3-1窄翼緣31
3-2-3-2寬翼緣32
第四章有限元素分析35
4引言35
4-1有限元素分析法簡介35
4-2疊層複合材料樑之有限元素模型建立37
4-3NASTRAN之設定41
4-4範例一43
4-5範例二46
4-6範例三48
第五章數據分析與結構最佳化設計51
551
5-1數據判讀51
5-1-1疊層I型樑51
5-1-2疊層T型樑54
5-1-3結果與討論64
5-2結構與疊層最佳化設計65
5-2-1範例四65
5-2-2範例五68
第六章結論69
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