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標題: 含加強樑複合材料疊層板之大變形與靈敏度分析
Large Deflection and Sensitivity Analysis of Stiffened Composite Laminated Plates
作者: 陳一賢
關鍵字: 加強樑複合材料;靈敏度
出版社: 機械工程研究所
本文主要目的是應用有限元素方法探討含加強樑複合材料疊層板承受單軸向力、橫向載重、與合成力時之大變形及其靈敏度的問題。本文採用高階位移場理論,配合蒙卡門面(von Karman)應變,來建立非線性板、樑之有限元素模式,其中板元素為每個節點有七個自由度和等參四邊形九點元素,而樑元素為每個節點有七個自由度之一維等參三點元素。再根據板、樑有限元素間位移的調和性(compatibility)藉著座標轉換關係及虛功原理,推導出加強板之平衡方程式,再利用牛頓-雷甫森疊代法(Newton-Raphson method)求解。而對於疊層加強板之靈敏度分析(sensitivity analysis),則採用有限元素模式配合adjoint變數方法,選擇應變能為目標函數(cost function),疊層板纖維角度為設計變數(design variable),推導出靈敏度分析的公式。本文最後以實例針對十字疊層、對稱及反對稱角疊層加強板之大變形及其靈敏度等問題作一探討。

The aim of this thesis is to employ the finite element and adjoint variable methods to study the large deflection and to do sensitivity analysis of stiffened composite laminated plates. A higher-order displacement theory in conjunction with von Karman strains are used in the derivation of the nonlinear finite element models of plate and beam. The elements being used are nine-node isoparametric quadrilateral plate element and three-node isoparametric quadratic element. Each node has seven degrees of freedom. By considering the compatibility between the displacement fields of plate and beam elements and invoking the principle of minimum total potential energy, the governing equations of stiffened plates are derived. These nolinear equations are then solved by Newton-Raphson method. For sensitivity analysis the adjoint variable method is adopted, where the strain energy is chosen as a cost function, while the fiber angles of laminae are taken as design variables. At last, detailed numetical studies are carried out for the cases of cross-and angle-ply stiffened laminated plates.
Appears in Collections:機械工程學系所

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