楊永斌臺灣大學：土木工程學研究所呂詩瑤Lu, Shih-YaoShih-YaoLu2007-11-252018-07-092007-11-252018-07-092006http://ntur.lib.ntu.edu.tw//handle/246246/50134土木工程結構最大的特徵在於其龐大的尺度，以及施工的不確定性，故分析模型的更新比在其他任何一個領域都來的重要。本文旨在為發展一簡單而快速的有限元素模型更新方法，以符合工程師所需，並以建築結構最常利用的「剪力屋架」模型作為研究的主題。 有限元素模型更新的方法，大致可分為二大類：參數更新法和直接更新法。參數更新法因為可確保更新後矩陣的物理涵義而被廣泛接受，但其中所需的參數選擇程序極為棘手；直接更新法如字面隱含，其最大優勢為無須經由迭代計算，因此可降低發散的可能與過多的計算成本。本文利用滿足正規化條件更新系統質量矩陣，並結合廣義特徵值問題以更新勁度矩陣；巧妙地將未知系統矩陣整理為向量形式，其連接資訊可以輕易保存建築物之物理結構及簡化校正系統矩陣的計算量。比較本文與文獻上存在之方法，可發現計算效能有重大之改善。 爲檢驗更新方法的可行性，本文模擬了數個建築物較常遭遇的情形，其結果是肯定的。The general characteristics of a civil engineering structure is its relative large scale and uncertainties in construction. An important problem is to update the analysis model of the structure so that it can produce results as close as possible to those observed in the field. The purpose of this thesis is to develop a simple and efficient finite element updating method that can meet the needs of engineers in practice. To facilitate the derivation, the most often used shear buildings are taken as the example of study. In general, two categories of methods are used for model updating, i.e., the direct and parameter updating methods. The parameter updating methods were widely used because they can preserve the physical meanings of the updated matrices, but the procedure for determining the parameters is generally complicated. The direct updating methods, as the title implies, have the advantage of not relying on iterations, while eliminating the possibilities of divergence and excessive computation. This paper presents a new approach, by which the mass matrix is updated utilizing the condition of normalization, and the stiffness matrix is updated by requiring it to satisfy the generalized eigenvalue properties associated with the structure. By manipulating the unknown system matrices into vector forms, the connectivity information can be easily implemented to preserve the physical configuration of the structure, and to reduce the computational efforts required to update the system matrices. A comparison is made between the proposed updating method and other methods existing in the literature, which indicates that the proposed method is easier to formulate. To demonstrate the applicability of the proposed updating method, several typical examples in practice were studied. The applicability and efficiency of the proposed method is confirmed.誌謝 / Ⅰ 摘要 / Ⅲ 目錄 / Ⅶ 表目錄 / ⅩⅠ 圖目錄 / ⅩⅤ 1 緒論 1 1.1 研究動機與目的 / 1 1.2 論文架構 / 3 2 模型更新方法之發展介紹 7 2.1 參數更新法 / 8 2.1.1　簡介 / 8 2.1.2 逆特徵靈敏度矩陣法 / 11 2.1.3 待更新參數之選擇 / 17 2.2 直接更新法 / 18 2.2.1 簡介 / 18 2.2.2 拉格朗治乘子法 / 20 2.2.3 矩陣微擾理論 / 25 3 剪力屋架之有限元素法模擬 33 3.1　有限元素法 / 33 3.1.1 簡介 / 33 3.1.2 模型更新 / 35 3.1.3 模態量測 / 36 3.2　剪力屋架模型 / 38 3.2.1 剪力屋架模型之建立 / 38 3.2.2 剪力屋架模型之自由振動分析 / 44 3.2.3 正規化模態之正交性 / 48 4 新直接更新法之推導及應用 65 4.1　新直接更新法之推導 / 65 4.1.1 質量矩陣之更新 / 66 4.1.2 勁度矩陣之更新 / 69 4.2 新直接更新法之應用 / 74 4.2.1 應用(一) / 75 4.2.2 應用(二) / 76 4.2.3　應用(三) / 78 4.2.4　應用(四) / 79 4.3 直接更新法之比較 / 81 4.3.1 比較(一) / 81 4.3.2 比較(二) / 82 4.3.3 小結 / 83 5 數值模擬 107 5.1　簡介 / 107 5.2 模擬方法 / 108 5.3 質量矩陣之更新 / 110 5.3.1 實際結構質量較理論模型為小 / 110 5.3.2 實際結構質量較理論模型為大 / 111 5.4 勁度矩陣之更新 / 112 5.4.1 實際結構勁度較理論模型為小 / 112 5.4.2 實際結構勁度較理論模型為大/ 112 5.5 質量及勁度矩陣之更新 / 113 5.5.1 實際結構的質量和勁度皆較小 / 113 5.5.2 實際結構質量較小但勁度較大 / 114 5.5.3 實際結構質量較大但勁度較小 / 115 5.5.4 實際結構的質量和勁度均較大 / 115 5.6 小結 / 116 6 結論與展望 149 6.1　結論 / 149 6.2 未來展望 / 150 參考文獻 1532019155 bytesapplication/pdfen-US模型更新Model updatingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50134/1/ntu-95-R93521214-1.pdf