以結構動力特性更新剪力屋架之有限元素模型

Abstract

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.