| 摘要: | 結構修正再分析問題對於結構分析、再設計及最佳化過程中不斷扮演關鍵性角色。本文在對已有的一些研究文獻和成果綜述的基礎上，就如何提高結構修正動態再分析方法的精度、計算速度以及收斂範圍等內容開展了進一步研究。 隨著科技的進步，人們對工程結構的特性和品質要求越來越高，很多複雜因素在設計階段就必須加以考慮，導致結構動力學模型自由度數目的日益增長，應用正規方法對其動態特性進行一次計算分析就需耗費可觀的時間、經費和人力，有時甚至是行不通的。故如何降低計算花費是結構修正再分析的重點。結論是要降低計算花費，必須在進行修正再分析時，避免對修正結構再進行完整分析，經前人之研究，以初始結構之動態資訊作為再分析之依據，選擇適當的再分析方法，將可有效達到預期目標。因此初始結構動態資訊之精確與否，將影響再分析之結果。本文以矩陣為基礎之Chebyshev 譜法，即所謂的微分化矩陣，解析結構動態特性。並經由Matlab矩陣特徵值指令去分析具有不同邊界條件之結構的模態參數。接著，利用初始結構資訊進行結構再分析探討。首先由精確解為著眼點，以代數方法探討修正結構再分析問題，以等慣性轉換求解動態勁度矩陣之隱根，並導出將特徵值定位的計算方法；繼而在隱根為已知下探討隱向量的特質及解法。接著探討修正結構再分析之近似解法。本文舉出多種近似解法並以數值例比較各算法之精確度，進而選用以縮減基為依據之組合近似法作為再分析最佳工具。作者首先探討縮減基之理論背景，進而以此為依據深入綜整組合近似法於靜態結構及動態結構之解法及其精確度之掌握。其結果顯示無論結構小修正或大修改，組合近似法均能有效且精確的得到近似解。 The problem of structural modification and reanalysis plays a key role in the structure analysis, redesign and optimization of a structural system. Based on the previous researches, the present thesis tends to investigate deeply the methods of structural modification and dynamic reanalysis to increase the accuracy and computational efficiency under the same convergent criterion. As the advance of technology, the request for the characteristics and qualification of engineering structure becomes higher and higher. Many complex factors must be taken into consideration during the design stage, and it results in the increase of freedom in the structural dynamic model. The conventional, one-time computational analysis for the dynamic characteristics is highly consumed in time, cost, and man-power, and may not be workable sometime. The structural modification and reanalysis aims to reduce the computational cost. To reduce the computational cost, a complete analysis of the modified structure is avoided in the redesign and reanalysis stage. Based on the previous researches, the dynamic information of the original structure can be used as the basis of the reanalysis. A proper analytical method, plus accurate dynamic information of the original structure, will largely affect the results of reanalysis. The present thesis analyzes the structural dynamic characteristics by the matrix-based Chebyshev spectral method, or so called differentiation matrix method. A m-file of matrix characteristic value in Matlab is then adopted to analyze the model parameters of the structure subjected to different boundary conditions. The structure reanalysis is then preceded based on the initial structural information. To assure accurate solutions, algebraic method is used to investigate the modified structural, re-analysis problem, equal inertia transformation is then used to find out the implicit roots of the dynamic, stiffness matrix. A computational method is derived to find out the eigenvalues. Based on the known implicit roots, the characteristics and solutions of the implicit vectors are investigated. The present thesis illustrates several approximate methods and compares the corresponding accuracy. A combined approximation method based on the reduced basis is then used as the best tool of reanalysis. The present thesis investigates the theoretical ground of reduced basis, and then derives the solutions by combined approximate method for static structural system, as well as dynamic structural system. Results show that the combined approximate can effectively and accurately find out the approximate solutions for a minor modified structure, even for a major modified structure. |
