黃德淑

學號：607380234 (De-Shu Huang)

論文名稱

整合電腦輔助設計與科學計算軟體於對應不確定擬靜態外力之系統極端反應研究 (Integration of Computer-Aided Design and Scientific Computation Applications in Assessing Peak System Responses to Uncertain Quasi-Static Loads)

關鍵詞

有限元素法、MATLAB 偏微分方程工具箱、載重反應關聯法、力學計算、擬靜態分析 (Finite element method, MATLAB PDE toolbox, Load-response correlation, Mechanical calculation, Quasi-static analysis)

DOI

https://doi.org/10.6846/TKU.2020.00594

中文摘要

有限元素法為現今重要學術研究方法之一，同時在工程上，也仰賴有限元素法之計算，甚至是現在許多商業結構分析軟體中，特別主打有限元素分析法分析模式。在本論文中，最主要計算核心即為有限元素法，使用 MATLAB 偏微分方程工具箱結合由 AutoCAD 繪圖軟體製作並匯出的 3-D 模型檔案，運用工具箱分析模式計算出結構之勁度矩陣和變位反應，還有完全透過 MATLAB 輸入資訊和計算模式分析的 2-D 模型，與 3-D 模型完全不一樣的模型導入方式，但依舊能計算出 2-D 模型的勁度矩陣。

在擬靜態分析和載重反應關聯法之不確定擬靜態外力透過指定平均數和標準差產生之隨機數列模擬，擬靜態分析接著以所有數據之外力計算所有自由度之變位反應，再找出每個自由度最大值和最小值變位，並取出由 MATLAB 偏微分方程工具箱分析出之每個自由度變位反應的最大值和最小值與擬靜態分析做比較，兩種分析方式必須得到相同的結果；載重反應關聯法接著以隨機數列之平均數、標準差和相關係數來計算個自由度尖端反應，並與擬靜態分析做比較，兩種分析方式會得到相近的結果。

英文摘要

Nowadays, the finite element method is one of important method of academic research. Simultaneously, the calculation in the engineering region also depends on the finite element method. Even in the multiple business structural analysis software, the finite element method in some of the structural analysis software is promoted mainly. In this thesis, the finite element analysis is the main core of calculation and MATLAB PDE toolbox combined with 3-dimension model from AutoCAD is exerted to calculate the stiffness matrix of model and displacement. Furthermore, 2-dimension model information is completely inputted, read and calculated through MATLAB. It is different way from the operation of 3-dimension model.

In quasi-static analysis and load-response correlation (LRC) method, the average and standard deviation is assigned to generate random number sequence which is used to simulated the uncertainty quasi-static loads. In the quasi-static analysis, all the data in the random number sequence is used in the calculation. Then, the maximum and minimum displacements can be found out and compared with the maximum and minimum displacements from MATLAB PDE toolbox analysis. The quasi-static analysis and the MATLAB PDE toolbox analysis must obtain the same results. The averages and standard deviations of the random number sequence are exerted in the load-response correlation (LRC) method to calculate peak response of every degree of freedom. Then, the comparison between the quasi-static analysis and the load-response correlation (LRC) method may be closed to each other.