殼結構物之動力分析

Abstract

殼結構為一常見之建築結構體，於人民的福址有相當重要的關 係，如核能電廠圍阻體等。而台灣位於地震帶，殼結構動力分析之 重要性更是不可忽略。在已發表的文獻中，有關殼結構物動力分析 之報告，其所發展的理論幾乎都是在時間域(time domain)中作推 導，使用直接積分(direct integration)作運算，而其缺點則為計 算規模龐大及費時甚久。本文企圖由另一角度，即頻率域(frequency domain)，尋求一種既快速又能縮小計算容量的方法來解決殼結構 之動力問題。 本研究以有限元素法來模擬殼結構，使用8結點之殼等參數元 素(shell isoparametric element)為基本元素。利用FRONTAL SOLVER的特性，可以只取結構體某些特殊結點作運算考慮。首先， 利用本研究之有限元素程式，預先建立一組結構體在承受單位複指 數振盪函數eiwt作用下，待測結點所產生的反應。利用快速富立葉 轉換法(Fast Fourier Transform)，將實際作用的振盪(excitation) 函數，轉換成頻率域中的富立葉級數，利用簡易內差可得結構體在 頻率域中以富立葉級數存在的結構反應，最後經一次富立葉逆轉換， 求得時間域中結構系統的反應。 由驗證結果顯示：本研究之有限元素模型與快速富立葉轉換程 式，皆具有極佳的精確度與收斂性。所以，利用本研究之方法，亦 即有限元素模式、FRONTAL SOLVER及快速富立葉轉換法之聯合應用， 可以克服傳統上在時間域中求解，記憶體容量佔用過大及運算速度 太慢的問題。

The shell structures gain a great deal of attention due to its numerous practical applications such as the containment of nuclear power plant. The dynamic analyses of shell structures are thus very important especially in Taiwan which is located on an active earthquake region. In past, the dynamic responses of shell structures were almost calculated from direct integration method in time domain; and always encountered problems of huge memories occupying and large computational efforts. The purpose of this paper is to find an appropriate method that can avoid these problems. Instead of traditional time domain, frequency domain is applied in this research. An 8 nodes isoparametric shell finite element is used to model the shell structure. Some important key nodes can be chosen, instead of total nodes, when using FRONTAL solver. First, the structural response datum are set up corresponding to unit-complex-exponential excitation function eiwt. Then the excitation applied is transformed into Fourier series in frequency domain by applying Fast-Fourier-Transforms (F.F.T.). The structural responses on those key nodes can be obtained by utilizing the interpolation technique. After a final inverse Fourier transformation, the responses versus the time history will be obtained. From the verification, it is shown that the finite element model and F.F.T. program perform very good precision and convergency. Finally, a shell structure is presented to obtain its dynamic response due to certain ground excitation. It is shown that the analytical procedure subjected int his research provides a convenient way to solve the dynamic response of shell structure and does overcome the problems of memory and computing speed.