有限元素分析軟體，主要分為前處理器、處理器、後處理器等三大部分。本研究主要針對處理器部分做探討，配合另外兩位研究生於前處理、後處理及視窗介面設計之開發，共同發展一以MFC(Microsoft Foundation Class)為基本架構之有限元素分析視窗程式。

　　本文於前處理器中，提供節點填滿、複製及元素複製等功能，方便使用者利用節點及元素建構模型。使用者可很便利的在視窗介面上選用以上之功能或利用指令輸入視窗來完成以上功能於處理器中，本文主要探討熱傳及彈性力學問題。熱傳問題方面，主要探討熱傳導及熱對流問題。彈性力學部份以平面應力、平面應變及破壞力學探討為主。在求解線性聯立方程组時，若分析較大之模型，利用網格產生器產生大量的節點及元素，高斯消去法之求解效率不足。為了提高求解之速度，本文引入預加條件共軛梯度法以達到快速解題之要求。本文探討ㄧ張裂型裂縫之破壞力學問題，配合網格產生器，以四邊形及三角形元素來網格化整個模型，並在裂縫尖端處以奇異型三角形元素來處理，並利用位移外插法，求出裂縫尖端之應力強度因子並與理論之應力強度因子比較。

　A finite element software is composed of preprocessor, processor and postprocessor. The main purpose of this research is to treat the processor part of the finite element. Our research will cooperate with the other two graduate students to develop a finite element software with graphical user interface based on the MFC framework.

　In the our preprocessor, users can use the “fill”, “ngen”, and “egen” commands to construct the finite element model. These commands can be selected in the windows menu bar or can be input in the command line windows conveniently. Our processor investigates the heat transfer problems and elasticity problems. In the heat transfer problems, it mainly investigates conduction and convection problems. In the elasticity problems, it mainly investigates plane stress, plane strain and fracture mechanics problems. To obtain the solutions of the linear equations, the Gauss elimination method was used to solve the problems. Using mesh generator in a large finite element model will obtain a great deal of the nodes and elements, but the Gauss elimination method is not effective to solve problems. In order to raise the efficiency of obtaining the solution of the linear equations, we adopt the preconditioned conjugate gradient method to obtain the solution of the linear equations. In this research, we also investigated an opening mode crack problem of the fracture mechanics. We utilized the mesh generator and use the triangle element and quadrilateral element to mesh whole model. We dispose a singular element near the tip of the crack and use the method of displacement extrapolation to obtain the stress intensity factor in the tip of the crack and compare with the theoretical stress intensity factor in the tip of the crack.

[1]余政蓬,“預加條件共軛梯度法與三度空間有限元素問題之研究”, 國立成功大學機械工程研究所碩士論文, 1995.
[2]林建利,“物件導向程式設計在有限元素法之應用”, 國立中央大學數學研究所碩士論文, 1999.
[3]Jack Chessa, “Programing the Finite Element Method with Matlab”, Northwestern University, 2002.
[4]David Roylance, “Finite Element Analysis”, Department of Materials Science and Engineering Massachusetts Institute of Technology, Cambridge, 2001.
[5]Marco L. Bittencourt, Cláudio A. C. Silva, “Object-oriented Programming Applied to the Development of Structural Analysis and Optimization Software”, Journal of the Brazilian Society of Mechanical Sciences, vol.23, 2001.
[6]陳明凱,“平行有限元素法之負載平衡探討”, 國立成功大學機械工程研究所碩士論文, 2001.
[7]劉衛民,“平面彈力有限元素法之探討”, 私立淡江大學土木工程研究所碩士論文, 1994.
[8]林源富,“運用高階有限元素解破裂點尖端應力強度因子”, 國立成功大學機械工程研究所碩士論文, 2002.
[9]ERIC B.BECKER, GRAHAM F.CAREY, J.TINSLEY ODEN“Finite Elements An Introduction”, Prentice-Hall, U.S.A, 1981.
[10]ANSYS Menu, “Derivation of Heat Flow Matrices”, ANSYS Theory Reference, Reversion 5.1, pp.6-4-6, 1994.
[11]許宏孝,“應用有限元素法作高壓高頻變壓器之三維穩態熱傳分析”,私立逢甲大學電機工程研究所碩士論文, 2004.
[12]何信葳,“新型三维六面體元素之研究” , 國立成功大學機械工程研 究所碩士論文, 2003.
[13]David S.Burnett, “Finite Element Analysis”, Addsion Wesley, U.S.A, 1987.
[14]廖益盛,“以雙L型樑試驗量測複合材料貼片與混凝土界面之混合模式破壞韌性－數值分析”, 私立逢甲大學土木及水利工程研究所碩士論文, 2003.
[15]Y.Murakami, “Stress Intensity Factors Handbook”, Pergamon Press, 2000.
[16]Dr.A.-V.Phan, “ANSYS TUTORIAL-2-D Fracture Analysis”, University of South Alabama.
[17]ANSYS Menu, “Post1-Crack Analysis”, ANSYS Theory Reference, Reversion 5.1, pp.19-32-35, 1994.