本文的主要目的在於探討複合共焦橢圓柱體在承受扭力後，柱體橫斷面的翹曲行為，以及具有多層共焦橢圓內含物之複合傳導體受到二維熱勢能後，其溫度及流場的行為，在此利用兩相鄰共焦橢圓的邊界連續條件建立出矩陣化的疊代關係式，提供了在複合共焦橢圓柱的問題上，有更結構化的方式來解決此種問題，基於這個便利性進而探討了具弱層或硬層多層共焦橢圓複合桿件受扭轉後的行為以及二維熱傳導問題中外在所施加的熱勢能階次對於複合體內的溫度場變化的關係與共焦橢圓內含物當中最內層流場對於階次的變化等問題。

This paper discused that after the composite confocal elliptical cylinder bearing torsion, the cross-section's actions ,meat warping function of composite confocal elliptical cylinder. And, the two dimensions metrix which have the compsite confical elliptical inclusions with heat potential to find their potential and courrent's actions. We can use continuity of boundary condition for two continuos confocial ellipical to construct the relation of the stuck of matrix to supply the methold to solve this kind of problems. Because of the conveninet. We ask the composit confocal elliptical with strong layers or weak layers for their warping functions. Except, we ask the confocal elliptiacl relations between inermost layer's courrrent and the boundary of the potental's order.

J. R. Booker & S. Kitipornchai, “Torsion of multilayered rectangular section.”, J. Engng Mech, 97, pp. 1451-1468, 1971

T. Chen, “Torsion of a rectangular checkerboard and the analogy between rectangular and curvilinear cross-section.”, Quart. J. Mech. Appl. Math, 54, pp. 227-241, 2001

T. Chen, “A confocally multicoated inclusion under antiplane shear : Some new result.”, submitted for publication, 2003

T. Chen & Y. L. Huang, “Saint-Venant torsion of a two-phase circumferentially symmetric compound bar.”, J. Elasticity, 53, pp. 109-124, 1998

T. C. T. Ting, T. Chen & K. S. Li, “Torsion of an isotropic shaft of arbitrary cross-section imbedded with multicoated or graded circular cylinders of cylindrically orthotropic materials.”, submitted for publication, 2003

L. M. Jiji, Heat transfer essentials: A Textbook., Begell House, Inc. New York,1998

Y. M. Kuo & H. D. Conway, “Torsion of composite tubes and cylinders.”, Int. J. Solids Struct., 9, pp. 1553-1565, 1973

E. H. Mansfield, “Neutral holes in plane sheet—reinforced holes which are elastically equivalent to uncut sheet.” Quart. J. Mech. Appl. Math. 6, 370-378, 1953

J. C. Maxewell, Treatise on Electricity and Magnetism. 3 rd Edition , Oxford University Press, Oxford, 1904

N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, 1953

I. S. Sokolnikoff, Mathematical theory of elasticity, McGraw-Hill, New York, 1956
S. P. Timoshenko & J. N. Goodier, Theory of Elasticity. McGraw-Hill, New York, 1970

李國琛，具正交異向性與功能漸變性圓柱內含物桿件抗扭轉剛度之分析，國立成功大學土木工程研究所碩士論文，2002。

柯嵋鐘，利用保角變換解析含孔洞或內含物的傳導問題，國立成功大學土木工程研究所碩士論文，2001。

陳彥材，堆積複合橢圓柱之扭轉，國立成功大學土木工程研究所碩士論文，2002。

黃易立，彈性樑的扭轉剛度，國立成功大學土木工程研究所碩士論文，1998。