本文探討懸臂梁不完全固定端的支撐問題，不完全固定支撐考慮為一具彈性性質的彈性體，因此懸臂梁支撐之局部行為可模擬為楔形體進行分析，首先楔形體考慮為單一材料或雙層材料及考慮楔形體表面不同邊界條件下進行楔形體尖端應力奇異性大小之分析。其次，對於楔形體材料應力場奇異性強度的分析，本文利用ABAQUS軟體針對三種不同的情況進行分析，由有限元素分析的數值結果推得不同彈性支撐條件下應力奇異性的強度。

This paper consider the problem of a cantilever beam with partially fixed-support. . The partially fixed-support is treated as an elastic body with different elastic material. Therefore, the local stress behavior of the corner of the cantilever beam may be viewed as a wedge problem. First, the stress singularity of the wedge is analyzed by regarding the wedge as being composed by a single or bi-layer materials with wedge’ s surface subjected to different boundary conditions. Second, the intensities of stress singularity at the corner of the cantilever beam are analyzed with ABAQUS software. Three different support conditions are modeled in this thesis and results are presented.

參考文獻
[1] A.H England, Complex variable methods in elasticity, Wiley-Interscience, U.K.(1971)
[2] D.B. Bogy and E.Sternberg, The effect of couple-stresses on the corner singularity due to an asymmetric shear loading, International Journal of Solids and Structures, Vol. 4, pp.159-174(1968)
[3] E.Reissner, Note on the theorem of the symmetry of the stress tensor, Journal of Mathematics and Physics Vol. 2, pp.192-194(1944)
[4] I.S. Sokolnikoff, Mathematical theory of elasticity McGraw-Hill, New York(1956)
[5] J.Dundurs and M.S. Lee, Stress concentration at a sharp edge in contact problems, Journal of Elasticity, Vol. 2, pp.109-112(1972)
[6] J.H. Michell, On the direct determination of stress in an elastic solid, with application to the theory of plates, Proceedings of the London Mathematical Society, Vol. 31, pp.100-124(1899)
[7] J.R. Barber, Elasticity, (1992)
[8] M.Comninou, Stress singularities at a sharp edge in contact problem with friction, Zeitschrift für angewandte Mathematik und Physik, Vol. 27, pp.493-499(1976)
[9] M.Comninou, The interface crack, ASME Journal of Applied Mechanics, Vol.44, pp.631-636(1977)
[10] M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, ASME Journal of Applied Mechanics, Vol.19, pp.526-528(1952)
[11] N.I. Muskhelishvili, Singular Integral Equations, (English translation by J.R.M. Radok, Noordhoff, Groningen, 1953)
[12] N.I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, 4th edition, Noordhoff international Publ., Netherlands(1977)
[13] R.D. Gregory, Green’s functions, bi-linear forms and completeness of the eigenfunctions for the elastostatic strip and wedge, Journal of Elasticity, Vol.9, pp.283-309(1979)
[14] V.V. Meleshko and A.M.Gomilko, Infinite systems for a biharmonic problem in a rectangle, Proceedings of the Royal Society of London, Vol. A453, pp.2139-2160(1997)