本文以陳長鈕教授所發明數值積分表示微分元素法，藉以分析考慮剪變形的變斷面曲樑之面內變形及振動問題。
　　考慮剪變形的因素，稱為Timoshenko樑，和尤拉─柏努力樑的另一種樑是不同的，當橫斷面尺寸與長度比，為不可忽略的有限值時。Timoshenko樑受橫向力作用，同時因剪力會產生剪變形，所以剪變形對樑整體變位，為一不可忽略之值。
　　數值積分表示微分元素法，是一種具有高度耦合特性的數值分析法，也因為具有高度耦合的特性，在分析計算時可減少誤差，得到較佳的收斂，因而大幅降低計算機的運算量。

　　The thesis involves the application of DQEM, invented by Dr. Chang-New Chen, to the in-plane deflection and vibration analyses of non-uniform Timoshenko curved beams.
　　The theory of Timoshenko beam which considers the effect of shear deformation is different from the Euler-Bernoulli beam theory which neglects the effect of shear deformation and is used to the analysis of slender beams. When an external force is applied to a relatively short beam, internal shear force will cause shear deformation. Therefore, the use of Timoshenko curved beam theory is necessary for analyzing generic curved beam structures.
　　DQEM is a highly accurate analysis method. By using this method, error can be effectively reduced and convergence can be improvement. Consequently, the CPU-time required can be drastically reduced.

【1】 Bellman, R.E., and Casti, J., “Differential Quadrature and Long-term Itegration” , Journal of mathematical Analysis and Application, Vol. 34, pp. 235-238, 1971.

【2】 林育男〝數值積分表示微分元素法的研究〞,國立成功大學造船及船舶機械工程研究所碩士論文(1995)

【3】 彭成彥〝數值積分表示微分元素法薄壁變斷面樑分析模式〞,國立成功大學造船及船舶機械工程研究所碩士論文(1996)

【4】 宋治勇〝數值積分表示微分元素法振動分析模式〞國立成功大學造船及船舶機械工程研究所碩士論文(1996)

【5】 Chen, C. N.,〝The Two-dimensional Frame Model of The Differential Quadrature Element Method〞,Computers & Structures,27-32, 1996.

【6】 C.W. Lim, C.M.Wang,S. Kitipornchai〝Timoshenko curve beam bending solutions in terms of Euler-Bernoulli solutions, Mechanics.,67 179-190, 26 July 1996

【7】 Chen,C.N. “Differential Quadrature Element Analysis Using Extended Differential Quadrature” , Computer and Mathematics with Applications, Vol. 39, pp. 65-79, 2000.

【8】 黃笑園, “應用DQEM於分析具任意曲率之曲樑的面內彈性力學問題” , 國立成功大學造船及船舶機械工程研究所碩士論文, 2001.

【9】 Bellman, R.E., kashef, B. G. and Casti, J., “Differential Quadrature: A technique for the rapid solution of nonlinear differential equation” , Journal Computer Phy., Vol. 10, pp. 40-52, 1972.

【10】 Howson, W.P., and Jemah, A.K., “Exact Out-of-Plane Natural Frequencies of Curved Timoshenko Beams” , Journal of engineering Mechanics, January, pp. 19-24, 1999.

【11】 Kang, K., Bert, C. W. and Striz, A. G., “Vibration Analysis of Shear Deformable Circular Arches By The Differential Quadrature Method” , Journal of Sound and Vibration, Vol. 181, pp. 353-360, 1995.

【12】 Irie, T., Yamada, G. and Tanaka, K., “Natural Frequencies of Out-of-Plane Vibration of Arcs” , Journal of Applied Mechanics, Vol. 49, pp. 910-913, 1982.

【13】 Volterra, Enpico and Gaines, J. H., “Advanced strength of materials” , Prentice-Hall, pp. 230-235, 1971.

【14】 Timoshenko, and Gere, “Theory of Elastic Stability” , McGraw-Hill, 1961.

【15】 Suzuki, K., and Takahashi, S., “Out-of-Plane Vibration of Curved Bars Considering Shear Deformation and Rotatory Inertia” , Bulletin of the JSME, Vol. 21, No. 2, pp. 1206-1213, 1981.

【16】 黃志偉, “數值積分表示微分元素法剪變形變斷面樑分析模式” , 國立成功大學造船及船舶機械工程研究所碩士論文, 1997.

【17】 王以震, “應用DQEM於求解具剪變形之任意複合變斷面樑結構物之靜變形問題” , 國立成功大學造船及船舶機械工程研究所碩士論文, 2001.

【18】 官志達, “應用DQEM於求解具剪變形之任意複合變斷面樑結構物之振動問題” , 國立成功大學造船及船舶機械工程研究所碩士論文, 2001.