發展無限元素法於結構動力之應用

Applications of infinite element method in dynamic problems of structures

黃耀民(Yao-Min Huang)

指導教授 ： 鄭志鈞

國立中正大學/工學院/機械工程學系/碩士(2012年)

摘要

本研究基於阻抗耦合法提出改良式無限元素法(Modified infinite element method, M-IEM)以改善無限元素法於動態問題中的運算準確性。其中，改良式無限元素法的元素網格模式仍與無限元素法相同，但是以阻抗耦合法代替古揚簡化法應用於無限元素法之多層結構耦合，其將能夠毫無近似地合成完整系統之響應。論文中以含有裂縫之結構的動態響應為例，來驗證方法可行性與計算準確性；而結果顯示改良式無限元素法除計算效率比有限元素法更加優越之外，其運算求得的數值結果亦比傳統的無限元素法更加準確。最後，將應用改良式無限元素法於含有奇異點之平板的動態問題，計算具中心開口裂縫之雙材料平板結構的動態響應。

關鍵字

無限元素法 ； 阻抗耦合法 ； 裂紋結構

並列摘要

A modified infinite element method (M-IEM) based on the receptance method is proposed to improve the accuracy of the infinite element method (IEM) applied to dynamic problems. The proposed M-IEM uses the same element meshing technique as IEM but uses the receptance method to assemble the infinite elements without any approximation. To demonstrate the methodology and evaluate its performance, the dynamic characteristics of structures with cracks are investigated. Results show that the proposed M-IEM not only requires less computation time than FEM, but also provides a more accurate numerical result than that of traditional IEM. Applications of the proposed M-IEM in the dynamic analysis of the cracked structures made by bi-material are also demonstrated.

並列關鍵字

Infinite element method ； Impedance method ； cracked structure

參考文獻

[1] R. J. Guyan, “Reduction of stiffness and mass matrices,” American Institute of Aeronautics and Astronautics Journal, 3(2), p.380, 1965.

[4] R. W. Thatcher, “Singularities in the solution of Laplace’s equation in two dimensions,” Journal of the Institute of Mathematics and Its Applications, Vol. 16, pp. 303-319, 1975.

[5] R. W. Thatcher, “On the finite element method for unbounded region,” SIAM Journal on Numerical Analysis, Vol. 15, pp. 466-477, 1978.

[10] C. G. Go, and Y. S. Lin, “Infinitely small element for the problem of stress singularity,” Computers & Structures, Vol. 37, No. 4, pp. 547-551, 1991.

[11] C. G. Go, and G. C. Chen, “On the use of an infinitely small element for the three-dimensional problem of stress singularity,” Computers & Structures, Vol. 45, No. 1, pp. 25-30, 1992.