含有限長裂紋之彈壓電複合層板動力破壞分析

Dynamic Fracture Analysis of a Finite Crack between Purely Elastic and Piezoelectric Liminate

許吉勝(Chi-Sheng Hsu)

指導教授 ： 應宜雄

淡江大學/工學院/航空太空工程學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00913

摘要

本文研究主題為運用積分轉換法、奇異性積分方程與切比雪夫多項式法展開於含有限長裂紋之彈壓電複合層板動力破壞分析，文中求得此彈壓電複合層板承受反平面均佈應力與平面均佈電位移時裂紋尖端的應力強度因子和電位移強度因子，最後利用Durbin的數值拉普拉斯逆轉換法求得數值解，並與文獻上已知的結果做比較，以驗證本文結果的準確性。

關鍵字

有限長裂紋 ； 彈壓電複合層板 ； 動力破壞 ； 應力強度因子

並列摘要

In this study, the dynamic fracture analysis of a finite crack between purely elastic and piezoelectric laminate is investigated. The purely elastic and piezoelectric laminate is subjected to uniformly anti-plane stress and in-plane electric displacement impacts. The solutions are determined by using integral transforms, singular integral equations, and Chebyshev polynomial expansions. The transient solutions for intensity factors are obtained by Durbin’s numerical inversion of Laplace transform method. The numerical results are evaluated and discussed in detail.

並列關鍵字

finite crack ； Purely Elastic and Piezoelectric laminate ； dynamic fracture ； stress intensity factor

參考文獻

廖雪吩 (2007)，應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究，淡江大學航空太空工程學系碩士班碩士論文。

Dubner, R. and Abate, J., (1968) “Numerical inversion of Laplace transforms by relating them to the finite Fourier Cosine transform,” JACM 15, 115–123.

Durbin, F., (1974) “Numerical inversion of Laplace transforms: an efficient improvement to Duber and Abate’s method,” The Computer Journal 17, 371–376.

Chen, Z.T., and Karihaloo, B.L., (1999) “Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact,” International Journal of Solids and Structures 36, 5125–5133.

Wang, B.L., Han, J.C., and Du, S.Y., (2000) “Electroelastic fracture dynamics for multilayered piezoelectric materials under dynamic anti-plane shearing,” International Journal of Solids and Structures 37, 5219–5231.