應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究

Dynamic Fracture Analysis of a Piezoelectric Crack by Using Numerical Inversion of Laplace Transform

廖雪吩(Hsueh-Fen Liao)

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(2007年)

https://doi.org/10.6846/TKU.2007.00880

摘要

本文研究主題為應用數值拉普拉斯逆轉換法於無窮域內含不可誘電邊界靜止裂紋之壓電材料動力破壞問題，求解一含有限長靜止裂紋之壓電材料於裂紋面上受均佈反平面動態應力及平面動態電位移負載的暫態問題。本文運用了三種數值拉普拉斯逆轉換法分別為Durbin方法、趙氏方法ㄧ及趙氏方法二，首先利用簡單函數範例來比較這些數值法的準確性，並由計算經驗分別建議三種數值法的參數設定範圍；最後以數值拉普拉斯逆轉換法配合積分轉換技巧，解析含裂紋之壓電材料動力破壞問題，並將所求得之應力強度因子數值解做詳細的計算與討論。

關鍵字

壓電材料 ； 數值拉普拉斯逆轉換法 ； 有限長裂紋 ； 動力破壞 ； 應力強度因子

並列摘要

In this study, the dynamic fracture analysis of an infinite piezoelectric material containing a finite crack with impermeable boundary conditions is investigated by using numerical inversion of Laplace transform. The finite crack is subjected to uniformly anti-plane stress and in-plane electric displacement impacts. Three numerical methods, Durbin’s method, Zhao’s method 1 and Zhao’s method 2 are used in this study. The accuracy is examined through some specified functions and the applicable numerical parameters are suggested respectively by the experience of calculation. Finally, the dynamic fracture analysis of a piezoelectric crack is carried out by numerical inversion of Laplace transform and the technique of integral transformation. Numerical solutions for dynamic stress intensity factors are evaluated and discussed in detail.

並列關鍵字

piezoelectric ； numerical inversion of Laplace transform ； finite crack ； dynamic fracture

參考文獻

Arai, M., Sato, Y. and Adachi, T., (2003) “Elastodynamic crack analysis by boundary element method using numerical inversion of Laplace transform ,” JSME International Journal, Series A: Solid Mechanics and Material Engineering , Vol. 46, pp. 131-139.

Bellman, R., Kalaba, R. E. and Lockett, J. A., (1966) “Numerical inversion of Laplace transform,” American Elsevier, New York.

Bleustein, J. L., (1968) “A new surface wave in piezoelectric materials,” Applied Physics Letters, Vol. 13, pp. 412-413.

Chen, Z.T. and Yu, S.W., (1997a) “Crack tip fields of piezoelectric materials under antiplane impact,” Chinese Science Bulletin, Vol. 42, pp. 1615–1619.

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, Vol. 36, pp. 5125–5133.