本文研究雙異質線彈性複合層板之暫態響應，解析含有限長裂紋之線彈性複合層板受反平面均佈動力負載時裂紋尖端之應力強度因子。文中將問題分為兩個部份，問題一先求解不含裂紋之複合層板於自由表面受反平面動力負載時之解，問題二則於拉普拉斯轉換域中在複合層板的裂紋面上反加問題一所產生的剪應力。解析時將利用奇異積分方程與切比雪夫多項式來求得轉換域中之解，最後再利用Durbin數值拉普拉斯逆轉換法獲得應力強度因子之時域解。數值計算時，將與文獻上施加應力在裂紋面上之解析解作比較，並作詳細之討論。 In this study, the transient response of a finite crack lying on the interface of a linearly elastic composite strip is investigated. The laminate is subjected to uniformly dynamic anti-plane loading on the free surfaces. This transient problem can be treated as the superposition of two problems. Problem 1 considers a crack-free laminate subjected to uniformly dynamic anti-plane loading on the free surfaces. While problem 2 concerns a linearly elastic laminate containing an interfacial crack with the crack faces subjected to the loads that cancel out the shear stress induced by problem 1. The solution procedures are based on the use of integral transforms, singular integral equations and Chebyshev polynomial expansions. Durbin’s method is used to carry out the numerical inversion of Laplace transform. The numerical results are evaluated and discussed in detail. Furthermore, the accuracy is examined through some specified cases in the literature.
