Abstract
拉普拉斯有限單元互疊法乃結合拉普拉斯轉換技巧與有限單元互疊法程序及數值拉普拉斯逆轉換方法之優點而來。此法已成功的發展於解決動彈性破裂問題。此法可運用有限板含多個中央裂縫與含多個邊緣裂縫問題之動態破裂應力強度因子之計算。利用拉普拉斯轉換技巧, 原本複雜之動態破裂問題能轉換成拉普拉斯域內之等效靜態破裂問題, 此拉普拉斯域內之靜態破裂問題將可利用有限單元互疊法加以解決, 同時時間域內之解可藉由 Honig及Hirdes發展之數值拉普拉斯逆轉換方法獲得。以此法所計算之動態應力強因子與已知文獻比較足以證明此法之正確性與優越性。此法僅需要使用相當簡單及規則的網眼即可得到準確結果, 同時對於一般數值方法必須考慮時間間隔之正確選取, 方能得到較準確結果,此法對時間間隔的選取並不影響結果之準確性, 本文亦針對應力波受到多裂縫及邊界的反射及繞射現象作一完整討論。此法亦可用於計算含不同裂縫長度、深度與角度之有限板之動態位移與應力響應。計算所得之位移、應力曲線可資應用於非破壞性檢測以量取裂縫位置及長度。The Laplace finite element alternating method which combinesthe Laplace transform technique and the finite elementalternating method is developed to deal with the elastodynamicanalysis of a finite plate with multiple cracks. By the Laplacetransform technique, the complicated elastodynamic fractureproblem is first transformed into an equivalent static fractureproblem in the Laplace transform doamin, and then solved by thedeveloped finite element alternating method. To do this, ananalytical solution of an infinite plate with a semi-infinitecrack subjected to exponentially distributed loadings on cracksurfaces in the Laplace transform domain is derived by Tsai andMa(1992). Finally, the real-time responses can be computed by anumerical Laplace inversion algorithm. The techniqueestablished is applicable to the calculation of dynamic stressintensity factors of a finite plate with arbitrarilydistributed edge cracks or symmetrically distributed centralcracks. Only a simple finite element mesh with very limitednumber of regular elements is neccessary. In addition, thedynamic stress intensity factors at any specific instant can becomputed by a single time step instead of step by stepcomputations. The interaction among the cracks and finitegeometrical boundaries on the dynamic stress intensity factorsis also discussed. The present technique is further applied toexplore the elastodynamic response of a finite plate containingmultiple cracks with different lengths/depths/orientations. Theelastodynamic response of displacement and stress at anyspecific instant can be computed. Based on those, thecalibration curves on the plate could be used for thedevelopement of the nondestructive technique to detect thepresence, length, depth, position and orientation of the crack.