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 本文主要利用自相似勢能法分析 I 型、II 型、III 型裂縫非對稱延伸之動態行為，以及 I 型延伸裂縫受集中載重作用於裂縫表面之情形。假設一均質、等向性之彈性體，當時間■時，無裂縫存在，而當時間■時，裂縫開始形成並以定速度沿著x軸之正負方向延伸。針對非對稱延伸：假設有一均佈應力載重僅作用於■之裂縫表面，使得右側裂縫尖端之延伸速度為ms，而左側裂縫尖端之延伸速度為s，其中■且為常數。針對中央開裂之裂縫，其承受集中載重作用之問題，不再為自相似問題；但若考慮疊加，並引入座標原點平移及延時，則自相似勢能法仍可適用。 文中首先以自相似勢能法求得全解，再計算其裂縫表面位移及動應力強度因子。結果顯示，若裂縫延伸速度非常慢而趨近於零，則動應力強度因子等於靜態應力強度因子；若裂縫延伸速度接近於Rayleigh波之波速，則動應力強度因子為零。此外，自相似勢能法與疊加之結合亦可適用於向外擴展之均佈載重作用於部分裂縫表面之問題。
 This paper applies the method of self-similar potentials to analyze the dynamic behaviors of the problems of mode-I, mode-II, and mode-III cracks propagating nonsymmetrically and the phenomenon of mode-I crack propagating with a constant speed subjected to a concentrated load on the crack surface. It is assumed that an unbounded homogeneous isotropic elastic material is at rest for time ■. However, for time ■, a central crack starts to extend from zero length along the x-axis. For nonsymmetric extension, on the crack surfaces of ■, there exists uniform distributed load such that the rightmost crack tip propagates with speed ms, while the leftmost crack tip with speed s, where ■ and is constant. The problem of mode-I crack propagating with a constant speed subjected to a concentrated load on the crack surface is not a self-similar problem. However, the method of self-similar potentials in conjunction with superposition can be successfully applied if the origin shift and the time delay are considered. After the complete solution is obtained, attention is focused on the crack surface displacements and dynamic stress intensity factors. The results of this study show that the DSIF is equal to the static SIF when the crack-tip speed is zero, and DSIF is zero as the crack-tip speed approaches the Rayleigh-wave speed. Moreover, the combination of SSP method and the superposition scheme can be applied to the expanding uniformly distributed load acting on a portion of the crack surfaces.
 封面目錄第一章 緒論1.1 研究動機1.2 文獻回顧1.3 研究方法1.4 研究內容第二章 自相似勢能法之簡介2.1 前言2.2 平面應變問題之自相似勢能法2.2.1 運動方程式2.2.2 波動方程式2.2.3 (x,y,t)空間與θ複數平面之映射關係2.2.4 自相似勢能表示位移場及應力場2.3 反平面(anti-plane)問題之自相似勢能第三章 非對稱裂縫延伸之動態解析3.1 前言3.2 Ⅰ型裂縫問題3.2.1 問題之陳述3.2.2 問題之解3.2.3 裂縫張開位移與動應力強度因子3.3 Ⅱ型裂縫問題3.3.1 問題之陳述3.3.2 進行求解3.3.3 裂縫滑動位移與動應力強度因子3.4 Ⅲ型裂縫問題3.4.1 問題之陳述及求解3.4.2 裂縫撕開位移與動應力強度因子3.5 均佈應力載重作用於整個裂縫表面之Ⅰ型裂縫問題3.5.1 問題之陳述3.5.2 問題之求解3.5.2.1 均佈應力載重僅作用於左側裂縫表面之求解3.5.2.2 原問題之完整解第四章 受集中載重作用之Ⅰ型裂縫延伸之動態解析4.1 前言4.2 問題之陳述4.3 問題之求解4.3.1 第一部分(case A)之求解4.3.2 第二部分(case B)之求解4.3.3 第三部分(case C)之求解4.3.4 原問題之完整解4.4 動應力強度因子4.4.1 集中載重作用之DSIF之探討4.4.2 向外擴展之均佈載重作用之DSIF之探討第五章 結論與建議5.1 結論5.2 建議參考文獻作者簡介其他
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