AI 中文总结
研究移动冲击载荷下预应力干砂介质中两条移动共线裂纹的动态断裂行为，通过移动坐标系等方法转化问题，利用傅里叶积分变换等求解，得出相关表达式，揭示多因素对裂纹的影响，为相关工程结构设计提供见解。
AI 中文摘要
研究了在集中裂纹面载荷和移动冲击压力作用下，初始应力干砂介质中两条移动共线格里菲斯裂纹的动态断裂行为。通过移动坐标系将瞬态问题转化为稳态公式，并将初始应力和砂性的影响纳入控制方程。利用傅里叶积分变换得到特征方程和变换后的牵引位移关系。裂纹面、对称性和外表面条件将问题简化为耦合柯西型奇异积分方程。对于足够厚的条带，开发了渐近核约简，并使用有限希尔伯特变换解析求解所得方程。推导了裂纹密度函数、内外裂纹尖端的Ⅰ型应力强度因子和裂纹张开位移 的封闭形式表达式。从一般公式中恢复了几个极限情况，提供了分析一致性检验。结果表明了裂纹速度、裂纹几何形状、初始应力、砂性和移动冲击载荷对裂纹尖端强化和裂纹张开的综合影响。所提出的分析框架为涉及移动载荷的干砂介质的断裂评估和交通基础设施、岩土系统、地下开挖及其他工程结构的设计提供了有用的见解。
英文摘要
The dynamic fracture behaviour of two moving collinear Griffith cracks in an initially stressed dry sandy medium subjected to concentrated crack-face loading and moving punch pressure is investigated. A moving coordinate system transforms the transient problem into a steady state formulation, while the effects of initial stress and sandiness are incorporated into the governing equations. Fourier integral transforms are employed to obtain the characteristic equation and the transformed traction displacement relations. The crack face, symmetry, and outer surface conditions reduce the problem to coupled Cauchy type singular integral equations. For a sufficiently thick strip, an asymptotic kernel reduction is developed, and the resulting equations are solved analytically using the finite Hilbert transform. Closed form expressions are derived for the crack density functions, Mode I stress intensity factors at the inner and outer crack tips, and the crack opening displacement. Several limiting cases are recovered from the general formulation, providing analytical consistency checks. The results demonstrate the combined influence of crack speed, crack geometry, initial stress, sandiness, and moving punch loading on crack tip intensification and crack opening. The proposed analytical framework provides useful insights for fracture assessment and the design of transportation infrastructure, geotechnical systems, underground excavations, and other engineering structures involving dry sandy media subjected to moving loads.
