Elastic Wave Scattering and Dynamic Stress in Composite With Fiber
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摘要: 基于弹性波动理论,对纤维增强复合材料结构中弹性波多重散射与动应力集中问题进行了分析研究,给出了介质各区域弹性波分析解的表达式.根据位移与应力在各区界面处的连续条件,确定了未知弹性波模式系数.采用Hankel函数的加法定理,将不同局部坐标系中散射波场的表达式变换到了同一个局部坐标系中,以给出弹性波模式系数和动应力集中因子的表达式.分析了多相纤维基体中两个散射体的间距、界层区材料性质以及界层区和纤维核区截面尺寸的变化,对各区界面动应力集中系数的影响.分析表明,两个散射体的间距、界层区材料性质和结构尺寸的变化对复合材料的力学特性具有显著影响.作为算例,给出了纤维增强复合材料结构中各区界面动应力集中系数的数值结果,并对其进行了分析讨论.Abstract: Based on the theory of elastic dynamics,multiple scattering of elastic waves and dynamic stress concentrations in fiber-reinforced composite were studied.The analytical expressions of elastic waves in different region were presented and an analytic method to solve this problem was established.The mode coefficients of elastic waves were determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi-interfaces.By making use of the addition theorem of Hankel funcitions,the formulations of scattered wave fields in different local coordinates were transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors.The influence of distance between two inclusions,material properties and structural size on the dynamic stress concentration factors near the interfaces was analyzed.It indicates in the analysis that distance between two inclusions,material properties and structural size has great influence on the dynamic properties of fiber-reinforced composite near the interfaces.As examples,the numerical results of dynamic stress concentration factors near the interfaces in a fiber-reinforced composite are presented and discussed.
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