无限弹性介质中隧道内爆炸动力响应的解析解

Analytical Solution for the Dynamic Response of Tunnel to An Internal Explosion in Infinite Elastic Medium

基于圆柱形薄壳结构理论,建立爆炸荷载作用下隧道结构的动力平衡方程。采用积分变换法求得Fourier变换域内爆炸荷载作用下隧道位移场的积分表达式。结合具体算例,采用离散Fourier逆变换的数值计算方法,给出了爆心处隧道位移时程曲线、最大正应力时程曲线及某一时刻隧道位移幅值和最大正应力在x方向的变化曲线。其结果与数值计算结果相一致,验证了方法的可行性。

The dynamic balance equation of tunnel structure under an explosion loading action is established based on the theory of cylindrical thin shell structure. An integral equation in the Fourier transformed filed that represents the displacement field in tunnel under the explosion loading is deduced by using the integral transformation. Taking an engineering project as example, the time-history curves of displacement and maximum circular normal stress in explosion center are given by using the inverse fast Fourier transform （IFFT）. Furthermore, the variation curves of displacement and the maximum normal stress at a certain time in x direction are given also. The results show good agreement with the numerical computation results. This mean feasibility of the model and the method.