改进时域间断Galerkin有限元方法在弹塑性波传播数值模拟中的应用

APPLICATION OF THE MODIFIED TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD TO ELASTO-PLASTIC WAVE PROPAGATION SIMULATION

对于高频、强脉动荷载作用下的结构动力学波传播分析,对比于传统的时域算法,时域间断Galerkin方法能捕捉到波阵面的间断,有效地避免了由于间断引起的数值振荡.但时域间断方法却带来了波前面的虚假数值振荡.论文针对上述波前数值振荡的现象进行研究,通过引入人工阻尼的方法对时域间断Galerkin有限元方法进行进一步改进.数值结果表明,所发展的方法能够有效的滤掉强动荷载产生的波前数值振荡现象,同时降低了时域间断Galerkin方法的网格依赖性.

Compared with the traditional time-stepping algorithm, the Discontinuous Galerkin Finite Element Method（DGFEM） can capture the discontinuous of wave front and eliminate spurious numerical oscillations, which are common in simulating structural dynamics and wave propagation under high frequen cy and strong dynamic loading. However,DGFEM brings spurious numerical oscillations in wave-front. In the present paper,a modified DGFEM（m-DGFEM） is suggested by introducing artificial damping term. Numerical results show that the present method can effectively eliminate spurious numerical oscillations of wave-front and reduce mesh dependence of DGFEM.