数值流形方法的粘性边界问题初探

在实际工程数值流形方法分析中,采用固定约束边界的方法处理无限域或者半无限域的情况,边界处应力波的反射造成模拟结果与实际情况不符.本文基于Lysmer等人提出的粘性边界理论,在边界上设置阻尼器,推导相应粘性边界条件下流形单元刚度矩阵的数值计算格式,经岩石长条中弹性波传播算例,并与有限元结果对比,验证了该粘性边界的有效性,有利于数值流形方法的工程中推广应用.

Primary study on viscous boundary in numerical manifold method

In engineering analysis by numerical manifold method, infinite region or half infinite region is treated by fixed boundary. But stress waves reflect severely at fixed boundary. The simulative results are not in agreement with fact instances. So based on Lysmer's viscous boundary theory, a new viscous boundary is brought forward. This approach is based on the use of the independent dashpots in the normal and shear directions of specific boundaries, and then corresponding viscous boundary condition stiffness matrix is derived and implemented into the original NMM program. New method has been proven to be an effective method by a simple example, in which one dimensional elastic wave propagates in a long rock bar, and comparing with resultant stress wave obtained from different boundary by FEM. The result obtained from the FBC by NMM is in agreement with that by FEM. But the result obtained from the VBC by NMM does not agree with that from the non-reflection boundary by FEM. It is helpful for programming and the application of numerical manifold method to engineering.