弹性介质分向插值无限元

Directional interpolation infinite elements for elastic medium

无限元是一种有效的人工边界,可用于处理弹性波的传播问题。在传统动力无限元的基础上,提出了一种采用分向插值技术的新型动力无限元,详细地推导了这种无限元的形函数,建立了完全解析形式的刚度矩阵,以提高计算效率,采用该无限元边界,计算了弹性介质中的线源Lamb问题,通过对比解析解答的地基表面位移,验证了该无限元的有效性。算例分析表明,采用此类无限元时,有限元单元边长建议取不超过1/8剪切波波长,网格边界到激励源点的距离宜取5倍剪切波波长。无限单元中的幅值衰减系数对计算结果影响甚微,建议取较小值。

Infinite element is an effective artificial boundary, which can be utilised to address the elastic wave propagation problem. Based on the traditional dynamic infinite elements, we proposed a novel dynamic infinite element using a directional interpolation technique. The shape function of the element has been derived in detail. The totally analytical stiffness matrix related to the element is developed to improve the computation effectiveness. By using the infinite element mentioned above, Lamb problem with line source in an elastic medium is computed. The validity of the infinite element is verified by comparing the computed results with the analytical solution of displacements on the ground. The example analysis shows that the edge size in the finite element mesh should be less than 1/8 shear wavelength. The distance between an imposed source point and the mesh boundary should be equal to 5 times the shear wavelength. The amplitude attenuation coefficient in the infinite element has little effect on the calculation results, and thus a relatively small value is recommended.