Abstract:

 To address the challenge of absorbing outgoing waves in geotechnical dynamic analysis, an explicit mixed finite element time-domain perfectly matched layer (PML) based on the central difference integration scheme is proposed. The two-dimensional and three-dimensional semi-discrete finite element equations suitable for explicit integration were derived. A two-dimensional stress-displacement mixed element Q4/4 and a three-dimensional stress-displacement mixed element HEX8/8 were developed for spatial discretization. An extended central difference explicit integration scheme was proposed to solve the third-order dynamic equations arising from the three-dimensional PML formulation. The implementation was carried out in ABAQUS/Explicit, and several numerical experiments were conducted to analyze the absorption performance of the artificial boundary under varying conditions, including soil types, wave types, wave frequencies, and boundary thickness. The results indicate that the PML achieves conditional convergence under all computational conditions. When the PML thickness exceeds 10 elements, the normalized root mean square deviation between the truncated and enlarged model responses is less than 2%. The proposed integration scheme and numerical implementation exhibit good stability and computational accuracy. For different soil types, the PML demonstrates excellent absorption performance for outgoing waves of various types and frequencies. The research findings have broad applications in the geotechnical dynamic analysis.

Key words: artificial boundary, perfectly matched layer, mixed finite element, ABAQUS, elastic waves, VUEL