Explicit finite element perfectly matched layer for transient three‐dimensional elastic waves

Abstract

SUMMARYThe use of a perfectly matched layer (PML) model is an efficient approach toward the bounded-domain modelling of wave propagation on unbounded domains. This paper formulates a three-dimensional PML for elastic waves by building upon previous work by the author and implements it in a displacement-based finite element setting. The novel contribution of this paper over the previous work is in making this finite element implementation suitable for explicit time integration, thus making it practicable for use in large-scale three-dimensional dynamic analyses. An efficient method of calculating the strain terms in the PML is developed in order to take advantage of the lack of the overhead of solving equations at each time step. The PML formulation is studied and validated first for a semi-infinite bar and then for the classical soil-structure interaction problems of a square flexible footing on a (i) half-space, (ii) layer on a half-space and (iii) layer on a rigid base. Numerical results for these problems demonstrate that the PML models produce highly accurate results with small bounded domains and at low computational cost and that these models are long-time stable, with critical time step sizes similar to those of corresponding fully elastic models.

Effect of soil stiffness on seismic response of reinforced concrete buildings with shear walls

“…In linear SSI analysis, properties of the soil stratum are defined by its mass density, elastic modulus and Poisson's ratio. The width of the soil mass beyond the raft was considered as 0.2B and depth as 0.2B, where B is the half width of the raft [4]. In order to simulate the wave propagation in an unbounded soil medium, an absorbing layer material called Perfectly-Matched Layer (PML) material with a thickness of 0.8B beyond the soil layer was considered [4].…”

“…The width of the soil mass beyond the raft was considered as 0.2B and depth as 0.2B, where B is the half width of the raft [4]. In order to simulate the wave propagation in an unbounded soil medium, an absorbing layer material called Perfectly-Matched Layer (PML) material with a thickness of 0.8B beyond the soil layer was considered [4]. The various input parameters for the PML remain same as that of the corresponding equivalent linearelastic soil as given in Table 2.…”

“…The width and thickness of the soil medium beyond foundation were taken as 1.5 times and 2 times the least width of the raft foundation to ensure that waves reflected back from the outer boundary modelled using non-reflecting boundaries do not affect the results of the simulation [12]. In PML model, the width and depth of the soil mass beyond the foundation were considered as 0.2B, where B is the half width of the foundation [4]. In order to simulate the wave propagation in an unbounded soil medium, perfectly matched layer (PML) material with a thickness of 0.8B beyond the soil layer was considered [4].…”

“…In PML model, the width and depth of the soil mass beyond the foundation were considered as 0.2B, where B is the half width of the foundation [4]. In order to simulate the wave propagation in an unbounded soil medium, perfectly matched layer (PML) material with a thickness of 0.8B beyond the soil layer was considered [4]. The node incompatibility occurring between soil and structure due to varying degrees of freedom of shell element and solid element is overcome by soil-structure interface, a tied surface to surface contact.…”

Perfectly Matched Layer (Pml) for Transient Wave Propagation in a Moving Frame of Reference

“…Later PML was formulated for the elastic wave equation in e.g. [5,6,7]. However, in this approach the solution for the displacements is dependent on computation of the strains in each time step.…”