Harmonic response of layered halfspace using reduced finite element model with perfectly-matched layer boundaries

Abstract

The current paper investigates the use of perfectly-matched layers (PML) as absorbing elements for a finite element (FE) model simulating a semi-infinite medium. Due to the formulation of the FE-PML model, it is also possible to use a Craig-Bampton reduction to significantly reduce the number of degrees-of-freedom in the model, in an attempt to improve the computational efficiency of the simulation. The perfectly-matched layers use a complex-valued function to numerically stretch the apparent size of PML elements while allowing them to remain nominally small. The results from this investigation suggest the PML elements worked seamlessly with the FE elements to approximate the elastodynamic response of a 3D halfspace subjected to a surface load; the wave energy is completely absorbed by the PMLs regardless of incident angle or wavelength. Furthermore, the size of the model was reduced by approximately 32% using a Craig-Bampton reduction (CBR). The CBR transforms the system into a mixed set of coordinates, including both modal and spatial coordinates. The model reduction is accomplished by neglecting modal frequencies for the system above two and a half times the maximum forcing frequency of interest. By only transforming the frequency-independent FE section into modal coordinates, and leaving the frequency-dependent PML elements as spatial degrees-of-freedom, the mode-shapes must only be solved once and can then be reused for different forcing frequencies. The results from this investigation suggest this could provide computational benefits if a number of cases are being computed for different frequencies.