Radiation Damping Simulation in Finite Eelements Method Analysis Using Perfectly Matched Layer (PML)

In this research, perfectly matched layer has been implemented in the finite element method to simulate the radiation damping for soil-structure interaction analysis application. The perfectly matched layer (PML) has the ability to absorb and attenuate scattered waves under any angle of incidence and frequency, such that with the minimum dimensions of the modeling and the minimum amount of calculations, high-precision responses can be achieved. In order to time domain dynamic analysis by finite element method, a program is written utilizing MATLAB mathematical language, which is capable of analysis of different geometries, layering and dynamic/seismic loading in models with linear elastic behavior. The present program uses four-noded quadrilateral elements and uses the implicit Newmark method to solve the dynamic equation. The feature of theprogram is the implementation of PML, which can address the simulation of radiation damping in the finite element method correctly. This is done by rewriting the PML formulation, implementation in the finite element method, and step-by-step verifying the analysis of dynamic problems. First of all, to verify the dynamic analysis performance of the program, three simple examples have been solved, and the results show that theyare consistent with existing theories and the literature. Next, using PML, the problem of a rigid massless foundation vibration has been studied. Computing the impedance/compliance functions and comparing them with analytical or semi-analytical approaches existing in the technical texts, the efficiency and the precision of PML for surface loading conditions has been evaluated. In the frequency domain, the results are in good agreement with the previous studies. Besides, comparing the response from the reduced model (using PML) with the expected response from the extended mesh indicates that there is a complete match in the time domain. It is worth noting that this match is achieved while the model dimensions and the volume of data storage have been drastically reduced, but the accuracy of the answers has not varied. This reduction of dimension is such that if PML is located at a distance of up to a quarter of the foundation width, similar responses to larger models can be achieved.