Boundary treatments for the finite element analysis of shell vibration fields of architectural structures extracted with edge truncations

Abstract

The finite element analysis of a vibration field of a large-scale architectural structure is often conducted by extracting a local part to reduce the computational cost. A common way of extraction is to truncate the structure around the junction consisting of walls and floors. This paper proposes two boundary treatments to be given to the truncated edge. One is giving an impedance boundary condition of a junction. The impedance values are determined by the transfer matrix method (TMM). The other is a non-reflecting edge truncation realized by the perfectly matched layer (PML) shell element, which is a numerical model of the infinitely extending structure. Firstly, formulations of the two treatments are provided in detail. Secondly, impedances of basic shape junctions consisting of semi-infinite members are investigated by the TMM for a better understanding of the physical behavior. Thirdly, the proposed PML element is validated in two problem settings: the distance attenuation in the free field and the cross-junction's absorption property. An appropriate parameter tuning for the calculation using the PML element is also discussed.