Authors: Naohiro Nakamura
It is important to consider both the soil-structure interaction and nonlinear effects to accurately estimate the behavior of buildings during severe earthquakes. In addition, three dimensional (3D) models are needed to express the complex shape of buildings, basements, and piles. In recent years, large scale 3D time history nonlinear analyses using the finite element method (FEM) have been performed. Although the soil has a semi-infinite extent, a soil model needs to be generated as a finite region model in FEM analyses. Therefore, artificial wave boundary models are needed. Currently, simple models such as the cyclic boundary or the viscous boundary are often used mainly as the side wave boundary model. These simple models are simple to use but do not provide high accuracy. As a result, the wave boundary cannot be placed close to the analysis object, and the analysis modeling domain size and analysis load are enlarged. For this reason, it is desirable to improve the wave boundary accuracy and reduce the analysis domain size. Although the energy transmitting boundary is accurate and efficient for FEM earthquake response analysis, it can only be applied in the frequency domain. The author proposed the time domain transmitting boundary by applying a new method that can transform the frequency dependent function into the time domain. By using this time domain transmitting boundary, time domain analysis became possible. In this method, the analysis model can be divided into three parts: the inner field, the outer field, and the boundary itself. In the first paper, two in-plane problems were proposed. In the study, only the inner field can be treated as a nonlinear system. In the next study, the outer field and the boundary itself can be treated as a nonlinear system. In addition, a model was also proposed. In a previous study, this technique was expanded for 3D problems. The inner field is supposed to be hexahedron-shaped and the approximate time domain boundary was set around it. The boundary comprised two parts. One was the 2D in-plane time domain boundary and the other was the anti-plane time domain boundary. The efficiency of the proposed method was confirmed using some example problems. In this paper, based on these studies, 3D energy transmitting boundaries for nonlinear analyses are studied. First, an outline of the 3D transmitting boundary is provided. Then, improvements of the boundary for nonlinear problems are also explained. The efficiency of the proposed method was studied by comparison with a conventional viscous boundary. As a result, the efficiency of the proposed method was confirmed.
Keywords: component; Transmitting boundary, 3 Dimensional FEM, Time domain, Seismic Response Analysis, Nonlinear Analysis