Stability Analysis of an Explicit Integration Algorithm with 3D Viscoelastic Artificial Boundary Elements

Abstract

Viscoelastic artificial boundary elements are one of the most commonly used artificial boundaries when solving dynamic soil-structure interactions or near-field wave propagation problems. However, due to the lack of clear and practical stability criteria for the explicit algorithm that considers the influence of viscoelastic artificial boundary elements, the determination of the stable time increment in such numerical analyses is still a challenge. In this study, we proposed a numerical stability analysis method for the explicit algorithm with a 3D viscoelastic artificial boundary element based on the idea of a subsystem. Through this method, the artificial boundary subsystem that controls the stability of the overall numerical system is determined, and the analytical solution for the stability condition of the explicit integration algorithm with 3D viscoelastic artificial boundary elements is obtained. On this basis, the maximum time increment for solving dynamic problems with viscoelastic artificial boundary elements can be determined.

Improvement research on the stability of explicit integration algorithms with 3D viscoelastic artificial boundary elements

“…However, the subsystems established in this method usually contain a large number of nodes and thus the corresponding stability conditions can only be solved numerically. For the viscoelastic artificial boundary elements, Li et al (2020a) proved that the stability conditions of the overall numerical model can be derived by using several typical small subsystems that can represent the localized characteristics of the entire model, and proposed a stability analysis method based on the local subsystems. By using this method, the analytical stability conditions of the viscoelastic artificial boundary elements can be obtained, and the influence of various physical parameters on the numerical stability can be intuitively and quantitatively analyzed, then the stability improvement method can be investigated.…”

“…With the widespread application of viscoelastic artificial boundary elements in practical engineering (Bao et al, 2019;Liu et al, 2019a;Wu et al, 2021;Xu et al, 2022;Yang et al, 2011Yang et al, , 2019Zhang and Gu, 2020), the numerical stability issues has arisen, due to viscoelastic artificial boundary elements having different mass densities, stiffnesses and damping parameters than the internal medium. It has been proven that the stability conditions of the artificial boundaries are stricter than that of the internal domain (Li et al, 2020a). When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area.…”

“…, 2022; Yang et al ., 2011, 2019; Zhang and Gu, 2020), the numerical stability issues has arisen, due to viscoelastic artificial boundary elements having different mass densities, stiffnesses and damping parameters than the internal medium. It has been proven that the stability conditions of the artificial boundaries are stricter than that of the internal domain (Li et al. , 2020a).…”

Prediction method and experimental verification of vibration response caused by underground high-speed railways

“…In this study, a three-dimensional uniform viscoelastic artificial boundary was adopted. 28 The equivalent shear modulus G and the equivalent elastic modulus E of the three-dimensional viscoelastic artificial boundary element are calculated as follows:…”

“…In this study, a three-dimensional uniform viscoelastic artificial boundary was adopted. 28 The equivalent shear modulus G¯ and the equivalent elastic modulus E¯ of the three-dimensional viscoelastic artificial boundary element are calculated as follows:where G and G¯,respectively, are the shear modulus and equivalent shear modulus of the medium, E¯ is the equivalent elastic modulus, R is the distance from the vibration source to the artificial boundary, KBN and KBT are the normal stiffness and tangential stiffness of the spring, h is the thickness of the boundary element, υ∼ is the equivalent Poisson’s ratio, α is the ratio of the normal correction coefficient αN, and the tangential correction coefficient <...…”