Development of a fundamental‐solution‐less boundary element method for exterior wave problems

Song, Chongmin; Bazyar, Mohammad Hossein

doi:10.1002/cnm.964

Cited by 43 publications

(22 citation statements)

References 32 publications

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“…Generally, the convergence study of structural responses using high‐order elements is investigated to seek an appropriate scaled boundary finite element mesh for stochastic analysis. It has been demonstrated in previous studies that the discretization of SBFEM for deterministic problems can be performed most efficiently by means of high‐order elements . In order to demonstrate the capacity of the SGSBFEM, the responses achieved by the present work with different order p of PCE are verified by those obtained from MCS wherein the deterministic SBFEM calculation code is run by 10 000 samples.…”

Section: Numerical Examplesmentioning

confidence: 56%

The stochastic Galerkin scaled boundary finite element method on random domain

Minh

Gao

Saputra

et al. 2016

Numerical Meth Engineering

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Summary The research work extends the scaled boundary finite element method to non‐deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random‐field uncertainties. The aim is to blend the scaled boundary finite element method into the Galerkin spectral stochastic methods, which leads to a proficient procedure for handling the stress singularity problems and crack analysis. The Young's modulus of structures is considered to have random‐field uncertainty resulting in the stochastic behaviour of responses. Mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses (displacement, strain, and stress) and stress intensity factors of cracked structures. The feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Numerical Examplesmentioning

confidence: 56%

The stochastic Galerkin scaled boundary finite element method on random domain

Minh

Gao

Saputra

et al. 2016

Numerical Meth Engineering

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“…Only the boundary S visible from the scaling center O is discretized (see Figure 1(b) for a typical line element to be used in two-dimensional problems and Figure 1 can be lumped to the nodes [50]. [E 0 ] will be a block-diagonal matrix consisting blocks of size s × s (s = 2 or 3).…”

Section: Summary Of the Scaled Boundary Finite Element Methodsmentioning

confidence: 99%

“…[M 0 ] will be a diagonal matrix. The techniques of using Gauss-Lobatto-Legendre shape functions and quadrature are investigated by Song and Bazyar [50]. The internal nodal forces on a surface with a constant are obtained by integrating the surface traction over elements.…”

Section: Summary Of the Scaled Boundary Finite Element Methodsmentioning

confidence: 99%

“…A Padé series solution for the dynamic-stiffness matrix of an unbounded domain is developed by Song and Bazyar [49] for frequency-domain analyses. The sparsity and the lumping of the coefficient matrices of the scaled boundary finite element equation are exploited in [50]. The objective of this paper is to develop a high-order local transmitting boundary condition directly from the scaled boundary finite element equation.…”

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confidence: 99%

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A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry

Bazyar

Song

2007

Numerical Meth Engineering

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121

136

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A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continuedfraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary.Rigorous methods are, in general, spatially and temporally global. They are computationally expensive for large-scale problems and long-time calculations. One of the most popular rigorous methods is the boundary element method [11,12]. This method satisfies the governing equations in the problem domain and the radiation condition at infinity automatically by using a fundamental solution. Only the boundary needs to be discretized. However, it is very complicated to evaluate the fundamental solution when the material is anisotropic. The thin-layer method (consistent boundary condition) [13] has been developed for horizontally layered media. In this method, the boundary in the vertical direction is discretized and displacement functions in the horizontal direction satisfy the radiation condition at infinity. Exact non-reflecting boundary conditions, such as Dirichlet-to-Neumann (DtN) map [14], can be constructed from analytical solutions for unbounded domains. As analytical solutions are available only for simple geometries and material properties, their application is limited [4].The approximate methods are, in general, spatially and temporally local. They are computationally efficient by themselves, but have to be applied at a so-called artificial boundary sufficiently far away from the region of interest in order to obtain results of acceptable accuracy. This increases the total computational effort. The viscous boundary [15] consists of dashpots that absorb plane waves propagating perpendicularly to the artificial boundary. The Bayliss, Gunzburger and Turkel (BGT) boundary [16] annihilates selected terms of cylindrical or spherical waves. Infinite elements [5, 17] use decay functions representing the wave propagation toward infinity as shape functions of the displacements. In the method of perfectly matched layer [18], the domain of interest is surrounded by a fini...

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“…For more complex geometries, numerical approaches based on Finite Elements are usually applied. The formulation presented in this paper is based on the Scaled Boundary Finite Element Method (SBFEM) [4], [5], [6]. The cross-section of the waveguide is discretized using higher-order elements, while the direction of propagation is described analytically.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of ultrasonic guided waves using the Scaled Boundary Finite Element Method

Gravenkamp

Song

Prager

2012

2012 IEEE International Ultrasonics Symposium

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The formulation of the Scaled Boundary Finite Element Method is applied for the computation of dispersion properties of ultrasonic guided waves. The cross-section of the waveguide is discretized in the Finite Element sense, while the direction of propagation is described analytically. A standard eigenvalue problem is derived to compute the wave numbers of propagating modes. This paper focuses on cylindrical waveguides, where only a straight line has to be discretized. Higher-order elements are utilized for the discretization. As examples, dispersion curves are computed for a homogeneous pipe and a layered cylinder.

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Development of a fundamental‐solution‐less boundary element method for exterior wave problems

Cited by 43 publications

References 32 publications

The stochastic Galerkin scaled boundary finite element method on random domain

The stochastic Galerkin scaled boundary finite element method on random domain

A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry

Numerical simulation of ultrasonic guided waves using the Scaled Boundary Finite Element Method

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