The stable node-based smoothed finite element method for analyzing acoustic radiation problems

Hu, Xiaoguang; Cui, Xiangyang; Zhang, Qunyi; Wang, Gang; Li, Guangyao

doi:10.1016/j.enganabound.2017.02.009

Cited by 52 publications

(15 citation statements)

References 51 publications

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“…This paper will mainly focus on the study of the standard implicit coupling algorithm of OSPD with the stable node‐based smoothed finite element method (SNS‐FEM) to calculate static fracture problems and validate the proposed implicit DB‐CA, where linear triangular elements are used. It should be noted that the efficiency and accuracy of the SNS‐FEM have been demonstrated by acoustic analyses, electromagnetic analyses, transient heat transfer analyses, and stochastic analyses . Therefore, the SNS‐FEM is chosen to couple OSPD to reduce the computational cost on one hand and make this implicit DB‐CA much stable and accurate on the other, which is also a difference from the recent implicit coupling method where the traditional FEM is used.…”

Section: Introductionmentioning

confidence: 99%

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Bie

She

et al. 2019

Numerical Meth Engineering

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Summary A general local/nonlocal implicit coupling technique called the dual‐based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual‐horizon ordinary state‐based peridynamic model is proposed, in which the linearization of dual‐horizon ordinary state‐based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual‐based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.

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Section: Introductionmentioning

confidence: 99%

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Bie

She

et al. 2019

Numerical Meth Engineering

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Section: Introductionmentioning

confidence: 99%

“…The dispersion error increases conspicuously with the increasing wave number due to the overly-stiff property of the FEM model [29][30][31][32][33]. In order to eliminate the dispersion error effectively, a discretized model with proper stiffness is needed [29][30][31][32]. For this purpose, a strain smoothing method was proposed by Chen [34,35], and a generalized gradient smoothing (GGS) technique [36][37][38] has been further formulated by Liu.…”

Section: Introductionmentioning

confidence: 99%

“…The prominent inherent properties of the NS-FEM make it much attractive. However, the NS-FEM model exhibits "overly-soft" when it comes to time-dependent problems [29][30][31][32] such as dynamic problems and acoustic problems. As the "overly-soft" property can lead to temporal instability [37,38], the NS-FEM cannot be used for acoustic problems directly.…”

Section: Introductionmentioning

confidence: 99%

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Dispersion Error Analysis of Stable Node-Based Finite Element Method for the Helmholtz Equation

Hu¹,

Cui²,

Zhang³

et al. 2018

CICP

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Numerical dispersion error is inevitable when the finite element method is employed to simulate acoustic problems. Studies have shown that the dispersion error is essentially rooted at the "overly-stiff" property of the standard FEM model. To reduce the dispersion error effectively, a discrete model that provides a proper softening effects is needed. Thus, the stable node-based smoothed finite element method (SNS-FEM) which contains a stable item is presented. In this paper, the SNS-FEM is investigated in details with respect to the pollution effect. Different kinds of meshes are employed to analyze the relationship between the dispersion error and the parameter involved in the stable item. To ensure the SNS-FEM can be applied in the practical engineering problems effectively, the relationship is finally constructed based on the hexagonal patch for the commonly used unstructured mesh is very similar to it. By minimizing the discretization error, an optimal parameter equipped in this novel SNS-FEM is formulated. Both theoretical analysis and numerical examples demonstrate that the SNS-FEM with the optimal parameter reduces the dispersion error significantly compared with the FEM and the well performed GLS, especially for mid-and high-wave number problems. AMS subject classifications: 35J05, 65C20, 65N30, 65N22, 68U20, 81U30 Key words: Acoustic, numerical method, the stable node-based smoothed finite element method (SNS-FEM), dispersion error, hexagonal patches.

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“…Inspired by this concept, Wang et al reported a stable node-based smoothed finite element method (SNS-FEM) for 2D and 3D acoustic analysis; numerical experiments show that the proposed method successfully eliminates the temporal instability of the original nodal integration. 42,43 He et al presented an edge-based smoothed finite element method (ES-FEM) for 2D acoustic problems and studied its pollution effect in detail. 44 Besides, through a theoretical analysis of dispersion error, the uncertain parameter in the alpha finite element method ( -FEM) used in wave propagation problems was also determined by He ′ s group in 2015.…”

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confidence: 99%

Dispersion analysis of the gradient weighted finite element method for acoustic problems in one, two, and three dimensions

Wang

Zeng

Cui

et al. 2019

Numerical Meth Engineering

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Summary This paper reports a detailed analysis on the numerical dispersion error in solving one‐, two‐, and three‐dimensional acoustic problems governed by the Helmholtz equation using the gradient weighted finite element method (GW‐FEM) in comparison with the standard FEM and the modified methods presented in the literatures. The discretized system equations derived based on the gradient weighted operation corresponding to the considered method are first briefed. The discrete dispersion relationships relating the exact and numerical wave numbers defined in different dimensions are then formulated, which will be further used to investigate the dispersion effect mainly caused by the approximation of field variables. The influence of nondimensional wave number and wave propagation angle on the dispersion error is detailedly studied. Comparisons are made with the classical FEM and high‐performance algorithms. Results of both theoretical and numerical experiments show that the present method can effectively reduce the pollution effect in computational acoustics owning to its crucial effectiveness in handing the dispersion error in the discrete numerical model.

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The stable node-based smoothed finite element method for analyzing acoustic radiation problems

Cited by 52 publications

References 51 publications

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Dispersion Error Analysis of Stable Node-Based Finite Element Method for the Helmholtz Equation

Dispersion analysis of the gradient weighted finite element method for acoustic problems in one, two, and three dimensions

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