Augmented Numerical Manifold Method with implementation of flat-top partition of unity

He, Lei; An, Xinmei; Liu, Xiaoying; Zhao, Zhiye; Yang, Shengqiang

doi:10.1016/j.enganabound.2015.07.009

Cited by 23 publications

(13 citation statements)

References 50 publications

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“…Actually, as long as the number of flat‐top PU units keeps the same, the relative size of flat‐top elements and PU elements has almost no influence on the accuracy of numerical result. ()…”

Section: Construction Of Locally Refined Flat‐top Pu Meshmentioning

confidence: 99%

“…However, the most commonly used method to avoid the linear dependence is to add flat‐top re gions into the original PU‐based mesh system. () He et al and An et al has proven that it is linearly independent for the regularly patterned flat‐top PU mesh in one‐ and two‐dimensional spaces.…”

Section: Introductionmentioning

confidence: 97%

“…However, the most commonly used method to avoid the linear dependence is to add flat-top re gions into the original PU-based mesh system. [30][31][32][33][34][35][36] He et al 32 and An et al 36 has proven that it is linearly independent for the regularly patterned flat-top PU mesh in one-and two-dimensional spaces. For stress concentration and stress singularity problems, it is necessary to implement local refinement for flat-top PU based mesh, so that, not only the numerical accuracy can be improved with high-order local approximation but also the efficiency can be ensured through local refinement within specific area.…”

Section: Introductionmentioning

confidence: 99%

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Local refinement of flat‐top partition of unity based high‐order approximation

Liu

Zhao

et al. 2018

Numerical Meth Engineering

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Summary The high‐order approximation with regularly patterned flat‐top partition of unity mesh in one‐ and two‐dimensional cases has been proven linearly independent. However, for problems with stress concentration or stress singularity, local refinement within the regular mesh is necessary to improve the accuracy and efficiency. This paper introduces local refinement of flat‐top partition of unity mesh within the framework of high‐order approximation in one‐ and two‐dimensional spaces, respectively. Based on the traditional PU mesh, the construction of locally refined flat‐top PU mesh is straightforward. With the rank deficiency counting approach, linear independence is proven from element level for the locally refined mesh system. Based on the numerical solution procedure presented, two numerical examples are analyzed to verify the proposed approximation method.

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Section: Construction Of Locally Refined Flat‐top Pu Meshmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Local refinement of flat‐top partition of unity based high‐order approximation

Liu

Zhao

et al. 2018

Numerical Meth Engineering

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“…Compared with other numerical methods, eg, finite element–based methods and discrete element–based methods, the most distinguishing feature of the NMM is the adoption of a dual cover system, on which the nodes and elements are generated. Details of the finite cover systems and cover split techniques can be found in other works . In this section, a brief illustration of the NMM covers is presented with partition of unity (PU) function (also termed as weight function) for continuous and discontinuous deformation analyses.…”

Section: Fundamental Theory Of the Nmmmentioning

confidence: 99%

“…Details of the finite cover systems and cover split techniques can be found in other works. 43,45,[50][51][52] In this section, a brief illustration of the NMM covers is presented with partition of unity (PU) function (also termed as weight function) for continuous and discontinuous deformation analyses.…”

Section: Fundamental Theory Of the Nmmmentioning

confidence: 99%

Effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method

et al. 2017

Numerical Meth Engineering

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Summary Numerical stability by using certain time integration scheme is a critical issue for accurate simulation of discontinuous deformations of solids. To investigate the effects of the time integration schemes on the numerical stability of the numerical manifold method, the implicit time integration schemes, ie, the Newmark, the HHT‐α, and the WBZ‐α methods, and the explicit time integration algorithms, ie, the central difference, the Zhai's, and Chung‐Lee methods, are implemented. Their performance is examined by conducting transient response analysis of an elastic strip subjected to constant loading, impact analysis of an elastic rod with an initial velocity, and excavation analysis of jointed rock masses, respectively. Parametric studies using different time steps are conducted for different time integration algorithms, and the convergence efficiency of the open‐close iterations for the contact problems is also investigated. It is proved that the Hilber‐Hughes‐Taylor‐α (HHT‐α), Wood‐Bossak‐Zienkiewicz‐α (WBZ‐α), Zhai's, and Chung‐Lee methods are more attractive in solving discontinuous deformation problems involving nonlinear contacts. It is also found that the examined explicit algorithms showed higher computational efficiency compared to those implicit algorithms within acceptable computational accuracy.

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On hp refinements of independent cover numerical manifold method—some strategies and observations

Zhang

Zheng

et al. 2023

Sci. China Technol. Sci.

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Augmented Numerical Manifold Method with implementation of flat-top partition of unity

Cited by 23 publications

References 50 publications

Local refinement of flat‐top partition of unity based high‐order approximation

Local refinement of flat‐top partition of unity based high‐order approximation

Effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method

On hp refinements of independent cover numerical manifold method—some strategies and observations

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