Boundary moving least square method for 2D elasticity problems

Huang, Zhentian; Dong, Li Min; Huang, Dianwu; Lin, Ji; Han, Zi

doi:10.1016/j.enganabound.2019.06.005

Cited by 17 publications

(4 citation statements)

References 30 publications

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“…In the moving least squares approximate technique, a series of polynomial basis functions are adopted to approximate the unknown field quantity (Huang et al, 2019). Consider a field quantity u ( x ) defined in two-dimensional problem domain with many scattered nodes, its approximation function u h ( x ) is…”

Section: Approximation Function Of Hiefgmmentioning

confidence: 99%

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Zhou

Xue

2022

Journal of Intelligent Material Systems and Structures

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Piezoelectric materials have played an important role in industry due to a number of beneficial properties. However, most numerical methods for the piezoelectric materials need mesh, in which the mesh generation and remeshing are prominent difficulties. This paper proposes a Hermite interpolation element-free Galerkin method (HIEFGM) for piezoelectric materials, where the Hermite approximate approach and interpolation element-free Galerkin method (IEFGM) are combined. Based on the constitutive equation, geometric equation, and Galerkin integral weak form, the HIEFGM formulation for piezoelectric materials is established. In the proposed method, the problem domain is discretized by many nodes rather than the meshes, so the pre-processing of numerical computation is simplified. Furthermore, a new approximation technique based on the moving least squares method and Hermite approximate approach is used to derive the approximation function of field quantities. The derived approximation function has the Kronecker delta property and considers the field quantity normal derivatives of boundary nodes, which avoids the problem of imposing the essential boundary conditions and improves the accuracy of meshless approximation. The effects of the scaling factor, node density, and node arrangement on the accuracy of the proposed method are investigated. Numerical examples are given for assessing the proposed method and the results uniformly demonstrate the proposed method has excellent performance in analyzing piezoelectric materials.

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Section: Approximation Function Of Hiefgmmentioning

confidence: 99%

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Zhou

Xue

2022

Journal of Intelligent Material Systems and Structures

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“…Baseline correction and noise reduction method is necessary before peak detection. Moving least squares (MLS) is a well-developed and effective method for the approximation of scattered data, which is used to correct the baseline of spectra data [15]. The process of baseline correcting is as (3) Acquire the baseline of spectra data and output the spectrum data of baseline correction.…”

Section: Peak Detectionmentioning

confidence: 99%

A software system for rapid analysis of plastics using laser-induced breakdown spectroscopy

et al. 2020

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A: With the extensive use of plastic products, the recycling and reuse of plastics raises more concerns. Laser-induced breakdown spectroscopy (LIBS) has become a powerful technology for plastic analysis. To meet different analytical requirements, LIBS control system and analysis software was being continuously developed. However, existing software system only can realize the capability of LIBS system control or data analysis (peak detection or material identification). To improve the efficiency of LIBS instrument for plastic analysis, an integrated and full software is needed. In this work, analyis & test software was developed for rapid plastic analysis, which consists of LIBS control platform, plastic database, and analysis module which contains peak detection, qualitative and quantitative analysis. The software performance was validated, which provides an automatic processing for plastic analysis. Design approach of the software can be used for the development of similar instrument software and other samples analysis. K: Data processing methods; Pattern recognition, cluster finding, calibration and fitting methods; Plasma generation (laser-produced, RF, x ray-produced); Software architectures (event data models, frameworks and databases) 1Corresponding author.

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“…8 The introduction of the weight function with compact support makes the reconstructed curve or surface accurate and smooth, which has contributed to the wide application of the MLS in various fields. For example, the MLS is applied to solve elasticity problems, 9 the compressible Navier-Stokes, 10 Kuramoto-Sivashinsky, 11 and Burgers equation, 12 and estimate mathematical model based on discrete points. 13 Due to its good performance, the MLS method is often used in combination with other methods to construct shape function.…”

Section: Introductionmentioning

confidence: 99%

Surface reconstruction method for measurement data with outlier detection by using improved RANSAC and correction parameter

Luo

Tang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part B:

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The moving least squares (MLS) and moving total least squares (MTLS) are two of the most popular methods used for reconstructing measurement data, on account of their good local approximation accuracy. However, their reconstruction accuracy and robustness will be greatly reduced when there are outliers in measurement data. This article proposes an improved MTLS method (IMTLS), which introduces an improved random sample consensus (RANSAC) algorithm and a correction parameter in the support domain, to deal with the outliers and random errors. Based on the nodes within the support domain, firstly the improved RANSAC is used to generate a model for establishing the group of pre-interpolation and calculating the residual of each node. Subsequently, the abnormal degree of the node with the largest residual is evaluated by the correction parameter associated with the node residual and random errors. The node with certain abnormal degree will be eliminated and the remaining nodes are used to obtain the approximation coefficients. The correction parameter can be used for data reconstruction without insufficient or excessive elimination. The results of numerical simulation and measurement experiment show that the reconstruction accuracy and robustness of the IMTLS method is superior to the MLS and MTLS method.

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Boundary moving least square method for 2D elasticity problems

Cited by 17 publications

References 30 publications

A Hermite interpolation element-free Galerkin method for piezoelectric materials

A Hermite interpolation element-free Galerkin method for piezoelectric materials

A software system for rapid analysis of plastics using laser-induced breakdown spectroscopy

Surface reconstruction method for measurement data with outlier detection by using improved RANSAC and correction parameter

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