Relevant bibliographies by topics / Meshfree methods (Numerical analysis)

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Academic literature on the topic 'Meshfree methods (Numerical analysis)'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Meshfree methods (Numerical analysis)"

1

Liu, Wing Kam, Sergio R. Idelsohn, and Eugenio O�ate. "Announcement ?Meshfree Methods?" International Journal for Numerical Methods in Engineering 49, no. 5 (2000): 721–23. http://dx.doi.org/10.1002/1097-0207(20001020)49:5<721::aid-nme92>3.0.co;2-4.

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2

Garg, Sahil, and Mohit Pant. "Meshfree Methods: A Comprehensive Review of Applications." International Journal of Computational Methods 15, no. 04 (2018): 1830001. http://dx.doi.org/10.1142/s0219876218300015.

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The meshfree methods in computational mechanics have been actively proposed and increasingly developed in order to overcome some drawbacks in the conventional numerical methods. Over past three decades meshfree methods have found their way into many different application areas ranging from classical astronomical problems to solid mechanics analysis, fluid flow problems, vibration analysis, heat transfer and optimization to the numerical solution of all kind of (partial) differential equation problems. The present work is an effort to provide a comprehensive review of various Meshfree methods, their classification, underlying methodology, application area along with their advantages and limitations. Key contributions of mesh free techniques to the area of fracture mechanics have been discussed with applications of element free Galerkin method (EFGM) to fracture analysis as primary concern.
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3

Dumont, Serge, Olivier Goubet, Tuong Ha-Duong, and Pierre Villon. "Meshfree methods and boundary conditions." International Journal for Numerical Methods in Engineering 67, no. 7 (2006): 989–1011. http://dx.doi.org/10.1002/nme.1659.

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4

Gu, Yuan Tong. "An Adaptive Local Meshfree Updated Lagrangian Approach for Large Deformation Analysis of Metal Forming." Advanced Materials Research 97-101 (March 2010): 2664–67. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.2664.

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The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.
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Niemiec, Dominik, Roman Bulko, and Juraj Mužík. "The Meshfree Localized Petrov-Galerkin Approach in Slope Stability Analysis." Civil and Environmental Engineering 15, no. 1 (2019): 79–84. http://dx.doi.org/10.2478/cee-2019-0011.

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Abstract The article focuses on the use of the meshfree numerical method in the field of slope stability computations. There are many meshfree implementations of numerical methods. The article shows the results obtained using the meshfree localized Petrov-Galerkin method (MLPG) – localized weak-form of the equilibrium equations with an often used elastoplastic material model based on Mohr-Coulomb (MC) yield criterion. The most important aspect of MLPG is that the discretization process uses a set of nodes instead of elements. Node position within the computational domain is not restricted by any prescribed relationship. The shape functions are constructed using just the set of nodes present in the simple shaped domain of influence. The benchmark slope stability numerical model was performed using the developed meshfree computer code and compared with conventional finite element (FEM) and limit equilibrium (LEM) codes. The results showed the ability of the implemented theoretical preliminaries to solve the geotechnical stability problems.
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6

Belytschko, T., Y. Krongauz, J. Dolbow, and C. Gerlach. "On the completeness of meshfree particle methods." International Journal for Numerical Methods in Engineering 43, no. 5 (1998): 785–819. http://dx.doi.org/10.1002/(sici)1097-0207(19981115)43:5<785::aid-nme420>3.0.co;2-9.

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7

WANG, DONGDONG, and ZHENTING LIN. "A COMPARATIVE STUDY ON THE DISPERSION PROPERTIES OF HRK AND RK MESHFREE APPROXIMATIONS FOR KIRCHHOFF PLATE PROBLEM." International Journal of Computational Methods 09, no. 01 (2012): 1240015. http://dx.doi.org/10.1142/s0219876212400154.

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Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.
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8

Racz, Donat, and Tinh Quoc Bui. "Novel adaptive meshfree integration techniques in meshless methods." International Journal for Numerical Methods in Engineering 90, no. 11 (2012): 1414–34. http://dx.doi.org/10.1002/nme.4268.

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9

Zhang, Hongjun, Guangsong Chen, Linfang Qian, and Jia Ma. "FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis." Shock and Vibration 2019 (January 8, 2019): 1–23. http://dx.doi.org/10.1155/2019/3269276.

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The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.
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10

Alves, Carlos J. S., and Svilen S. Valtchev. "Numerical comparison of two meshfree methods for acoustic wave scattering." Engineering Analysis with Boundary Elements 29, no. 4 (2005): 371–82. http://dx.doi.org/10.1016/j.enganabound.2004.09.008.

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