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Journal articles on the topic 'Meshfree/meshless methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

GU, Y. T. "MESHFREE METHODS AND THEIR COMPARISONS." International Journal of Computational Methods 02, no. 04 (2005): 477–515. http://dx.doi.org/10.1142/s0219876205000673.

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In recent years, one of the hottest topics in computational mechanics is the meshfree or meshless method. Increasing number of researchers are devoting themselves to the research of the meshfree methods, and a group of meshfree methods have been proposed and used to solve the ordinary differential equations (ODEs) or the partial differential equations (PDE). In the meantime, meshfree methods are being applied to a growing number of practical engineering problems. In this paper, a detailed discussion will be provided on the development of meshfree methods. First, categories of meshfree methods

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2

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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3

Daxini, S. D., and J. M. Prajapati. "A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/247172.

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Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mec

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4

Sadono, Kresno Wikan. "Penyelesaian Numerik Advection Equation 1 Dimensi dengan EFG-DGM." MEDIA KOMUNIKASI TEKNIK SIPIL 22, no. 1 (2016): 51. http://dx.doi.org/10.14710/mkts.v22i1.12406.

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Differential equation can be used to model various phenomena in science and engineering. Numerical method is the most common method used in solving DE. Numerical methods that popular today are finite difference method (FDM), finite element method (FEM) dan discontinuous Galerkin method (DGM), which the method includes mesh based. Lately, the developing methods, that are not based on a mesh, which the nodes directly spread in domain, called meshfree or meshless. Element free Galerkin method (EFG), Petrov-Galerkin meshless (MLPG), reproducing kernel particle method (RKPM) and radial basis functi

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5

Shanazari, Kamal. "An Adaptive Domain Partitioning Technique for Meshfree-Type Methods." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/817026.

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An overlapping domain partitioning based on adapting nodes is presented for the meshless-type methods. The decomposition of the domain is carried out based on the distribution of the nodes produced rather than the geometry of the problem. A set of adaptive nodes is first generated using the dimension reduction and equidistributing along the coordinate directions with respect to arc-length monitor. The domain is then partitioned in such a way that the same number of nodes are allocated to the subdomains. A radial basis function collocation method is applied to each subdomain followed by assembl

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6

Barbier, E., and Nik Petrinic. "Multiple Crack Growth and Coalescence in Meshfree Methods with Adistance Function-Based Enriched Kernel." Key Engineering Materials 560 (July 2013): 37–60. http://dx.doi.org/10.4028/www.scientific.net/kem.560.37.

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Distance fields are functions defining the minimum distance between any generic point inspace and the boundaries of an object. This paper shows some important properties of these fields andtheir derivatives. In fact, for polygonal lines, the derivatives of distance fields are discontinuous overthe finite length of the segment, but continuous all around the end-points. An immediate consequenceis their application as intrinsic enrichment of weight functions in meshless methods, for the treatmentof multiple arbitrary cracks. By introducing such explicitly known function for the distance fields,di

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7

Khosravifard, Amir, and Mohammad Rahim Hematiyan. "A new method for meshless integration in 2D and 3D Galerkin meshfree methods." Engineering Analysis with Boundary Elements 34, no. 1 (2010): 30–40. http://dx.doi.org/10.1016/j.enganabound.2009.07.008.

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8

Sadono, Kresno Wikan. "Penyelesaian Numerik Persamaan Advection Dengan Radial Point Interpolation Method dan Integrasi Waktu Dengan Discontinuous Galerkin Method." Teknik 37, no. 2 (2016): 64. http://dx.doi.org/10.14710/teknik.v37i2.11640.

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Persamaan differensial banyak digunakan untuk menggambarkan berbagai fenomena dalam bidang sains dan rekayasa. Berbagai masalah komplek dalam kehidupan sehari-hari dapat dimodelkan dengan persamaan differensial dan diselesaikan dengan metode numerik. Salah satu metode numerik, yaitu metode meshfree atau meshless berkembang akhir-akhir ini, tanpa proses pembuatan elemen pada domain. Penelitian ini menggabungkan metode meshless yaitu radial basis point interpolation method (RPIM) dengan integrasi waktu discontinuous Galerkin method (DGM), metode ini disebut RPIM-DGM. Metode RPIM-DGM diaplikasika

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9

Zakrzewski, Nadia, Majidreza Nazem, Scott William Sloan, and Mark Cassidy. "On Application of the Maximum Entropy Meshless Method for Large Deformation Analysis of Geotechnical Problems." Applied Mechanics and Materials 846 (July 2016): 331–35. http://dx.doi.org/10.4028/www.scientific.net/amm.846.331.

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Traditional grid-based numerical techniques such as the Finite Element Method (FEM) are known to suffer when large deformations of the continuum are encountered. As such, there has been limited success using this class of methods to solve many of the complex problems encountered in computational geomechanics. The potential of Meshfree techniques for addressing this perceived deficiency has been recognised. This study presents a robust Maximum Entropy Meshless (MEM) method for the analysis of problems involving geometrical nonlinearity in computational geomechanics. The method is validated via

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10

Darbani, Mohsen. "The Meshfree Finite Element Method for Fluids with Large Deformations." Defect and Diffusion Forum 326-328 (April 2012): 176–80. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.176.

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The shallow water equations (SWE) is often simulated by using Eulerian descriptions. These phenomena may give rise to strong gradients and lead to large distortion of grids meshes. Hence classical finite elements methods may fall in simulating such problems. In this paper we present a meshless method, based on the natural element nethod (NEM). In a geometrical domain of a cloud of nodes, NEM uses the Voronoi cells and then its dual, namely Delaunay triangulation. Its main advantage lies in shape function of the natural neighbour interpolation, such that the position of natural neighbours is en

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11

Hidayat, Mas Irfan P., Bambang Ariwahjoedi, Setyamartana Parman, and Sonny Irawan. "A Meshfree Approach for Transient Heat Conduction Analysis of Nonlinear Functionally Graded Materials." International Journal of Computational Methods 15, no. 02 (2017): 1850007. http://dx.doi.org/10.1142/s021987621850007x.

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In this paper, an alternative meshfree approach is presented for transient heat conduction analysis of nonlinear functionally graded materials (FGMs). The main idea behind the introduced approach is to use collocation in local domains containing of sets of regular or scattered nodes and approximating the solution by B-spline basis functions. It combines the favorable properties of B-spline basis functions in having arbitrary degree for better resolution of solution, partition of unity and the Kronecker delta properties with low computational effort of collocation. The method is called as local

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12

Jiwari, Ram, and Alf Gerisch. "A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems." Engineering Computations 38, no. 6 (2021): 2666–91. http://dx.doi.org/10.1108/ec-05-2020-0291.

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Purpose This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time. Design/methodology/approach In a method of lines setting, a meshless method for their discretization

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13

PEKEDIS, MAHMUT, and HASAN YILDIZ. "NUMERICAL ANALYSIS OF A PROJECTILE PENETRATION INTO THE HUMAN HEAD VIA MESHLESS METHOD." Journal of Mechanics in Medicine and Biology 14, no. 04 (2014): 1450059. http://dx.doi.org/10.1142/s0219519414500596.

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In recent years, physicists, engineers and medical scientists have tried to demonstrate the biomechanics of gunshot wounds with numerical methods and experimental observations. Currently, the finite element method (FEM) is the most widely used numerical method among the studies related to ballistic wound injuries. However, when the FEM is used for the penetration analysis, the path of the projectile in the skull is subjected to extremely large deformations which will introduce errors due to distortion of elements. To overcome this error, the meshfree technique was established to simulate the g

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14

Liu, Xuemei, Ruiyi Wang, Yunhua Li, and Dongdong Song. "Deformation of Soft Tissue and Force Feedback Using the Smoothed Particle Hydrodynamics." Computational and Mathematical Methods in Medicine 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/598415.

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We study the deformation and haptic feedback of soft tissue in virtual surgery based on a liver model by using a force feedback device named PHANTOM OMNI developed by SensAble Company in USA. Although a significant amount of research efforts have been dedicated to simulating the behaviors of soft tissue and implementing force feedback, it is still a challenging problem. This paper introduces a kind of meshfree method for deformation simulation of soft tissue and force computation based on viscoelastic mechanical model and smoothed particle hydrodynamics (SPH). Firstly, viscoelastic model can p

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15

OSTAD, H., and S. MOHAMMADI. "A STABILIZED PARTICLE METHOD FOR LARGE DEFORMATION DYNAMIC ANALYSIS OF STRUCTURES." International Journal of Structural Stability and Dynamics 12, no. 04 (2012): 1250026. http://dx.doi.org/10.1142/s0219455412500265.

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The property of free movement of particles allows for most meshless particle methods to be efficiently used for simulation of solid problems involving large deformation as it removes the necessity of remeshing, which is one of the time-consuming parts of the traditional finite element method based on an updated Lagrangian formulation. One of the main sources of instabilities in meshfree particle methods, which approximate the strong form of partial differential equations, is the existence of extra high frequency vibrations. They are induced into the solution due to the use of truncated Taylor

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16

Basílio, Adam, Fran Sérgio Lobato, and Fábio de Oliveira Arouca. "Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution." Engineering Computations 37, no. 9 (2020): 3293–319. http://dx.doi.org/10.1108/ec-01-2020-0017.

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Purpose The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in

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17

Garg, Rajul, Harishchandra Thakur, and Brajesh Tripathi. "Numerical simulation of two-dimensional fins using the meshless local Petrov – Galerkin method." Engineering Computations 37, no. 8 (2020): 2913–38. http://dx.doi.org/10.1108/ec-07-2019-0340.

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Purpose The study aims to highlight the behaviour of one-dimensional and two-dimensional fin models under the natural room conditions, considering the different values of dimensionless Biot number (Bi). The effect of convection and radiation on the heat transfer process has also been demonstrated using the meshless local Petrov–Galerkin (MLPG) approach. Design/methodology/approach It is true that MLPG method is time-consuming and expensive in terms of man-hours, as it is in the developing stage, but with the advent of computationally fast new-generation computers, there is a big possibility of

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18

Nguyen, Nha Thanh, Minh Ngoc Nguyen, Thien Tich Truong, and Tinh Quoc Bui. "An improved meshless method for finite deformation problem in compressible hyperelastic media." Vietnam Journal of Mechanics, February 1, 2021. http://dx.doi.org/10.15625/0866-7136/15332.

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Hyperelastic materials are considered as special category of elastic solid materials because of their nonlinear complicated constitutive laws. Due to large strain state, the behaviour of such materials is often considered in finite deformation analysis. The nonlinear large deformation behavior of such materials is important. In this study, a novel meshless radial point interpolation method (RPIM) enhanced by Cartesian transformation method (CTM), an effective numerical integration, is presented for nonlinear behavior of hyperelastic media under finite deformation state with total Lagrange form

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