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Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.


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Journal ArticleDOI
TL;DR: In this paper, a three-scale modeling of multilayered structures consisting of heterogeneous layers is presented based on the multiscale seamless-domain method and homogenization theory.

4 citations

Journal ArticleDOI
TL;DR: A new point of view is introduced in the description and solution of neighborhood problems and, more specifically, to those arising in meshfree or simulations in computational mechanics when the problem involves two distinct sets of points whose positions change, and whose proximity needs to be repeatedly assessed.
Abstract: This article introduces a new point of view in the description and solution of neighborhood problems and, more specifically, to those arising in meshfree or simulations in computational mechanics. In particular, we focus on the solution of neighborhood computations when the problem involves two distinct sets of points whose positions change, and whose proximity needs to be repeatedly assessed. With this type of problems in mind, we reformulate the neighborhood concepts and propose a solution--implemented in an open source library--that possesses a simple interface, is suitable for parallelization, has very mild restrictions on the point data, depends only on the standard C++ library, and has a small memory impact. The presented algorithm employs hash tables to achieve constant time in point searches, integer lattices to define a grid of background cells, and classifies the two independent point sets. As a result, and in addition to the favorable features previously indicated, the method is very fast as compared with the available implementations for similar problem.

4 citations

Journal ArticleDOI
TL;DR: In this article, an adaptive mesh-free method was proposed to calculate the image stresses of the dislocations at the free boundaries and bicrystal interfaces, where the interface constraints are imposed using Lagrangian multiplier.
Abstract: This paper proposes an adaptive meshfree method to calculate the image stresses of the dislocations at the free boundaries and bicrystal interfaces. Based on the superposition method (van der Giessen and Alan Needleman, 1995) originally proposed for single crystal material with free boundaries, a weak formulation is developed for the bicrystal materials containing dislocations, where the interface constraints are imposed using Lagrangian multiplier. The meshfree approximation is introduced to improve the accuracy and smoothness from conventional FEM interpolation functions, and it is straightforward to adaptively enrich meshfree nodes at the surrounding area of dislocations to effectively improve the solution accuracy. The numerical examples demonstrate the effectiveness of the proposed method to calculate the image stress in 2D and 3D problems with various boundary and interface conditions using either the classical elasticity (J.P.Hirth and J.Lothe, 1982) or the singularity-free dislocation theory (M.Lazar, 2012, 2013, 2014; G.Po and M.Lazar, 2014).

4 citations

Journal ArticleDOI
TL;DR: A novel method to treat Neumann and Dirichlet boundary conditions in meshless discretizations of elliptic equations using nodal integration, which allows a convenient interpretation of necessary conditions to pass the linear patch test.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a Voronoi-based Discrete Least Squares Meshless (VDLSM) method is proposed to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks.
Abstract: A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897