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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, the meshless manifold method (MMMMM) is used to analyze transient deformations in dynamic fracture and the weak formulation of the partial differential equation for elastic dynamics is derived from the method of weighted residuals (MWR).
Abstract: In the paper, the meshless manifold method (MMM) is utilized to analyze transient deformations in dynamic fracture. The MMM is based on the partition of unity method and the finite coverage approximation which provides a unified framework for solving problems involving both continuums and dis-continuums. The method can treat crack problem easily because the shape function is not affected by the discontinuity in the domain. For localization problems at the tip of the discontinuity, these shape functions are more effective than those used in other numerical methods. The method avoids the disadvantages of other meshless methods in which the tip of a discontinuous crack is not considered. In meshless manifold method, the finite coverage approximation is used to construct the shape functions that overcome influences of the interior discontinuities in the displacement. Consequently, the meshless manifold method has some advantages in solving the discontinuity problems when the discontinuities are complex. When the dynamic fracture mechanics is analyzed by the MMM, the weak formulation of the partial differential equation for elastic dynamics is derived from the method of weighted residuals (MWR). The discrete space of the domain is used for the MMM. The Newmark family of methods is used for the time integration scheme. At last, the validity and accuracy of the MMM are illustrated by two numerical examples of which the numerical results agree with the analytical solution.

19 citations

Journal ArticleDOI
TL;DR: A methodology of meshless finite points method for the analysis of nonlinear material problems with proportional loading based on deformation theory is presented, based on a strong formulation, keeping the meshless characteristics of FPM.

19 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a method to build intrinsic enrichments of the underlying mesh-free discretisation for efficient simulation of three-dimensional crack propagation, removing the limitations of existing criteria.
Abstract: Distance fields are scalar functions defining the minimum distance of a given point in the space from the boundary of an object. Crack surfaces are geometric entities whose shapes can be arbitrary, often described with ruled surfaces or polygonal subdivisions. The derivatives of distance functions for such surfaces are discontinuous across the surface, and continuous all around the edges. These properties of the distance function were employed to build intrinsic enrichments of the underlying mesh-free discretisation for efficient simulation of three-dimensional crack propagation, removing the limitations of existing criteria (reviewed in this paper). Examples show that the proposed approach is able to introduce quite convoluted crack paths. The incremental nature of the developed approach does not require re-computation of the enrichment for the entire crack surface as advancing crack front extends incrementally as a set of connected surface facets. The concept is based on purely geometric representation of discontinuities thus addressing only the kinematic aspects of the problem, such to allow for any constitutive and cohesive interface models to be used.

19 citations

Journal ArticleDOI
TL;DR: The proposed method makes appropriate shape functions which possess the important Delta function property to satisfy the essential conditions automatically and provides the space-time approximations for the heat temperature derived by expanding the required approximate solutions using collocation scheme based on radial point interpolation method (RPIM).
Abstract: In this paper, we extend the application of meshfree node based schemes for solving one-dimensional inverse Cauchy-Stefan problem. The aim is devoted to recover the initial and boundary conditions from some Cauchy data lying on the admissible curve s(t) as the extra overspecifications. To keep matters simple, the problem has been considered in one dimensional, however the physical domain of the problem is supposed as an irregular bounded domain in $$\mathbb {R}^2$$R2. The methods provide the space-time approximations for the heat temperature derived by expanding the required approximate solutions using collocation scheme based on radial point interpolation method (RPIM). The proposed method makes appropriate shape functions which possess the important Delta function property to satisfy the essential conditions automatically. In addition, to conquer the ill-posedness of the problem, particular optimization technique has been applied for solving the system of equations $$Ax=b$$Ax=b in which A is a nonsymmetric stiffness matrix. As the consequences, reliable approximate solutions are obtained which continuously depend on input data.

19 citations

DissertationDOI
19 Dec 2005
TL;DR: In this article, the authors developed an automatic algorithm for the efficient simulation of multiple cracking in plain and reinforced concrete structures of medium size and used meshless methods to describe the growth of crack surfaces.
Abstract: The complex failure process of concrete structures can not be described in detail by standard engineering design formulas. The numerical analysis of crack development in concrete is essential for several problems. In the last decades a large number of research groups have dealt with this topic and several models and algorithms were developed. However, most of these methods show some difficulties and are limited to special cases. The goal of this study was to develop an automatic algorithm for the efficient simulation of multiple cracking in plain and reinforced concrete structures of medium size. For this purpose meshless methods were used to describe the growth of crack surfaces. Two meshless interpolation schemes were improved for a simple application. The cracking process of concrete has been modeled using a stable criterion for crack growth in combination with an improved cohesive crack model which can represent the failure process under combined crack opening and crack sliding very well. This crack growth algorithm was extended in order to represent the fluctuations of the concrete properties by enlarging the single-parameter random field concept for multiple correlated material parameters.

19 citations


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