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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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TL;DR: In this article, a mesh-free method is proposed to model the crack as a set of cohesive crack segments and avoid the representation of the crack surface. But the method does not capture complicated failure patterns of experimental data well.
Abstract: Fracture of prestressed concrete beams is studied with a novel and robust three-dimensional meshfree method. The meshfree method describes the crack as a set of cohesive crack segments and avoids the representation of the crack surface. It is ideally suited for a large number of cracks. The crack is modeled by splitting particles into two particles on opposite sides of the crack segment and the shape functions of neighboring particles are modified in a way the discontinuous displacement field is captured appropriately. A simple, robust and efficient way to determine, on which side adjacent particles of the corresponding crack segment lies, is proposed. We will show that the method does not show any "mesh" orientation bias and captures complicated failure patterns of experimental data well.

13 citations

Journal ArticleDOI
TL;DR: In this article, a displacement-based meshfree-enriched finite element method was proposed for the linear modeling of near-incompressible elasticity, which was generalized for the nonlinear analysis of elastomers.

13 citations

Journal ArticleDOI
TL;DR: A modified polynomial pressure projection stabilisation method is employed to stabilise and filter spurious pressure modes, where the gradient is corrected as proposed by Duan et al. (2014) to avoid the volumetric locking that occurs at the incompressible limit.

13 citations

Journal ArticleDOI
TL;DR: A new meshfree method based on a discrete transformation of Green's basis functions is introduced to simulate Poisson problems with complex morphologies to investigate the accuracy and convergence rate of the proposed Green's Discrete Transformation Method.

13 citations

Journal ArticleDOI
TL;DR: An efficient meshfree method based on radial basis functions (RBFs) to solve a system of partial differential equations arising from pricing options under the regime switching model and the uniqueness of solution is proved for the discretized system of equations.
Abstract: This paper is devoted to develop an efficient meshfree method based on radial basis functions (RBFs) to solve a system of partial differential equations arising from pricing options under the regime switching model. For global RBF methods, one of the major disadvantages is the computational cost and ill-conditioning associated with the dense linear systems that arise. So, we employ one of the local meshfree methods known as radial basis function based finite difference method. Then with an operator splitting method, sparse and well-conditioned system of complementarity problems are solved very fast for the American option. Also, the uniqueness of solution is proved for the discretized system of equations. Numerical examples presented in the last section illustrate the robustness and practical performance of the proposed algorithm for pricing European and American options.

13 citations


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