Topic
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: This paper presents a coupling of the meshless finite cloud method (FCM) and the standard (mesh-based) boundary element method (BEM), which is motivated by the complementary properties of both methods.
24 citations
TL;DR: Some enrichment techniques for the modeling of heterogeneous media in the presence of singularities such as cracks which overcome long-standing problems associated with the assumption of local periodicity in traditional asymptotic homogenization methods are presented.
24 citations
TL;DR: A review of mesh-free approaches for modeling plant cellular systems and their morphological changes during drying can be found in this article, where it is concluded that meshfree methods have unique advantages especially in terms of performance and versatility in this regard and there are potential future work in the areas of accommodating temperature variations, 3-D modelling and multiscale modelling.
24 citations
01 Jan 2006
TL;DR: A concurrent simulation technique for analysing the deformation of systems that need the integration of material properties from nanoscopic to macroscopic dimensional scales and has a promising potential to a wide class of multiscale systems.
Abstract: This paper presents a concurrent simulation technique for analysing the deformation of systems that need the integration of material properties from nanoscopic to macroscopic dimensional scales. In the continuum sub-domain, a weak-form meshfree based method using the radial basis function interpolation was employed, but in the atomic sub-domain, molecular dynamics analysis was used. The transition from the atomic to continuum domains was realized by transition particles which are independent of either the nodes in the continuum sub-domain or the atoms in the atomic sub-domain. A simple penalty method was used to ensure the compatibility of displacements and their gradients in the transition. A virtual cell algorithm was developed using a local quasi-continuum approach to obtain the equivalent continuum strain energy density based on the atomic potentials and Cauchy-Born rule. Numerical examples showed that the present method is very accurate and stable, and has a promising potential to a wide class of multiscale systems.
24 citations
TL;DR: Techniques for generation of nodes, MFD stars, formulas, equations, equations as well as local approximation technique and numerical integration schemes are discussed there.
Abstract: Meshless Finite Difference Method (MFDM) is nowadays a powerful engineering tool for numerical analysis of boundary value problems. Nowadays, its computational capabilities are not fully used mainly due to the lack of suitable commercial software. This paper briefly presents current state-of-the-art of the MFDM solution approach as well as deals with the selected computational aspects of the MFDM. A set of Matlab functions written by the author is attached to the paper. Techniques for generation of nodes, MFD stars, formulas, equations as well as local approximation technique and numerical integration schemes are discussed there.
24 citations