Free mesh method: A new meshless finite element method

SUMMARYThe meshless method is expected to become an e!ective procedure for realizing a CAD/CAE seamless system for analyses ranging from modelling to computation, because time-consuming mesh generation processes are not required. In the present study, a new meshless approach, referred to as the Node-By-Node Meshless method is proposed, in which only nodal data is utilized to discretize the governing equations, which are derived using either the principle of virtual work or the Galerkin method. In this method, three key methodologies are utilized: (i) nodal integration using stabilization terms, (ii) interpolation by the Moving Least-Squares Method, and (iii) a node-by-node iterative solver. This paper presents the formulation of the proposed method along with numerical results obtained for two-dimensional elastostatic and eigenvalue problems.

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“…Using equation (6), the component of displacement u utilized for dicretization is expressed as follows:…”

Section: Plate Problemmentioning

confidence: 99%

“…Both DEM, proposed by Nayroles [4], and EFGM, proposed by Belytschko [5], are methods for discretizing weak-formed governing equations using only distributed nodal data. Finally, FMM proposed by Yagawa [6], is a method used to evaluate local sti!ness and solve the global system matrix based on node-by-node procedures.…”

Section: Introductionmentioning

confidence: 99%

Node-by-node meshless approach and its applications to structural analyses

Nagashima

1999

Int. J. Numer. Meth. Engng.

103

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“…EFMM used for the structural analysis in this study is based on FMM [15,16], which is one of mesh-less methods. The most important feature of FMM is that it requires only the coordinate data of each node in analysis domains as the input information.…”

Section: Free Mesh Methodsmentioning

confidence: 99%

Parallel Computing of Fluid-Structure Coupled Analysis Using Supg/PSPG and Enriched Free Mesh Method

Nagaoka¹,

Nakabayashi²,

Yagawa³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The paper proposes a new analysis method for fluid-structure problems, which has nodal consistency at the fluid-structure interface and its calculation efficiency and accuracy are high. The incompressible viscous fluid analysis method using the P1-P1 element based on SUPG/PSPG developed by Tezduyar et al. is used for fluid analysis, while the high-accuracy analysis method based on EFMM developed by the authors is adopted for structure analysis. As the common feature of these methods, it is possible to analyze a fluid or a structure rather accurately by using the first order triangular of tetrahedral elements. In addition, variables are exchanged exactly at the common nodes on the fluid-structure boundary without deteriorating accuracy and calculation efficiency due to the interpolation of variables between nodes.The Present method is applied to a fluid-structure interaction problem by simulating the deformation of a red blood cell. At this time, to solve a bottleneck of EFMM that is needed a lot of time to make a stiffness matrix, we introduced a parallel processing to EFMM.

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“…EFMM is based on FMM (Free Mesh Method) [10] [11], which is one of mesh-less method. The most important feature of FMM is that it requires only the coordinate data of each node in analysis domains as the input information.…”

Section: Fundamental Concept Of Efmmmentioning

confidence: 99%