Cell‐based maximum entropy approximants for three‐dimensional domains: Application in large strain elastodynamics using the meshless total Lagrangian explicit dynamics method

@article{Mountris2019CellbasedME,
  title={Cell‐based maximum entropy approximants for three‐dimensional domains: Application in large strain elastodynamics using the meshless total Lagrangian explicit dynamics method},
  author={Konstantinos A. Mountris and George C. Bourantas and Daniel Mill{\'a}n and Grand Roman Joldes and Karol Miller and Esther Pueyo and Adam Wittek},
  journal={International Journal for Numerical Methods in Engineering},
  year={2019},
  volume={121},
  pages={477 - 491}
}
We present the cell‐based maximum entropy (CME) approximants in E3 space by constructing the smooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation method combining the properties of the maximum entropy approximants and the compact support of element‐based interpolants. The method is evaluated in problems of large strain elastodynamics for three‐dimensional (3D) continua using the well‐established meshless total Lagrangian explicit dynamics method. The… 
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References

SHOWING 1-10 OF 66 REFERENCES
Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems
In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection–diffusion problems at various Peclet numbers in
On the optimum support size in meshfree methods: A variational adaptivity approach with maximum‐entropy approximants
TLDR
The method is based on a variational approach, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions.
Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
TLDR
A one‐parameter family of approximation schemes that bridges continuously two important limits: Delaunay triangulation and maximum‐entropy (max‐ent) statistical inference are presented.
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Abstract A local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for
The Meshless Local Petrov-Galerkin Method for Large Deformation Analysis of Hyperelastic Materials
Nonlinear formulations of the meshless local Petrov-Galerkin method (MLPG) are presented for the large deformation analysis of hyperelastic materials which are considered to be incompressible or
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