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={ArXiv},
  year={2019},
  volume={abs/1905.04929}
}
In this paper, we extend the Cell-based Maximum Entropy (CME) approximants in E3 by constructing smooth approximation distance function to polyhedral surfaces. The motivation of this work is to evaluate the CME approximants in the context of large strain elastodynamics for three-dimensional solids using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. Several numerical examples are solved to evaluate the performance of CME in MTLED for both regular and irregular… 
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References

SHOWING 1-10 OF 70 REFERENCES
Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity
TLDR
A modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision is presented and a lockingfree small-strain elasticity formulation for mesh free methods is proposed.
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
We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum
Cell-based maximum entropy approximants
In this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation behind this work is
An adaptive meshfree method for phase-field models of biomembranes. Part I: Approximation with maximum-entropy basis functions
TLDR
The proposed adaptive meshfree method is more efficient than common tensor product methods, and simpler than unstructured C 0 finite element methods, applicable by reformulating the model as a system of second-order PDE.
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
Local Maximum Entropy Shape Functions Based FE-EFGM Coupling
In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local
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
Optimal transportation meshfree approximation schemes for fluid and plastic flows
We develop an optimal transportation meshfree (OTM) method for simulating general solid and fluid flows, including fluid–structure interaction. The method combines concepts from optimal
Information-flux method: a meshfree maximum-entropy Petrov-Galerkin method including stabilised finite element methods
Abstract An information-flux method incorporating a novel approach to stable methods is proposed. The method may be considered as a meshfree Petrov–Galerkin approximation scheme with basis functions
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