Cell-based Maximum Entropy Approximants for Three-Dimensional Domains: Application in Large Strain Elastodynamics using the Meshless Total Lagrangian Explicit Dynamics Method

Konstantinos A. Mountris, George Bourantas, Daniel Millan, Grand Joldes, Karol Miller, Esther Pueyo, Adam Wittek

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Abstract

We present the Cell-based Maximum Entropy (CME) approximants inE3space by constructing thesmooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation methodcombining the properties of the Maximum Entropy approximantsand the compact support of element-basedinterpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D)continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. Theaccuracy and efficiency of the method is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothnessof CME basis functions, the numerical stability in explicittime integration is preserved for large time step.The challenging task of essential boundary conditions imposition in non-interpolating meshless methods(e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essentialboundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scale elastodynamics in 3D. Copyrightc©2019 John Wiley & Sons, Ltd
Original languageEnglish
Pages (from-to)1-19
JournalInternational Journal of Numerical Methods in Engineering
Publication statusE-pub ahead of print - 5 Sep 2019

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Large Strain
Meshless
Elastodynamics
Maximum Entropy
Entropy
Three-dimensional
Cell
Boundary conditions
Kronecker Delta
Strain Energy Density
Moving Least Squares
Meshfree
Entropy Function
Meshless Method
Convergence of numerical methods
Numerical Stability
Compact Support
Approximation
Distance Function
Strain energy

Cite this

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title = "Cell-based Maximum Entropy Approximants for Three-Dimensional Domains: Application in Large Strain Elastodynamics using the Meshless Total Lagrangian Explicit Dynamics Method",
abstract = "We present the Cell-based Maximum Entropy (CME) approximants inE3space by constructing thesmooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation methodcombining the properties of the Maximum Entropy approximantsand the compact support of element-basedinterpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D)continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. Theaccuracy and efficiency of the method is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothnessof CME basis functions, the numerical stability in explicittime integration is preserved for large time step.The challenging task of essential boundary conditions imposition in non-interpolating meshless methods(e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essentialboundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scale elastodynamics in 3D. Copyrightc{\circledC}2019 John Wiley & Sons, Ltd",
keywords = "Meshless, Cell-based Maximum Entropy, Large strain elastodynamics, Explicit timeintegration, Weak Kronecker-delta, Essential boundary conditions imposition",
author = "Mountris, {Konstantinos A.} and George Bourantas and Daniel Millan and Grand Joldes and Karol Miller and Esther Pueyo and Adam Wittek",
year = "2019",
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T1 - Cell-based Maximum Entropy Approximants for Three-Dimensional Domains

T2 - Application in Large Strain Elastodynamics using the Meshless Total Lagrangian Explicit Dynamics Method

AU - Mountris, Konstantinos A.

AU - Bourantas, George

AU - Millan, Daniel

AU - Joldes, Grand

AU - Miller, Karol

AU - Pueyo, Esther

AU - Wittek, Adam

PY - 2019/9/5

Y1 - 2019/9/5

N2 - We present the Cell-based Maximum Entropy (CME) approximants inE3space by constructing thesmooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation methodcombining the properties of the Maximum Entropy approximantsand the compact support of element-basedinterpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D)continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. Theaccuracy and efficiency of the method is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothnessof CME basis functions, the numerical stability in explicittime integration is preserved for large time step.The challenging task of essential boundary conditions imposition in non-interpolating meshless methods(e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essentialboundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scale elastodynamics in 3D. Copyrightc©2019 John Wiley & Sons, Ltd

AB - We present the Cell-based Maximum Entropy (CME) approximants inE3space by constructing thesmooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation methodcombining the properties of the Maximum Entropy approximantsand the compact support of element-basedinterpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D)continua using the well-established Meshless Total Lagrangian Explicit Dynamics (MTLED) method. Theaccuracy and efficiency of the method is assessed in several numerical examples in terms of computationaltime, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothnessof CME basis functions, the numerical stability in explicittime integration is preserved for large time step.The challenging task of essential boundary conditions imposition in non-interpolating meshless methods(e.g., Moving Least Squares) is eliminated in CME due to the weak Kronecker-delta property. The essentialboundary conditions are imposed directly, similar to the Finite Element Method. CME is proven a valuablealternative to other meshless and element-based methods for large-scale elastodynamics in 3D. Copyrightc©2019 John Wiley & Sons, Ltd

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JO - International Journal of Numerical Methods in Engineering

JF - International Journal of Numerical Methods in Engineering

SN - 0029-5981

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