Out-of-plane elastic waves in 2D models of solids: a case study for a nonlocal discretization scheme with reduced numerical dispersion
type: Item
instance of: scholarly article
title: Out-of-plane elastic waves in 2D models of solids: a case study for a nonlocal discretization scheme with reduced numerical dispersion
zbMATH Open document ID: 1394.74070
DOI: 10.1155/2015/584081
author: Adam Martowicz
author: Massimo Ruzzene
author: W. J. Staszewski
author: J. J. Rimoli
author: T. Uhl
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: The paper addresses the problem of numerical dispersion in simulations of wave propagation in solids. This characteristic of numerical models results from both spatial discretization and temporal discretization applied to carry out transient analyses. A denser mesh of degrees of freedom could be a straightforward solution to mitigate numerical dispersion, since it provides more advantageous relation between the model length scale and considered wavelengths. However, this approach also leads to higher computational effort. An alternative approach is the application of nonlocal discretization schemes, which employ a relatively sparse spatial distribution of nodes. Numerical analysis carried out to study the propagation of elastic waves in isotropic solid materials is demonstrated. Fourier-based nonlocal discretization for continuum mechanics is introduced for a two-dimensional model undergoing out-of-plane wave propagation. The results show gradual increase of the effectiveness of this approach while expanding the region of nonlocal interactions in the numerical model. A challenging case of high ratio between the model length scale and wavelength is investigated to present capability of the proposed approach. The elaborated discretization method also provides the perspective of accurate representation of any arbitrarily shaped dispersion relation based on physical properties of modelled materials.
Mathematics Subject Classification ID: 74J15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 6926709
Wikidata QID: Q59119466
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/584081
OpenAlex ID: W2172925002
cites work: Optimized weighted essentially nonoscillatory third-order schemes for hyperbolic conservation laws
cites work: Peridynamics as an Upscaling of Molecular Dynamics
cites work: Numerical treatment of a modified MacCormack scheme in a nondimensional form of the water quality models in a nonuniform flow stream
cites work: Explicit high accuracy maximum resolution dispersion relation preserving schemes for computational aeroacoustics
cites work: Classroom Note:Calculation of Weights in Finite Difference Formulas
cites work: Staggered-grid finite difference method with variable-order accuracy for porous media
cites work: Dispersion-relation-preserving finite differene schemes for computational acoustics
cites work: A high order homogenization model for transient dynamics of heterogeneous media including micro-inertia effects
cites work: A dispersive nonlocal model for shear wave propagation in laminated composites with periodic structures
cites work: Time-splitting procedures for the numerical solution of the 2D advection-diffusion equation
cites work: Q3806014
cites work: Linear theory of nonlocal elasticity and dispersion of plane waves
description: scientific article; zbMATH DE number 6926709