Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions

Authors:
Kun Zhou;Qiang Du
Affiliations:
zhou@math.psu.edu and qdu@math.psu.edu;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

Citing 4
Cited 2

Finite element solution of boundary value problems: theory and computation

Finite element solution of boundary value problems: theory and computation
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Can the Nonlocal Characterization of Sobolev Spaces by Bourgain et al. Be Useful for Solving Variational Problems?

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A meshfree method based on the peridynamic model of solid mechanics

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Numerical Approximations for a Nonlocal Evolution Equation

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A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model

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Abstract

In this paper, we study the linear bond-based nonlocal peridynamic models with a particular focus on problems associated with nonstandard nonlocal displacement loading conditions. Both stationary and time-dependent problems are considered for a one-dimensional scalar equation defined on a finite bar and for a two-dimensional system defined on a square. The related peridynamic operators and associated functional spaces are analyzed. Applications to the numerical analysis of the finite-dimensional approximations to peridynamic models are also illustrated.