Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar

Weckner, Olaf and Emmrich, Etienne (2005) Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 6 (2). pp. 311-319. ISSN 1586-2070

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Abstract

In this paper, we develop an efficient numerical method based on Gauss-Hermite quadrature to calculate the one-dimensional dynamic response of a nonlocal, peridynamic bar composed of (inhomogeneous) linear material. The principal physical characteristic of the peridynamic theory is the presence of long-range forces leading to nonlinear dispersion relations while the principal mathematical characteristic is the presence of a stationary Barbashin operator in the integro-differential equation of motion. We calculate two examples corresponding to continuous and discontinuous, Riemann-like initial conditions. As the analytical solutions for these examples are known they serve as validation problems for the proposed numerical scheme.

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