Analytical solution of 1-dimensional peridynamic equation of motion

Yang, Zhenghao and Ma, Chien-Ching and Oterkus, Erkan and Oterkus, Selda and Naumenko, Konstantin (2023) Analytical solution of 1-dimensional peridynamic equation of motion. Journal of Peridynamics and Nonlocal Modeling, 5. 356–374. ISSN 2522-8978 (https://doi.org/10.1007/s42102-022-00086-1)

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Abstract

Peridynamics has been introduced to overcome limitations of classical continuum mechanics. Peridynamic equations of motion are in the form of integro-differential equations and analytical solutions of these equations are limited in the literature. In this study, a new analytical solution methodology for 1-Dimensional peridynamic equation of motion is presented by utilising inverse Fourier Transform. Analytical solutions for both static and dynamic conditions are obtained. Moreover, different boundary conditions including fixedfixed and fixed-free are considered. Several numerical cases are demonstrated to show the capability of the presented methodology and peridynamic results are compared against results obtained from classical continuum mechanics. A very good agreement between these two different approaches is observed which shows the capability of the current approach.

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