Analytical solution of 1-dimensional peridynamic equation of motion

Zhenghao Yang, Chien-Ching Ma, Erkan Oterkus, Selda Oterkus, Konstantin Naumenko

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
JournalJournal of Peridynamics and Nonlocal Modeling
Publication statusAccepted/In press - 15 Aug 2022


  • peridynamics
  • non-local
  • analytical
  • one-dimensional


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