Closed-form series solutions to peridynamic rod equations: Influence of kernel function

Authors

  • Konstantin Naumenko Otto von Guericke University Magdeburg, Institute of Mechanics, 39106 Magdeburg, Germany
  • Zhenghoa Yang National Taiwan University, Department of Mechanical Engineering, 10617 Taipei, Taiwan
  • Chien-Ching Ma National Taiwan University, Department of Mechanical Engineering, 10617 Taipei, Taiwan
  • Yang Chen Heilongjiang Academy of Forestry Design and Research, Department of Environmental Engineering Planning and Design, Harbin, China

DOI:

https://doi.org/10.24352/UB.OVGU-2023-062

Keywords:

Peridynamics, Rod, Kernel function, Closed-form solution

Abstract

Peridynamics is a generalized continuum theory that takes into account long range internal force/moment interactions.
The aim of this paper is to derive closed form analytical solutions for peridynamic rod equations with fixed-fixed and fixed-free
boundary conditions. A family of kernel functions is introduced to analyze the influence on the results for rods under distributed
static load and free vibrations for different initial conditions. To validate the derived solutions, nonlocal results are compared
against classical results for different boundary conditions and horizon sizes. One can observe that when the horizon size approaches
zero, the results according the non-local and local theories converge to each other. Introduced kernels indeed play different roles in
both statics and dynamics. In particular, the Gauss type kernel function gives the results which are closest to the classical solutions.

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Published

2023-11-16 — Updated on 2023-11-21

How to Cite

Naumenko, K. (2023) “Closed-form series solutions to peridynamic rod equations: Influence of kernel function”, Technische Mechanik - European Journal of Engineering Mechanics, 43(2), pp. 259–270. doi: 10.24352/UB.OVGU-2023-062.

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