Peridynamic Solutions for Timoshenko Beams

E. Thomas Moyer, Michael J. Miraglia

Naval Surface Warfare Center/Carderock Division, W. Bethesda, USA.

DOI: 10.4236/eng.2014.66034                

Abstract

Peridynamics is a recently developed formulation for continuum mechanics which describes material deformation using a nonlocal approach. Unlike Classical Continuum Mechanics (CCM) where the conservation equations are cast into partial differential equations, Peridynamics describes the deformation in terms of integro-differential equations. Additionally, peridynamics permits a natural length scale that is absent in CCM. This facilitates the modeling of complex material behavior and fracture which is not dependent on the numerical discretization length scale. In this paper, we develop a Peridynamic formulation for a Timoshenko beam. Full details and numerical examples are presented for both bending and axial behavior. While the development in this paper is limited to elastic, infinitesimal deformations, the approach can be extended to finite inelastic deformations.

Keywords

Peridynamics, Timoshenko Beam, Beam Bending, Dynamic Deformation

Conflicts of Interest

The authors declare no conflicts of interest.

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