An Euler-Bernoulli beam formulation in an ordinary state-based peridynamic framework

Every object in the world has a three-dimensional geometrical shape and it is usually possible to model structures in a three-dimensional fashion, although this approach can be computationally expensive. In order to reduce computational time, the three-dimensional geometry can be simplified as a beam, plate or shell type of structure depending on the geometry and loading. This simplification should also be accurately reflected in the formulation that is used for the analysis. In this study, such an approach is presented by developing an Euler-Bernoulli beam formulation within ordinary state-based peridynamic framework. The equation of motion is obtained by utilizing Euler-Lagrange equations. The accuracy of the formulation is validated by considering various benchmark problems subjected to different loading and displacement/rotation boundary conditions.