Study of three-dimensional Euler-Bernoulli beam structures using element-based peridynamic model

An element-based peridynamic (EBPD) model is developed to represent the Euler-Bernoulli beam. The force density is described by the two-node beam elements with three displacement and three rotation freedom degrees. The dynamic and static problems of the EBPD beam model are derived from Lagrangian formalism and variation principle, respectively. The Newmark and Gauss elimination methods are used to solve dynamic and static problems. The damage criterion expressed by the critical strain energy density is extended to the EBPD beam. Moreover, two different schemes of boundary conditions are discussed. Finally, various benchmark cases subjected to different loading and boundary conditions are used to validate the proposed EBPD beam model.

Automated summary

An element-based peridynamic (EBPD) model is developed for the representation of the Euler-Bernoulli beam, with dynamic and static problems derived using Lagrangian formalism and variation principle. The Newmark and Gauss elimination methods are applied for solving these problems, while also extending the damage criterion to the EBPD beam and discussing different boundary condition schemes. Various benchmark cases are used to validate the proposed EBPD beam model under different loading and boundary conditions.