In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end, and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.
- Euler-Lagrange equations