Some analytical solutions to peridynamic beam equations

Abstract Peridynamics (PD) has been introduced to account for long range internal force/moment interactions and extend the classical continuum mechanics (CCM). PD equations of motion are derived in form integro‐differential only few analytical solutions these presented literature. The aim this paper is present beam both static dynamic loading conditions. Applying trigonometric series, general deflection function derived. For several examples case including simply supported cantilever beam, coefficients series a closed form. case, solution applying variable separation with respect time axial coordinate. Several numerical cases illustrate solutions. Furthermore, results compared against obtained from theory (CBT). A very good agreement between two different approaches observed small horizon sizes (HSs), which shows capability current approach.