A peridynamic formulation for planar arbitrarily curved beams with Timoshenko-Ehrenfest beam model

In this study, a peridynamic formulation is proposed for analysis of planar arbitrarily curved beams. Assumptions of Timoshenko-Ehrenfest beam model are considered such that linear kinematic relations are described by displacements of the beam axis and rotation of the cross-section. Equilibrium conditions and boundary conditions are derived by means of the principle of virtual work. Then, peridynamic functions are constructed, and incorporated with equilibrium conditions to develop a peridynamic formulation. Several examples are exhibited to examine the performance of the proposed formulation in some regards, i.e., numerical accuracy, convergence properties, and locking effects. It is delineated that the proposed formulation provides a good level of precision for the analysis of relatively thick beams. However, membrane and shear locking effects are present in the analysis of slender beams, and peridynamic functions of higher polynomial degree can be used to mitigate these unfavorable effects.