Modeling of peridynamic beams and shells with transverse shear effect via interpolation method

Abstract

Peridynamics is a nonlocal theory which can easily handle discontinuities such as cracks, while it is computationally more expensive compared with finite element method (FEM). Beams and shells, as the main units of structural idealization, can tremendously improve the computational efficiency for complex structures. This study presents new peridynamic (PD) beam and shell models with the effect of transverse shear deformation based on the micro-beam bond and the Timoshenko beam theory. Interpolation method is used for describing axial, torsional, bending and transverse shear deformations as well as the corresponding strain energy densities of the micro-beam bond. The micro moduli for PD beam and shell models can be solved spontaneously. The deflections of the PD models for thin/thick beams and shells are captured accurately due to the high-order relationships between the transverse forces/bending moments and the deflections/rotational angles of the micro-beam bond. Also, no restrictions are needed on the material parameters in the PD models. The simulation results prove the high precision of the presented PD beam and shell models.