Peridynamic shell membrane formulation

Peridynamics (PD) is a non-local continuum theory that enables failure prediction. It enables both crack initiation and propagation as well as crack branching. Also, it has been utilized to model simplified structures such as beams, plates and shells. In this study, a new peridynamic shell membrane formulation is presented. The equations of motion are obtained by using Euler-Lagrange equations. The bond constant is determined by comparing peridynamic and classical equations of motion for shell membranes for a special condition of peridynamic internal length parameter, horizon, approaching zero. Comparison of peridynamic results with analytical results for a benchmark problem confirms the validity of the present shell membrane formulation.