Peridynamic formulation for Timoshenko beam

It is common to encounter structures with complex geometries including aerospace and ship structures. Moreover, in these structures one dimension can be either much smaller or bigger than other two dimensions. In such cases, special formulations were developed such as beam, plate and shell formulations. These formulations are available both in classical and non-classical frameworks. In this study, a new peridynamic formulation is presented for Timoshenko beams. Peridynamic equations are obtained by using Euler-Lagrange equations and Taylor's expansion. To validate the newly developed peridynamic formulation, a Timoshenko beam subjected to central point load under simply supported, clamped and mixed (clamped-simply supported) boundary conditions is considered. Peridynamic results are compared against finite element analysis solutions and a very good agreement is observed between the two solutions.