Analytical Solution of 1-Dimensional Peridynamic Equation of Motion

Peridynamics has been introduced to overcome limitations of classical continuum mechanics. Peridynamic equations of motion are in the form of integro-differential equations and analytical solutions of these equations are limited in the literature. In this study, a new analytical solution methodology for 1-dimensional peridynamic equation of motion is presented by utilising inverse Fourier transform. Analytical solutions for both static and dynamic conditions are obtained. Moreover, different boundary conditions including fixed-fixed and fixed-free are considered. Several numerical cases are demonstrated to show the capability of the presented methodology and peridynamic results are compared against results obtained from classical continuum mechanics. A very good agreement between these two different approaches is observed which shows the capability of the current approach.