Symmetries and Nonlocal Continuum Mechanics
Abstract:
In this study the symmetry group properties of the one-dimensional elastodynamics problem in nonlocal continuum
mechanics is discussed by using an approach developed for symmetry group analysis of integro-differential equations with
general form. This approach is based on the modification of the invariance criterion of the differential equations, which
include nonlocal variables and integro-differential operators. Lie point symmetries of the nonlocal continuum mechanics
equation are obtained based on solving nonlocal determining equations by using a new approach. The symmetry groups for
different types of kernel function and the free term including the classical linear elasticity case are presented.