Group Invariant Solutions of the Two-Dimensional Elastodynamics Problem in the Polar Coordinate System

Abstract

Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method. In the polar coordinate system, three group invariant solutions are constructed by the invariants of the Lie group, which are admitted by the governing equations for the two-dimensional elastodynamics problem. The graphical figures of the group invariant solutions are presented, and the physical meanings of the group invariant solutions are expounded in some cases.