Lie Symmetry Analysis and Conservation Laws of the Axially Loaded Euler Beam

By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of beams formulated. After introducing infinitesimal transformations, determining equations proposed via point transformations acting on original equations. generators symmetries systems presented with Maple. vector fields given to span subalgebra systems. Conserved vectors derived by using two methods, namely, multipliers method and Noether’s theorem. Noether conserved quantities obtained structure equation, satisfied gauge functions. fluxes conservation laws could also be multipliers. relations between them discussed. Furthermore, transformed into ODEs exact explicit provided.