Quality analysis of nonlinear elasticity theory for the stability problems of planar laminated curved beams. Problem statement

The one-dimensional equations that describe the geometrically nonlinear deformation with arbitrary displacements and small strains are constructed for the planar laminated curved beams based on the Timoshenko model taking into account transverse compression. The equations are based on the relations of the classical nonlinear theory of elasticity for the case of realizing plane stressed state in a beam and also on the similar relations previously proposed in the consistent variant. Based on the equations constructed, we form the linearized equations of the neutral equilibrium of beams that enables investigating all possible buckling modes under the action of conservative forces and a stationary temperature field.