Stability Analysis Method of Flat Rod Systems, Based on Forces Approximations

Abstract

AbstractThe stability problems solution of plane rod systems by the finite element method based on the stresses is presented. The proposed method is based on a combination of the additional energy functional and the possible displacements principle. The algebraic equilibrium equations are included in the functional using Lagrange multipliers, which are the displacements of nodes. To solve stability problems, the functional considering the additional energy from longitudinal deformations arising from the bending of the rods. The buckling shape over the finite element region is approximated by a linear function. Two variants of internal forces approximations in the finite element length are considered: linear and piecewise constant. On the example of straight rods stability analysis, a circular arch, and a two-story frame for various finite element meshes, it is shown that the use of piecewise constant approximations of internal forces allows one to obtain the lower boundary of the critical forces. When using linear approximations of internal forces, the solution converges to the critical forces exact value from above and gives an upper bound of critical forces.KeywordsStabilityRod systemForces approximationsFunctional