Refined finite element of rods for stability calculation

The article deals with the application of a rod finite element with five degrees of freedom in a node to solve problems of stability of planar rod systems. In the presented finite element, additional degrees of freedom are introduced in the nodes in the form of curvature and axial deformation. Additional degrees of freedom provide a higher degree of approximation of displacements and deformations along the length of the finite element, which can be useful for calculation of rods with variable rigidity, as well as for solving geometrically nonlinear problems and stability problems. In this paper the elements of stiffness matrix and the elements of geometric matrix of the finite element are obtained. The results of the calculation of straight rods and frames under various conditions of support and various loads are presented. A comparison is made with the results of calculations using a classic finite element with three degrees of freedom. It is shown that the introduction of additional degrees of freedom at the nodes, in the form of the curvature of the axis and longitudinal deformation, makes it possible in a few cases to more accurately determine the value of the critical load. In this case, the system has more degrees of freedom, so the approximation of the forms of stability loss is more accurate.