Elastic Critical Axial Force for the Torsional-Flexural Buckling of Thin-Walled Metal Members: An Approximate Method

Thin-walled centrically compressed members with non-symmetrical or mono-symmetrical cross-sections can buckle in a torsional-flexural buckling mode. Vlasov developed a system of governing differential equations of the stability of such member cases. Solving these coupled equations in an analytic way is only possible in simple cases. Therefore, Goľdenvejzer introduced an approximate method for the solution of this system to calculate the critical axial force of torsional-flexural buckling. Moreover, this can also be used in cases of members with various boundary conditions in bending and torsion. This approximate method for the calculation of critical force has been adopted into norms. Nowadays, we can also solve governing differential equations by numerical methods, such as the finite element method (FEM). Therefore, in this paper, the results of the approximate method and the FEM were compared to each other, while considering the FEM as a reference method. This comparison shows any discrepancies of the approximate method. Attention was also paid to when and why discrepancies occur. The approximate method can be used in practice by considering some simplifications, which ensure safe results.

Analysis of Relationship between Lateral Stability and Dynamic Characteristic of Continuous Welded Rail Track

The axial buckling threshold force of continuous welded rail (CWR) depends on lateral stability of railway track. The conventional CWR buckling models are based on track static parameters and behavior. In this paper, a dynamic finite element model for investigating the relationship between the rail nature frequencies and the critical buckling axial force of CWR track is presented. This model consists of rails, sleepers and foundation, and covers factors of interest such as track curvature, supporting distance between adjoining sleepers. With the new dynamic model, numerical computations and analyses are performed. The correlations among the critical axial force of rail, the lateral stability and the nature frequencies of CWR track are studied. The computational results of the new dynamic model show a great agreement with the field testing results.

Effect of Different Winding Angle of Fiberglass on Parametric Stability of Structurally Anisotropic Cylindrical Axisymmetric Shells

In this paper, the dynamical stability analysis of anisotropic cylindrical shells under uniformly distributed periodic extensional axial force is presented, while the winding angle varies. Fiberglass reinforced plastic is considered as a homogeneous solid anisotropic material. The shell’s elastic properties depend on the winding angle of fiberglass. The effect of the winding angle on the critical axial force is investigated. The intervals of winding angles at which the parametrically unstable vibration happen are determined

Stability and Natural Characteristics of a Supported Beam

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

Research on Vibration and Instability of the Double-Span Beam Base on Transfer Matrix

The vibration and instability of a beam which is Double-span Euler Beam with axial force is studied by transfer matrix method. The transfer matrix of transverse free vibration and axial compression of the beam is derived. Then based on the assembled transferring matrix, the effect of the position of intermediate support on the natural frequencies and Euler critical axial force of the beam is discussed, which offered a useful method to start research of vibration of complicated framework.

CONTINUUM MODEL FOR STABILITY ANALYSIS OF CARBON NANOTUBES UNDER INITIAL BEND

Stability analysis of carbon nanotubes (CNT) under initial bend is conducted using continuum elastic beam models for both single wall nanotube (SWNT) and double wall nanotube (DWNT). A discrete beam model is proposed for simulating the mechanism of kink instability, a local buckling phenomenon, of CNTs. Theoretical analysis of the critical axial load for kink instability is carried out with the elastic beam model. Based on the theoretical analysis, the size effect of CNTs on the critical axial force is studied. By setting the initial bend to be zero, the current model can be used to predict the buckling load of a straight CNT as well.