In-plane dynamic buckling of duoskelion beam-like structures: discrete modeling and numerical results

In this contribution, a previously introduced discrete model for studying the statics of duoskelion beam-like structures is extended to dynamics. The results of numerical simulations performed using such an extended model are reported to discuss the in-plane dynamic buckling of duoskelion structures under different loading and kinematic boundary conditions. The core instrument of the analysis is a discrete beam element, which, in addition to flexure, also accounts for extension and shearing deformations. Working in the setting of dynamics, inertial contributions are taken into account as well. A stepwise time integration scheme is employed to reconstruct the complete trajectory of the system, namely before and after buckling. It is concluded that the duoskelion structure exhibits exotic features compared with classical beam-like structures modeled at macro-scale by Euler–Bernoulli’s model.

Mechanical Modeling and General Analytical Solution for the Dynamic Buckling of Plane Structures Using a Beam-Column Element with Varying End Restraints

The stability of structures is an important aspect that the designer must pay particular attention to in order to ensure safety against collapse. This investigation is concerned with analytical and numerical analyses of the dynamic buckling of plane structures. A rigorous mechanical model is proposed, consisting of a beam-column element with nodal ends possessing two rotational springs of rigidities acting in parallel with the bending stiffness of the beam-column. The model is first analyzed with respect to the dynamic behavior by investigating the influence of the variation in the stiffness of the nodal springs on the fundamental frequency of the proposed mechanical model. Compression axial loading is applied to the beam-column in order to study the nonlinear dynamic behavior by introducing buckling. This novel approach is used to highlight the interaction between the fundamental frequency and the critical buckling load. Simple examples are treated using the approach and the results are compared with those obtained from a global analysis. The results revealed that it is possible to reproduce the stability analysis of a global structure by simply analyzing a target element, taking into account all elements adjacent to it with less than 1% error on the results.

DYNAMIC BEHAVIOR OF REINFORCED CONCRETE COLUMN UNDER ACCIDENTAL IMPACT

The analysis of scientific literature shows that to date, the physical parameters of the deformation of reinforced concrete bar structures during their dynamic buckling and the influence of the dissipative properties of the structural system on this process remain insufficiently studied. In this regard, the paper proposes an analytical solution to the problem of dynamic buckling of a reinforced concrete column when it is loaded with an impact load, taking into account the presence of initial geometric and (or) physical imperfections and damping properties of the system, as well as an analysis and assessment of the column deformationparameters based on the obtained analytical solution. An expression for the dynamic deflection of a bar element under its axial loading with a high-speed shock load, taking into account damping, is obtained in an analytical form. For practical calculations in a quasi-static formulation, the paper proposes an expression for the dynamic factor kd of bar structures under axial shock load. A numerical example of calculating a reinforced concrete column using the obtained analytical expressions with and without damping is considered. It was found that the maximum deflection of the elastic axis of the column under high-speed loading was achieved at t = 0.04 s. In this case, the total dynamic deflection taking into account damping was 4.8% less than the deviation without taking into account damping and 1.18 times more than the corresponding static value.