EVALUATION OF THE BUCKLING OF FRAME STRUCTURES UNDER DYNAMIC LOADING, TAKING INTO ACCOUNT THE INERTIAL COMPONENTS OF INTERNAL FORCES
Abstract
An approach to directly assessing the stability of a flat frame structure under unsteady dynamic loading is proposed and numerically investigated. In contrast to the traditional choice of a single static or quasi-static calculation case, at each step of integrating the equation of motion, an instantaneous stability problem is formed, taking into account the inertial components on the left-hand side of the operator equation and in the local forces that determine the geometric rigidity of the calculation model. The contribution of longitudinal and transverse forces, as well as nodal bending moments in resisting the loss of stability of beam elements of the Timoshenko model, is considered together. The method is implemented in the author's finite element program in Python and compared with the nonlinear quasi-static calculation in the Simulia Abaqus/Standard PC environment using the Riks method (Static, Riks). The buckling resistance of the load-bearing frame structure of an industrial building was studied. Its finite element model includes 246 nodes and 369 finite elements. The equation of motion is solved in the time interval 0 – 129.99 sec with a step of 0.01 sec. Analysis of the entire time history showed the presence of single spectral emissions; after checking the temporal stability of the eigenvalues, the physical minimum of the stability margin factor Λmin (SMF) was established at step 7913 (time t = 79.13 s, Λmin = 25.10992). Additionally, the multimode event at step 4138 and time slices selected based on the maximum displacements of nodes in hazardous areas are considered. For two slices generated using the same exact method, SIMULIA Abaqus confirmed the same ranking: the critical value of the load proportionality factor (LPF) obtained using the Ricks method is 48.21736 for t = 41.38 s and 44.42943 for t = 79.13 s. It is shown that the absolute values of the direct SMF and LPF are not identical due to the difference in the formulations of the problem being solved, but the consistency of the dangerous moment in time confirms the diagnostic value of the proposed method