Characteristics of bifurcation and buckling load of space truss in consideration of initial imperfection and load mode

Abstract

Abstract:This study investigated characteristics of bifurcation and critical buckling load by shape imperfection of space truss, which were sensitive to initial conditions. The critical point and buckling load were computed by the analysis of the eigenvalues and determinants of the tangential stiffness matrix. The two-free-nodes example and star dome were selected for the case study in order to examine the nodal buckling and global buckling by the sensitivity to the eigen buckling mode and the analyses of the influence, and characteristics of the parameters as defined by the load ratio of the center node and surrounding node, as well as rise-span ratio were performed. The sensitivity to the imperfection of the initial shape of the two-free-nodes example, which occurs due to snapping at the critical point, resulted in bifurcation before the limit point due to the buckling mode, and the buckling load was reduced by the increase in the amount of imperfection. The two sensitive buckling patterns of the numerical model are established by investigating the displaced position of the free nodes, and the asymmetric eigenmode greatly influenced the behavior of the imperfection shape whether it was at limit point or bifurcation. Furthermore, the sensitive mode of the two-free-nodes example was similar to the in-extensional basis mechanism of a simplified model. The star dome, which was used to examine the influence among several nodes, indicated that the influence of nodal buckling was greater than that of global buckling as the rise-span ratio was higher. Besides, global buckling is occurred with reaching bifurcation point as the value of load ratio was higher, and the buckling load level was about 50%-70% of load level at limit point.

Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method

“…The maximum displacement is suddenly amplified at and does not vary in proportion to because of the effect of the geometrical nonlinearity. In addition, the rapidly changing maximum displacement as increases, between 1000 and 1100 kN, is expected as the critical point, and the at the point refers to the dynamic buckling load under a step excitation [ 1 , 14 ]. Figure 3 b shows the trajectory in the phase space to observe the attractor before and after dynamic buckling.…”

“…The trajectory when converges on the other centre in the limit cycle attractor, as shown in Figure 5 b. However, in this case, it is possible to have two points of the system converge to a limit set, and these fixed point attractors and trajectories in the phase space are sensitive to the initial condition [ 14 ].…”

“…Five ratios of were used: 0.05, 0.1, 0.15, 0.2 and 0.25. Here, the static critical buckling load level is shown in Table 1 , and the dynamic buckling load was determined using the Budiansky-Roth criterion [ 1 , 14 ].…”

“…Kassimali and Bidhendi [ 11 ] investigated the stability problem based on an Eulerian formulation that considered arbitrarily large displacements, and Tada and Suito [ 12 ] examined the static and dynamic post-buckling of discrete compressive members using a vibration model. Kim et al [ 13 ] considered damping in their study of dynamic buckling of shallow trusses and explained that the structure was more sensitive to indirect snapping than direct snapping [ 14 , 15 ]. Although there are reduction techniques for dynamic analysis [ 16 , 17 ], there are few studies on analytical approaches or the nonlinear dynamic stability of space trusses.…”

Application of multistage homotopy perturbation method to the nonlinear space truss model

“…This figure indicates that the shallow DFN model is very sensitive to initial condition. Generally, DFN model is well known as shallow space truss dome which is sensitive to the initial condition (Shon et al, 2013).…”