The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.

This paper investigates the characteristics of unstable behaviour and critical buckling load by joint rigidity of framed large spatial structures which are sensitive to initial conditions. To distinguish the stable from the unstable, a singular point on equilibrium path and a critical buckling level are computed by the eigenvalues and determinants of the tangential stiffness matrix. For the case study, a two-free node example and a folded plate typed long span example with 325 nodes are adopted, and these adopted examples' nonlinear analysis and unstable characteristics are analyzed. The numerical results in the case of the two-free node example indicate that as the influence of snap-through is bigger; that of bifurcation buckling is lower than that of the joint rigidity as the influence of snap-through is lower. Besides, when the rigidity decreases, the critical buckling load ratio increases. These results are similar to those of the folded-typed long span example. When the buckling load ratio is 0.6 or less, the rigidity greatly increases.

본 연구에서는 갤로핑/플러터와 웨이크 갤로핑과 같은 공력불안정현상을 이용한 에너지 수확 장치에 대한 적용가능성을 검토하였다. 이를 위해서, 작은 규모의 에너지 수확 장치를 설계 및 제작하였고, 이 장치들의 효율성과 효과를 증명하기 위한 일련의 실험을 수행하였다. 이러한 시험 결과로부터 공력불안전형상(갤로핑/플로터 및 웨이크 갤로핑)을 이용한 에너지 수확 시스템의 적용 가능성이 증명되었다.

트러스형 공간 구조물은 무주의 대공간을 덮을 수 있는 장점과 구조적 성질이 동일한 등가 연속체 쉘 로 치환하여도 비교적 정확한 해를 얻을 수 있다는 장점으로 인해 21세기 첨단 구조물의 한 장인 초대형 구조물 분야에 많이 활용되고 있으며, 효율적인 부재의 이용과 대량생산의 가능성으로 인해 많은 발전을 해 왔다. 그러나 이러한 쉘 형태의 공간 구조물은 구조 거동의 특성상 주로 구조안정문제가 구조설계에서 해결해야하는 핵심적인 기술력이 되며, 이를 어떻게 해결하여야 할 것인가의 문제는 아직도 많은 연구자들에게 난제로 남아 있다. 즉, 연속체 쉘 구조의 원리에서 긴 경간을 얇게 만들면, 뜀좌굴과 분기좌굴같은 불안정 거동이 나타나게 되며, 이러한 쉘형 구조 시스템에서 구조 불안정 문제의 특징은 초기 조건에 매우 민감하게 반응한다는 것이고, 이런 문제들은 수학적으로 비선형 문제에 귀착하게 된다. 따라서, 본 논문에서는 공간 프레임형 구조물의 불안정 현상을 살펴보기 위하여, 다양한 파라메타중 초기불완전량과 rise-span 비가 트러스 구조물의 불안정 현상에 미치는 영향을 알아보고자 하며, 이를 위해 1-자유절점 공간구조물, 2-자유절점 공간구조물, 다-자유절점 공간구조물을 예제로 채택하여 불안정 거동을 살펴보고자 한다.

The structure system that is discreterized by continuous shells is usually used to make a large space structures and these structures show the collapse mechanisms that are captured at over the limit load, and snap-through and bifurcation are most well known of it. For the collapse mechanism, rise-span ratio, element stiffness and load mode are main factor, which it give an effect to unstable behavior. Moreover, resist force of structure can be reduced by initial condition and initial imperfection significantly. In order to investigate the instability of shell structures, the finite deformation theory can be applied and it becomes a nonlinear mathematics in which use equation of tangential stiffness incrementally. With an initial imperfection, using simple example and Flow Truss Dome, the buckling characteristics of space truss is main purpose of this paper, and unstable behavior is studied by proposed the numerical method. Also, by using MIDAS, this research work analyzes displacements and inner forces as the design load of model, and the ratio of buckling load of design load is investigated.

The characteristics of structural behavior for a cable dome shows a strong nonlinearity and very sensitive by the initial imperfection. The instability phenomenon of Geiger-type cable dome structure is generated due to the in-plane twisting near the critical load level. In this study, therefore, the effect of bracing reinforcement resisting to the in-plane twisting is investigated for the Geiger-type model reinforced by bracing. The effect of initial imperfection is also studied because the structural instability phenomenon of shell-like structure is very sensitive according to the initial condition.

세계적으로 대공간 구조물의 건설은 점점 늘어나고 있으며, 이러한 증가 추세와 함께 붕괴 사고 또한 점차 늘어나고 있다. 보다 안전하고 경제적인 구조물의 구축을 위해서는 사고 및 붕괴의 원인이 정확히 규명되어야 한다. 따라서 이러한 규명을 위하여 대공간 구조물의 붕괴 메커니즘의 정확한 규명이 필요하며, 많은 연구자들에 의한 연구가 보고되고 있다. Step 하중 하에서의 동적 파괴 메커니즘은 비교적 많은 연구가 진행되어 왔으나, 주기성을 가진 동적 외력에 의한 파괴 메커니즘에 관한 연구는 거의 없는 실정이며, Step 하중하에서의 메커니즘과는 매우 다르리라 예상된다. 본 연구는 주기성을 가진 동적 외력에 의한 얕은 EP 쉘(Elliptic Paraboloidal Shell)의 동적 불안정 현상을 Fourier 스펙트럼을 이용하여 분석한다. 즉 1 자유도의 얕은 EP 쉘의 동적 좌굴 현상과 파라메트릭 공진 현상과의 상호 작용을 파악하기 위하여 비선형 응답의 연속 스펙트럼(runing spectrum)을 이용한다. 연구 결과, 동적 불안정 현상은 외력의 성질에 따라 크게 다른 메커니즘을 나타내는 것을 알 수 있다.

Long span structures like space-structures have instability phenomenon, jump buckling or bifurcation. And these instability phenomenon responds very sensitivity, depend on the initial condition. In this study, define the 1-degree of freedom space structure and when model has beating load, analysis critical load of model using 3D contour map for load, variable , displacement in the axial. The analysis results, when  is 1.0, is able to see the lowest critical load and the resonance phenomenon.

This study aims to apply homotopy method to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carring out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4).