تجزیه و تحلیل حساسیت از سیستم های tensegrity به علت کاهش عضو

Tensegrity systems typically contain a large number of members, and possess a high degree of statically indeterminacy. However, a number of members are critical to system integrity and serious strength reductions can be produced by loss of any of them. Furthermore, when these members are lost suddenly, their forces are shed in a dynamic manner into the structure, causing more severe damage. This paper presents a numerical study on the sensitivity of tensegrity systems to both gradual and sudden member losses, taking into account both geometric and material nonlinearities. Also, other parameters, considered in this work, include the self-stress level, slenderness ratios of struts and damping ratios. The conclusions, drawn from this study, can in turn, lead to the suggestion of some guidelines for the design of such systems.

Tensegrity systems are innovative systems in the spatial structures field and refer to a special type of tensile structures that can offer an alternative to traditional space structures. A tensegrity structure is defined as “a system in a stable self equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components” [1]. These systems exist under pre-stressed (self-stressed) configurations. The initial stresses contribute to the system’s rigidity and stability. Tensegrity systems have specific advantages that merit their consideration for use as engineering structures. First, most tensegrity structures are lightweight structures, making them suitable for various space applications [2]. Second, their members can serve simultaneously as sensors, actuators and load carrying elements. Therefore, having incorporated sensors and actuators, tensegrity structures have considerable promise as smart structures [2]. Third, for using as a mechanism in the folding process, the lengths of the tension links (cables) can be easily adjusted. The folding and deployment capabilities of these systems will allow the use of tensegrity systems as deployable space structures with promising future aerospace applications. Fourth, tensegrity systems are capable of large displacement, belonging to the class of flexible structures [3]. There are also several disadvantages that must be overcome to make tensegrity structures useful. First, most tensegrity systems are not conventionally rigid; they usually exhibit an infinitesimal mechanism and must be pre-stressed to resist deformation in the direction of the mechanism 4. and 5.. Second, tensegrity systems generally tend to be susceptible to vibration because of the infinitesimal mechanism [5]. Third, tensegrity systems only exist under specific geometries. The nodal positions cannot be specified arbitrarily for a tensegrity structure. Thus, some positions cannot be achieved with a tensegrity structure [6]. Tensegrity systems are mainly statically and kinematically indeterminate systems. They typically contain a large number of members, and possess a high degree of statically indeterminacy. The stability analyses performed on these systems have indicated that despite of high redundancy, buckling of a strut (or set of struts) or rupture of a cable may cause a progressive collapse to occur 7. and 8.. In fact, in the case of local collapse in which strut snap-through or cable rupture is occurred, a large amount of kinetic energy is released at a local region of the structure, which can cause the overall collapse of the system. There are some researches regarding the effect of member loss on the ordinary space trusses, studied by many researchers as Hanaor [9], Murtha-Smith [10], El-sheikh [11] and Malla [12]. It was illustrated that a loss of a member in a critical truss area was more serious than a loss in another area. Since this phenomenon was rapid, dynamic effects could develop, leading to a further damage in the space truss. Ben Kahla and Moussa [13] have performed a numerical investigation into the effect of sudden rupture of a cable component in a beam-like tensegrity system, without applying external loads, using nonlinear dynamic time history analysis. Oppenheim and Williams [5] examined the dynamic behavior of a simple elastic tensegrity structure. It is confirmed, analytically and numerically, that the energy decay of such a system is slower than that of a linear-damped system. Abedi and Shekastehband [7] have studied the stability behavior of continuous strut square grids with node-to-node connection of simplexes under static loading conditions, taking into account the effects of post-buckling response of the struts and post-yield response of the cables. Nevertheless, so far no study was conducted to confirm and examine the effect of member loss on the nonlinear behavior of double layer tensegrity systems under external loads. In tensegrity systems, a number of members are critical, with the loss of any of them likely to produce serious strength reductions. When a member is lost suddenly in tensegrity system which is under load, e.g. due to the failure of a faulty connection, the energy stored in the system is released and this induces a state of transient vibration about the new equilibrium position. The members of the system will therefore experience transient forces and displacements greater than the values derived from static analysis, and consequently, there is the possibility that these dynamic forces may cause buckling of a struts or rupture of a cable. Failure of a second member will cause further vibration resulting in progressive collapse of other members before a new equilibrium state is reached. It is, therefore, important to account for the dynamic effects caused by the member loss in the evaluation of response of these systems in the cases that member loss occurs. In practice, members of a tensegrity system may be lost due to a poor member node connection. In fact, having one or more faulty connections in a structure, containing hundreds of connections, is a realistic possibility. The existence of geometric imperfections (e.g. lack of fit) may cause this to occur prematurely under a small portion of the total design load. In such a case, it can be argued that this member has in effect been lost [11]. Generally, progressive collapse lasts for a short duration. Therefore, it is impossible to prevent progressive collapse in a structure once it occurs. This increases the importance of understanding response of the structure during member loss. One of the most effective methods to assess the vulnerability of a structure to progressive collapse is the alternate path analysis method. In this method, the defected structure is analyzed at specified load level (e.g. design load level) to investigate the performance of the structure under distributed loads due to member loss. Then, in order to avoid the propagation of local collapse, the structure is designed in a way to sustain local collapse (i.e. member loss) and produce a new path to transmit the loads [10]. In the present study, a numerical investigation into the static and dynamic response of tensegrity systems in the event of gradual and sudden member loss was carried out. The study includes progressive collapse in two configurations. The response and characteristic of the studied structures include load- deflection response in static analysis and displacement–time history of the configurations in the dynamic analyses. The aims of the present study are as follows: • Identifying the critical members by assessing vulnerability of tensegrity systems upon removing them; • Determination of the collapse mechanisms of tensegrity systems due to gradual and sudden member loss; • Evaluation of the effects of various parameters as self-stress level, slenderness ratio of struts and damping ratio on the progressive collapse of these systems.

The study reported herein is concerned with the investigation into the effects of member loss on the vulnerability of tensegrity systems. Two tensegrity square grid configurations, with regular and irregular layout of struts, were studied. The patterns of the connections were node-to-node. Configuration 1 was geometrically rigid containing no infinitesimal mechanisms, whereas configuration 2 was geometrically flexible containing several infinitesimal mechanisms. The effects of the self-stress level, slenderness ratios of struts and damping ratios on the vibration behavior of tensegrity systems due to gradual and sudden member loss were investigated. The gradual member loss of these tensegrity systems resulted often in local collapse due to slacking of cables (mechanism No. 1) and combination of slacking of cables and local collapse with dynamic snap-through (mechanism No. 2). Three vibration behaviors due to the sudden member loss were determined as oscillatory behavior, partial progressive collapse and full progressive collapse. The results of this study are used to obtain certain conclusions regarding the sensitivity of tensegrity systems to member loss. Strictly speaking, the scope of the conclusions is limited to the configurations considered for the analysis. However, it is likely that the conclusions are of more general applicability. 1. Although a nonlinear static collapse analysis which predicts that a damaged tensegrity system should be safe and can sustain additional load, it was illustrated that in several cases cannot provide a correct and realistic picture of the behavior of the damaged tensegrity system. It was observed that using a static approach would lead to a significant overestimate of the load carrying capacity of the structure. 2. It was shown that gradual member loss can cause reduction of strength up to 36% and 41.74% in configuration 1 with self-stress level=S and View the MathML source1.2S, respectively. Lower cables and struts were the most critical members. These amounts for configuration 2, due to gradual member loss, were 30.82% and 36.82% with self-stress level=S and View the MathML source1.2S, respectively. In configuration 2, most of the critical members belonged to struts. In both configurations, gradual loss of an edge member produced a limited reduction in the strength of the systems (almost below 10%). 3. In configuration 1, the sudden loss of critical members (located at mid-span or close to that) at 60% ultimate load level caused the system to experience partial or full progressive collapse. However, in configuration 2, because of the flexibility of the system, often oscillatory behavior and partial progressive collapse were observed. According to the results, with high self-stress level, the sensitivity of tensegrity systems to sudden loss of edge members is more than that of mid-span members, and in several cases, the oscillatory behavior was changed to partial or full progressive collapse. 4. In determining the effect of sudden member loss on the behavior of tensegrity systems, damping ratios are the most significant parameters. According to the results, in most cases, by decreasing damping ratios from 1.5% and 2.5% to low amounts, the oscillatory behavior was changed to partial or full progressive collapse. 5. In order to avoid the propagation of local collapse upon sudden loss of a critical member in tensegrity systems, it is necessary to perform alternate path analyses by which the critical members are identified and a new path for transmitting the loads is found. In addition, special attention must be paid in the fabrication and erection of critical members.