# In Search of Lightweight Deployable Tensegrity Columns
## 4 Methods  
This article is based on computer simulations to qualitatively and quantitatively compare four tensegrity columns. All the models were built in the same manner.  
The FE analyses were carried out using SOFiStKi software (SOFiStKi AG, Germany, Version 12.01-27, Copyright 1996-2011, Licence: Faculty of Civil Engineering WUT). FEM [22,23] was used to statically analyze the final configurations of the structures--to find forces in the structural members and deflections of the columns, determine the load carrying capacity, etc. The calculations included self-stress and were based on the geometrically non-linear theory [24]. Self-equilibrated sets of forces were determined using the spectral analysis of stiffness matrices. The mesh in the analysis was natural and suitable for pin joined structures. The accuracy of the FEM model for geometrical nonlinear problems was validated and confirmed for tensegrity structures in previous papers by the authors [11,25]. The material properties in FE models correspond to the parameters specified in Section 3.  
The MBD analyses were carried out using MSC Adams software (MSC Software Adams View, Version: Adams 2019.2, Build: 2019.2.0-CL661333 on Jun 19, 2019, Address: 4675 MacArthur Court, Newport Beach, CA 92660). The detailed description of the model building method can be found in [17]. The movement during the deployment was defined as \(\Delta L=f(time)\), so there was a constant velocity of the chosen active cables, and all the other active cables lengths were calculated according to Tables 2-5. The choice of the constant-velocity cables showed no substantial effect on the global behavior of the structure during the preliminary model verification. The following preliminary assumptions were made for the simulations:  
1. The self-stress was calculated a priori for the defined height \(H=4\) m. This means that during the deployment, the self-stress values do not meet tensegrity equilibrium, and the structure is not a real tensegrity system.
2. The joints are assumed to be ball-and-socket joints working without friction. Since in this case, the friction would act as a damper for velocity changes, it is assumed that the worst case scenario is simulated, and the structure eigen-properties must assure stability during the deployment.
3. The cables are modeled as springs with rigidity, which corresponds to the steel cable rigidity.
4. Due to the fact that the cables consist of a cable part and a spring part connected in series, it is not possible to have a zero length in the simulations, and in some cases, this leads to the impossibility of achieving maximal compactness for storing.
5. The collisions between the struts are not analyzed assuming shaping the target structure in such a way to prevent this phenomenon. For instance, this can be achieved by doubling the struts so one goes into the other one or, in the case of the joints, by applying already developed solutions (e.g., as described in [13]).  
Figure 6: Octahedron column—designations.  
There are no additional supports (e.g., guides) assumed to help sustain the shape during the deployment.  
The method applied in this paper was validated by comparing the results obtained from MBD and FE simulations at various steps of the analysis. Initial self-stress values were applied in the Adams models; afterwards, the simulations were started, and the values of the internal forces in the structural elements were registered. Afterwards, three configurations of each structure were chosen, for which the models in SOFiSTiK were built, and these configurations were analyzed statically using FEM. In this way, the self-stress states were compared. The results obtained from both approaches were consistent, which proves the reliability of the proposed method.