Geometrical Nonlinear Analysis of Tensegrity Based on a Co-Rotational Method

Abstract

Tensegrities are structures whose integrity is based on a balance between tension and compression. A numerical procedure is presented for the geometrical nonlinear analysis of tensegrity structures. This approach is based on a co-rotational method where the major component of geometrical non-linearity is treated by a co-rotational filter. This is achieved by separating rigid body motions from deformational displacements. The outcomes evince that the efficiency of the co-rotational approach is considerably greater than those using total Lagrangian and updated Lagrangian formulations for space rod elements, which have more rigid body movement modes than deformational modes. Numerical examples illustrate that the displacements of tensegrity systems depend on the applied force density coefficient and external loading values. Furthermore, in the analysis of tensegrity structures, constraints such as the yield strength of all elements and zero stiffness of string elements becoming slack at any equilibrium configuration must be allowed for.

A shape memory alloy rod element based on the co-rotational formulation for nonlinear static analysis of tensegrity structures

“…The local stress, transformation strain, and consistent tangent module obtained from the above procedure can now be used in the CR approach. The CR formulation for the 3D rod element has already been developed by Crisfield (1990), Faroughi and Lee (2014), and Faroughi et al (2015). The method is briefly explained in this section.…”

“…The CR approach is based on the idea of separating the rigid body motions from the purely deformational motions and is particularly useful in problems with large displacements or rotations, but with small strains. For a space rod element with three translational and two rotational rigid body modes, and only one axial deformational mode, the CR approach is extremely efficient because existing high-performance linear elements can be reused as core elements in the geometrically nonlinear context, after large rigid body motions have been isolated (Eriksson and Faroughi, 2013; Faroughi and Lee, 2014; Felippa and Haugen, 2005; Nour-Omid and Rankin, 1991). However, the main advantage of the CR formulation in SMA applications is its capability to separate the material nonlinearity from the geometrical nonlinearity (Battini and Pacoste, 2006).…”

“…The nonlinear analysis of tensegrity structures is still a challenge, because tensegrities are both kinematically and statically indeterminate (Tran and Lee, 2011). Many researchers have studied the nonlinear static analysis of tensegrity structures using different formulations, such as the total and updated Lagrangian (Ben Kahla and Kebiche, 2000; Kebiche et al, 1999) and the CR approaches (Faroughi and Lee, 2014). In all of the cited references, the material of the tensegrity structure is linear and elastic.…”

“…In this article, the three-dimensional (3D) rod element–based CR formulation developed by Faroughi and Lee (2014) is considered, together with a small strain SMA model (Auricchio and Petrini, 2002; Souza et al, 1998) that accounts for both the pseudo-elastic and the shape memory effects. Only one dimension of the 3D thermo-mechanical SMA model, proposed by Souza et al (1998) and modified by Auricchio and Petrini (2002), is used.…”

Parametric Analysis of Tensegrity Plate-Like Structures: Part 1—Qualitative Analysis

“…Tensegrity plates composed of Quartex modules were considered, among others, by Wang and Xu [22], Faroughi and Lee [23] and Sulaiman et al [24] (Figure 2). Wang and Xu used semidefinite programming (SDP) to determine the optimal topology of the tensegrity plate-like structure consisting of nine modules.…”