In the present paper, a novel cellular metamaterial that was based on a tensegrity pattern is presented. The material is constructed from supercells, each of which consists of eight 4-strut simplex modules. The proposed metamaterial exhibits some unusual properties, which are typical for smart structures. It is possible to control its mechanical characteristics by adjusting the level of self-stress or by changing the properties of structural members. A continuum model is used to identify the qualitative properties of the considered metamaterial, and to estimate how the applied self-stress and the characteristics of cables and struts affect the whole structure. The performed analyses proved that the proposed structure can be regarded as a smart metamaterial with orthotropic properties. One of its most important features are unique values of Poisson’s ratio, which can be either positive or negative, depending on the applied control parameters. Moreover, all of the mechanical characteristics of the proposed metamaterial are prone to structural control.

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The concept of tensegrity is understood in many ways. This term is often improperly used for structures that have some, but not necessarily the key, tensegrity properties. The concept of tensegrity systems is misused in reference to both mathematical models and completed engineering structures. The aim of the study is to indicate which of the plane (2D) trusses presented in the literature are erroneously classified as tensegrities. Singular value decomposition of the compatibility matrix and spectral analysis of the stiffness matrix with the effect of self-equilibrated forces is used for the analysis. A new precise definition of tensegrity trusses is proposed and implemented.

Abstract:The present paper discusses different aspects of the structural control of smart systems with a focus on tensegrity structures. Special attention is paid to unique features of tensegrity systems, referred to by the authors as inherent, which are induced by infinitesimal mechanisms that are balanced with self-stress states. The following inherent properties are defined: self-control, self-diagnosis, self-repair and self-adjustment (active control). All these features are thoroughly described and illustrated on a series of analyses performed on numerical models of various tensegrity systems. The presented examples of the analyses of different tensegrity modules and multi-module structures show that it is possible to control their properties by adjusting the pre-stressing forces. Moreover, it is proven that the adjustment of self-stress forces in a tensegrity system allows one to repair the damaged structure by compensating the damaged member.

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Origami is an old art of paper folding. From mechanical point of view origami can be defined as a folded structure. In the present paper a comparative study of four origami inspired folded plate structures is presented. Longitudinal, facet, egg-box and Miuraori origami modules are used for the analysis. The models are based on six-parameter shell theory with the use of the finite element method. Convergence analysis of each module is presented. Numerical study of roof folded plates in oriented to the comparison of maximal displacements and stresses in the structures. Some parametric analysis is also presented.

The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

The present paper is dedicated to an evaluation of novel cellular metamaterials based on a tensegrity pattern. The materials are constructed from supercells, each of which consists of a number of simplex modules with different geometrical proportions. Mechanical properties of the metamaterial can be controlled by adjusting the level of self-equilibrated forces or by changing the properties of structural members. A continuum model based on the equivalence of strain energy of the 3D theory of elasticity with a discrete formulation is used to identify the qualitative properties of the considered metamaterials. The model allows the inclusion of nonlinearities related to the equations of equilibrium in actual configuration of the structure with self-equilibrated set of normal forces typical for tensegrities. The lattices are recognised as extreme metamaterials according to the eigensolution of the equivalent elasticity matrices of the continuum model. The six representative deformation modes are defined and discussed: stiff, soft and medium extensional modes and high (double) as well as low shear modes. The lattices are identified as unimode or nearly bimode according to the classification of extreme materials.