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A novel method for determining the feasible integral self-stress states for tensegrity structures
Full text linkThe form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. This form-finding problem leads to the evaluation of both the self-stress in the elements and the shape of the tensegrity structure. This paper presents a novel method for determining feasible integral self-stress states for tensegrity structures, that is self-equilibrated states consistent with the unilateral behaviour of the elements, struts in compression and cables in tension, and with the symmetry properties of the structure. In particular, once defined the connectivity between the elements and the nodal coordinates, the feasible self-stress states are determined by suitably investigating the Distributed Static Indeterminacy (DSI). The proposed method allows for obtaining feasible integral self-stress solutions by a unique Singular Value Decomposition (SVD) of the equilibrium matrix, whereas other approaches in the literature require two SVD. Moreover, the proposed approach allows for effectively determining the Force Denstiy matrix, whose properties are strictly related to the super-stability of the tensegrity structures. Three tensegrity structures were studied in order to assess and discuss the efficiency and accuracy of the proposed innovative method
Phase Transitions, Hysteresis and Bifurcation for Generalized Mooney-Rivlin Elastic Bodies
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Phenomenological rate-independent uniaxial hysteretic models: A mini-review
Full text linkA great variety of phenomenological models has been proposed over the years to model rate-independent hysteretic forces in structural mechanics. The classification of such models is usually based on the type of equation that needs to be solved to evaluate the output variable. In particular, we distinguish among algebraic, transcendental, differential and integral models. For algebraic (transcendental) models, an algebraic (a transcendental) equation needs to be solved to compute the output variable; conversely, differential equations are employed for differential models, whereas equations expressed in integral form characterize integral models. This paper provides a mini-review of the most adopted phenomenological rate-independent uniaxial hysteretic models. Such models are selected in order to provide a complete overview of the four types of previously mentioned models, currently available in the literature. In particular, we illustrate the fundamental characteristics of each model and discuss their peculiarities in terms of 1) number of adopted parameters and variables, 2) physical interpretation of parameters and related calibration procedures, 3) type of hysteresis loop shapes that can be simulated
Periodic bifurcations of an incompressible elastic tube subject to pure circular shearing
No full textMinimal mass and self-stress analysis for innovative V-Expander tensegrity cells
Full text linkTensegrity structures are an intriguing kind of structures by virtue of their deployability, scalability and high stiffness to mass ratio. Fraddosio et al. recently proposed a family of five innovative V-Expander elementary tensegrity cells, characterized by an increasing degree of geometrical complexity, and designed as a morphological evolution of a concept originally proposed by Motro and Raducanu. Here, we study the mechanical behavior of these innovative V-Expander elementary tensegrity cells by referring to different topologies; in particular, we analyze for such cells the feasible self-stress states in the cases in which the components in compression are composed of 2, 3, 4 and 6 struts, respectively. In addition, we evaluate the minimal mass of the cells taking into account the buckling strength of members in the self-equilibrium states according to the indications of standard building codes
Stability, bifurcation and post-critical behavior of a homogeneously deformed incompressible isotropic elastic parallelepiped subject to dead-load surface tractions
No full textWe study the equilibrium homogeneous deformations of a homogeneous parallelepiped made of an arbitrary incompressible, isotropic elastic material and subject to a distribution of dead-load surface tractions corresponding to an equibiaxial tensile stress state accompanied by an orthogonal uniaxial compression of the same amount. We show that only two classes of homogeneous equilibrium solutions are possible, namely symmetric deformations, characterized by two equal principal stretches, and asymmetric deformations, with all different principal stretches. Following the classical energy-stability criterion, we then find necessary and sufficient conditions for both symmetric and asymmetric equilibrium deformations to be weak relative minimizers of the total potential energy. Finally, we analyze the mechanical response of a parallelepiped made of an incompressible Mooney–Rivlin material in a monotonic dead loading process starting from the unloaded state. As a major result, we model the actual occurrence of a bifurcation from a primary branch of locally stable symmetric deformations to a secondary, post-critical branch of locally stable asymmetric solutions
The Magnus expansion and some of its applications in bifurcation problems for non-linear elastic solids
No full textBifurcating periodic twist-like deformations for a class of compressible isotropic elastic materials
No full textIn the present paper we study the emergence of bifurcating periodic twist-like deformations for an infinitely long isotropic compressible elastic parallelepiped confined between and attached to parallel plates which are subject to a relative shear displacement. We specialize our analysis by considering a generalized form of the Blatz-Ko strain energy function. In particular, through a numerical example, we determine a range of critical values of the applied shearing strain, and discuss some features of such periodic solutions
A model for hysteretic dissipation in shape-memory alloys subject to multiaxial stress states
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