778 research outputs found
On the compact wave dynamics of tensegrity beams in multiple dimensions
This work presents a numerical investigation on the nonlinear wave dynamics
of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact
loading on a chain of tensegrity prisms and lumped masses allows us to apply on
a smaller scale recent results on the propagation of compression solitary waves
in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D
beams reveal - for the first time - the presence of compact compression waves
in two- and three-dimensional tensegrity lattices with slender aspect ratio.
The dynamics of such systems is characterized by the thermalization of the
lattice nearby the impacted regions of the boundary. The portion of the
absorbed energy moving along the longitudinal direction is transported by
compression waves with compact support. Such waves emerge with nearly constant
speed, and slight modifications of their spatial shape and amplitude, after
collisions with compression waves traveling in opposite direction. The analyzed
behaviors suggest the use of multidimensional tensegrity lattices for the
design and additive manufacturing of novel sound focusing devices
On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms
We study the geometrically nonlinear behavior of uniformly compressed
tensegrity prisms, through fully elastic and rigid--elastic models. The
presented models predict a variety of mechanical behaviors in the regime of
large displacements, including an extreme stiffening-type response, already
known in the literature, and a newly discovered, extreme softening behavior.
The latter may lead to a snap buckling event producing an axial collapse of the
structure. The switching from one mechanical regime to another depends on the
aspect ratio of the structure, the magnitude of the applied prestress, and the
material properties of the constituent elements. We discuss potential acoustic
applications of such behaviors, which are related to the design and manufacture
of tensegrity lattices and innovative phononic crystals
Parametric Design of Minimal Mass Tensegrity Bridges Under Yielding and Buckling Constraints
This paper investigates the use of the most fundamental elements; cables for
tension and bars for compression, in the search for the most efficient bridges.
Stable arrangements of these elements are called tensegrity structures. We show
herein the minimal mass arrangement of these basic elements to satisfy both
yielding and buckling constraints. We show that the minimal mass solution for a
simply-supported bridge subject to buckling constraints matches Michell's 1904
paper which treats the case of only yield constraints, even though our boundary
conditions differ. The necessary and sufficient condition is given for the
minimal mass bridge to lie totally above (or below) deck. Furthermore this
condition depends only on material properties. If one ignores joint mass, and
considers only bridges above deck level, the optimal complexity (number of
elements in the bridge) tends toward infinity (producing a material continuum).
If joint mass is considered then the optimal complexity is finite. The optimal
(minimal mass) bridge below deck has the smallest possible complexity (and
therefore cheaper to build), and under reasonable material choices, yields the
smallest mass bridge.Comment: 56 pages, 25 figures, 13 tables. Internal Report 2014-1: University
of California, San Diego, 201
A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions
The equilibrium problem of unreinforced masonry vaults is analyzed via a constrained thrust network approach. The masonry structure is modeled as no-tension membrane (thrust surface) carrying a discrete network of compressive singular stresses, through a non-conforming variational approximation of the
continuous problem. The geometry of the thrust surface and the associated stress field are determined by means of a predictor–corrector procedure based on polyhedral approximations of the thrust surface and membrane stress potential. The proposed procedure estimates the regions exposed to fracture damage
according to the no-tension model of the masonry. Some numerical results on the thrust network and crack pattern of representative vault schemes are given
Mechanical modeling of innovative metamaterials alternating pentamode lattices and confinement plates
This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice of the face cubic-centered unit cell typically analyzed in the current literature on pentamode materials. The studied systems exhibit only three soft deformation modes in the infinitesimal stretch-dominated regime, as opposed to the five zero-energy modes of unconfined pentamode lattices. We develop analytical formulae for the vertical and bending stiffness properties and study the dependence of such quantities on the main design parameters: the lattice constant, the solid volume fraction, the cross-section area of the rods, and the layer thickness. A noteworthy result is that the effective compression modulus of the analyzed structures is equal to two thirds of the Young modulus of the stiffest isotropic elastic networks currently available in the literature, being accompanied by zero-rigidity against infinitesimal shear and twisting mechanisms. The use of the proposed metamaterials as novel seismicisolation devices and impact-protection equipment is discussed by drawing comparisons with the response of alternative devices already available or under development
On a Moderate Rotation Theory of Thin-Walled Composite Beams
A small strain and moderate rotation theory of laminated composite thin-walled beams is formulated by generalizing the classical Vlasov
theory of sectorial areas. The proposed beam model accounts for axial, bending, torsion and warping deformations and allows one to predict critical loads and initial post-buckling behaviour. A finite element approximation of the theory is also carried out and several numerical applications are developed with reference to lateral buckling of composite thin-walled members. The sensitivity of critical load to secondorder effects in the pre-buckling range is pointed out
METHOD AND APPARATUS FOR WAVE GENERATION AND DETECTION USING TENSEGRITY STRUCTURES
This disclosure relates to an apparatus based on tensegrity structures (referred to as tensegrity apparatus) for the transmission of special solitary waves with adjustable profile into a material or structure, and the detection of such waves from a material or structure
Experimental investigation of the softening-stiffening response of tensegrity prisms under compressive loading
The present paper is concerned with the formulation of new assembly methods
of bi-material tensegrity prisms, and the experimental characterization of the
compressive response of such structures. The presented assembly techniques are
easy to implement, including a string-first approach in the case of ordinary
tensegrity prisms, and a base-first approach in the case of systems equipped
with rigid bases. The experimental section shows that the compressive response
of tensegrity prisms switches from stiffening to softening under large
displacements, in dependence on the current values of suitable geometric and
prestress variables. Future research lines regarding the mechanical modeling of
tensegrity prisms and their use as building blocks of nonlinear periodic
lattices and acoustic metamaterials are discussed
A lumped stress method for plane elastic problemsand the discrete-continuum approximation
This paper proposes a rational method to approximate a plane elastic body through a latticed structure composed of
truss elements. The method is based on the introduction of a relaxed stress energy that allows an extension of the
original problem to a larger space of admissible stress fields, including stresses concentrated along lines. Use is made of
polyhedral approximations of the Airy stress function. The truss analogy is employed to obtain a displacement formulation. The paper includes several numerical applications of the method to sample problems, a numerical convergence study and comparisons with exact solutions and standard finite element approximations
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