Tensegrity structures attract the interest of researchers working in many different areas, including engineering, mathematics, architecture, biology, among the others, and have also inspired beautiful sculptures and artworks. Such structures consist of spatial assemblies of rigid compressive members (bars) and deformable (prestressed) tensile elements (strings or cables), which typically feature geometrically nonlinear mechanical behavior. Tensegrity networks have been employed as model systems in a large variety of form-finding and dynamical control problems of engineering and architecture (refer, e.g., to Skelton and de Oliveira, Tensegrity Systems. Springer, 2010, and references therein). It has been shown in Skelton and de Oliveira (2010) that such structures can form minimal mass systems for given loads, through assemblies of repetitive units forming beautiful ‘tensegrity fractals’. The mechanical response of tensegrity structures relies on the basic laws of attraction and repulsion between mass particles and can be suitably adjusted by playing with basic variables, such as mass positions, topology of connections, size, material and prestress of tensile members. It has been recognized in recent years that they well describe the mechanics of a number of biological structures, such as cell cytoskeletons, the red blood cell membrane, spider fibers, the muscle-bone systems, among others. In this work we examine the continuum limit of a special class tensegrity structures, which consists of Michell trusses with variable complexity (Skelton and de Oliveira, 2010). On employing a suitable variational approach to 2D elastic problems (Lumped Stress Method, Fraternali, Mech. Adv. Mat. Struct., 14:309-320, 2007) we show that the thrust network exhibited by such structures converges to a continuum stress field, as the number of nodes approaches infinity. We employ both mathematical and numerical arguments, and discuss optimization strategies of the examined tensegrity scheme.
On the Continuum Limit of Tensegrity Structures
FRATERNALI, Fernando;
2012-01-01
Abstract
Tensegrity structures attract the interest of researchers working in many different areas, including engineering, mathematics, architecture, biology, among the others, and have also inspired beautiful sculptures and artworks. Such structures consist of spatial assemblies of rigid compressive members (bars) and deformable (prestressed) tensile elements (strings or cables), which typically feature geometrically nonlinear mechanical behavior. Tensegrity networks have been employed as model systems in a large variety of form-finding and dynamical control problems of engineering and architecture (refer, e.g., to Skelton and de Oliveira, Tensegrity Systems. Springer, 2010, and references therein). It has been shown in Skelton and de Oliveira (2010) that such structures can form minimal mass systems for given loads, through assemblies of repetitive units forming beautiful ‘tensegrity fractals’. The mechanical response of tensegrity structures relies on the basic laws of attraction and repulsion between mass particles and can be suitably adjusted by playing with basic variables, such as mass positions, topology of connections, size, material and prestress of tensile members. It has been recognized in recent years that they well describe the mechanics of a number of biological structures, such as cell cytoskeletons, the red blood cell membrane, spider fibers, the muscle-bone systems, among others. In this work we examine the continuum limit of a special class tensegrity structures, which consists of Michell trusses with variable complexity (Skelton and de Oliveira, 2010). On employing a suitable variational approach to 2D elastic problems (Lumped Stress Method, Fraternali, Mech. Adv. Mat. Struct., 14:309-320, 2007) we show that the thrust network exhibited by such structures converges to a continuum stress field, as the number of nodes approaches infinity. We employ both mathematical and numerical arguments, and discuss optimization strategies of the examined tensegrity scheme.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
