Related papers: Mathematics of stable tensegrity structures
We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
A general force-perturbation-based criterion for solid instability is proposed, which can predict instability including crease without priori knowledge of instability configuration. The crease instability is analyzed in detail, we found…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
Structural stability is a necessary condition for successful construction of an assembly. However, designing a stable assembly requires a non-trivial effort since a slight variation in the design could significantly affect the structural…
A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars or struts connected by cables with tension. In this paper we show an exact relation between the maximum dimension that a…
Piping inspection robots play an essential role for industries as they can reduce human effort and pose a lesser risk to their lives. Generally, the locomotion techniques of these robots can be classified into mechanical and bioinspired. By…
We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…
Motivated by constraint-based CAD software, we develop the foundation for the rigidity theory of a very general model: the body-and-cad structure, composed of rigid bodies in 3D constrained by pairwise coincidence, angular and distance…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
Experimental analysis of the mechanics of a deformable object, and particularly its stability, requires repetitive testing and, depending on the complexity of the object's shape, a testing setup that can manipulate many degrees of freedom…
Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum.…
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
Modeling and simulation of complex systems is key to explore systems dynamics. Many scientific approaches were developed to represent dynamic structure systems but most of these approaches are efficient for some kinds of systems and…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
Dualities have been known to map space trusses and plate structures to each other since the 1980-s. Yet the computational similarity of the two has not been used to solve the unfamiliar plate structure with the methods of the well known…