We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite.

Technical Notes and Correspondence on the Rank Minimization Problem Over a Positive Semidefinite Linear Matrix Inequality

A prestressed cable-strut structure is usually regarded as a mechanism before being prestressed. Under the action of initial prestresses, the internal infinitesimal mechanisms can be rigidi...

Feasible Prestress Modes for Cable-Strut Structures with Multiple Self-Stress States Using Particle Swarm Optimization

Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming

Tensegrity structures resemble biological tissues: A structural system that holds an internal balance of prestress. Owing to the presence of prestress, biological tissues can dramatically change their properties, making tensegrity a promising platform for tunable and functional metamaterials. However, tensegrity metamaterials require harmony between form and force in an infinitely–periodic scale, which makes the design of such systems challenging. In order to explore the full potential of tensegrity metamaterials, a systematic design approach is required. In this work, we propose an automated design framework that provides access to unlimited tensegrity metamaterial designs. The framework generates tensegrity metamaterials by tessellating blocks with designated geometries that are aware of the system periodicity. In particular, our formulation allows creation of Class-1 (i.e., floating struts) tensegrity metamaterials. We show that tensegrity metamaterials offer tunable effective elastic moduli, Poisson’s ratio, and phononic bandgaps by properly changing their prestress levels, which provide a new dimension of programmability beyond geometry.

Unraveling Tensegrity Tessellations for Metamaterials with Tunable Stiffness and Bandgaps

Design of a new tensegrity cantilever structure

Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming

Minimum energy adaptive structures – All-In-One problem formulation

Form-finding of tensegrity structures via rank minimization of force density matrix

This paper proposes a general approach for topology-finding of tensegrity structures. The ground structure method that is widely used in topology optimization of truss structures is employed. An optimization model, using the member connections and the internal forces of members as variables, is developed to find self-stressed tensegrities under given constraints on member distribution, configuration symmetry, and node stability. Mixed integer linear/quadratic programming is used to solve the optimization problem. Numerical examples are carried out to verify the proposed approach. Compared to previous approaches, the proposed approach is able to find a wider scope of tensegrity structures that have a maximum of k (k≥1) struts connecting to a single node and is able to deal with objective functions in quadratic form.

General Approach for Topology-Finding of Tensegrity Structures

This paper proposes a general approach for topology optimization of tensegrity structures. The optimization problem is formulated in the framework of a mixed-integer linear programming. Com...

Yafeng Wang

Papers

Finding member connectivities and nodal positions of tensegrity structures based on force density method and mixed integer nonlinear programming

Minimum energy adaptive structures – All-In-One problem formulation

Form-finding of tensegrity structures via rank minimization of force density matrix

General Approach for Topology-Finding of Tensegrity Structures

Topology Optimization of Tensegrity Structures Considering Buckling Constraints