Use case
Minimal mass design of active tensegrity structures
Read how the nonlinear optimization solver Artelys Knitro helped structural engineers, in this article from “Engineering Structures”.


  • Finding the equilibrium between compression and tension constraints
  • Minimizing the mass of a system while maintaining structural stability


  • Mass and prestress levels reduction of structure design
  • Low-carbon engineering structural design

Tensegrity, for tensional integrity, is a structural principle whereby solid components such as bars or struts are bound together by cables so that the components are subject to compression forces while the cables are subject to tension forces. Tensegrity is used to design large-span structures such as bridges and domes, deployable structures in the aerospace field or novel soft robots.

The authors propose a general approach for the design of active tensegrity structures, that is, equipped with actuators that can actively adapt to external loads. Such active structures use less material than passive ones, thus have smaller masses.

An optimization model is designed where the variables on structure and actuators are continuous or binary, and nonlinear constraints are involved. The result is a mixed-integer nonlinear program (MINLP) that minimizes the total mass of the system while maintaining structural stability. Using this approach, three typical active tensegrity structures are designed: a cantilever beam, a dome and a pedestrian bridge.

The authors use the Branch-and-Bound and the interior-point algorithms of Artelys Knitro to solve the MINLP with all parameters set as default, and adopt the multi-start feature to improve the solution quality. On all three case studies, the authors reach up to 40% mass reductions and prestress levels are decreased by up to 60% when compared to the equivalent passive designs.

This work extends the application of mathematical programming techniques in the structural engineering field. The proposed methodology has great potential and application value for future lightweight and low-carbon engineering structural design to reduce the environmental impact of architecture and buildings.



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