A general approach to minimal mass tensegrity

This work is motivated by the fundamental questions in engineering mechanics: Does continuum guarantee a minimal mass structure? What is a more mass efficient way to design structures? Moreover, what are the fundamental laws of the new approach? This paper provides a general unified approach for the minimal mass design of any solid or hollow bar tensegrity structures with any given external forces subject to the structure equilibrium conditions and the maximum stress constraints of structure members (strings yield, bars yield or buckle) in a compact matrix form. The methodology yields several nonlinear programming problems. Local stability is assured by checking the modes of failure of all the structure members, and global stability is guaranteed by solving a linear matrix inequality with the derived stiffness matrix. To further reduce mass, the choice of the cross-section of bars are also discussed. For practical problems, joint mass is considered as a penalty to the total structure mass. The principles developed in this paper demonstrates a fundamental insight into both materials and structures.