The structural performance of the periodic truss

Matrix methods of linear algebra are used to analyse the structural mechanics of the periodic pin-jointed truss by application of Bloch's theorem. Periodic collapse mechanisms and periodic states of self-stress are deduced from the four fundamental subspaces of the kinematic and equilibrium matrix for the periodic structure. The methodology developed is then applied to the Kagome lattice and the triangular–triangular (T–T) lattice. Both periodic collapse mechanisms and collapse mechanisms associated with uniform macroscopic straining are determined. It is found that the T–T lattice possesses only macroscopic strain-producing mechanisms, while the Kagome lattice possesses only periodic mechanisms which do not generate macroscopic strain. Consequently, the Kagome lattice can support all macroscopic stress states. The macroscopic stiffness of the Kagome and T–T trusses is obtained from energy considerations. The paper concludes with a classification of collapse mechanisms for periodic lattices.