Collapse of periodic planar lattices under uniaxial compression, part I: Quasi-static strength predicted by limit analysis

The collapse strength is analyzed for typical periodic planar lattices under uniaxial compression. In this part, the quasi-static strengths of the lattices are predicted by limit analysis, with the consideration of the elastic effect and large deformation effect. The planar lattices are firstly classified into bending-dominated and membrane-dominated structures. Collapse strength of typical bending-dominated lattices, such as hexagonal and rhombus structures, has identical initial lower bound and upper bound, so that the equivalent stress–strain curve of a bending-dominated lattice possesses a plateau. On the contrary, the equivalent stress–strain curve of a membrane-dominated lattice, such as square, triangular or Kagome structure, usually contains a peak followed by a sharp drop without a plateau. Consequently, the energy absorption behavior of the bending-dominated lattices is similar to type I structure, while that of the membrane-dominated lattices is similar to type II structure.