Pseudo-membrane method for two-dimensional lattice structure with periodic cable-link cells

In-plane effective elastic properties of a two-dimensional lattice structure with periodic cable-link- hinged unit cells are investigated using a pseudo-membrane (PM) method, a kind of homogenization approach. By PM method, a lattice structure can be homogenized into a continuum (PM) with respect to the same local and global stiffness. The elastic parameters, e.g., elastic modulus, Poisson's ratio and shear modulus, of its PM are expressed as functions of the material and geometry of the cables and links in the unit cell. The analytical results show the parameters depend on the local stress/strain states, e.g., the tension modulus is different from the compression one along the same direction. Therefore, the PM of lattice structure shows a bi-modulus material. To verify the correctness of the parameters, two cantilever beams of identical size under the same loading conditions are investigated. The positions of the neutral planes of the beams are obtained, both of analytically and numerically. The relative error between the deflections of the neutral planes of two beams is very small.