Pseudo-membrane method and its application

Pseudo-Membrane approach was presented to give the relationship between the lattice structures with unit cells and their homogenized continuum structures. In the method, a 2D lattice structure with periodic microstructure (or unit cell) was adopted and was considered as homogeneous continuum pseudo-membrane (PM) based on their equivalent mechanical behavior in the present work. A rectangular unit cell made up of pinning poles was introduced. The elastic constitutive parameters of the pseudo-membrane were expressed by the material and geometric parameters of poles in the lattice unit cell. It was found that, when the material parameters of poles in unit cell were kept fixed, modifying the geometric parameters of the lattice structure proportionally did not change the elastic constitutive property of the pseudo-membrane. The property, called as the geometry intrinsic property of lattice structure, was significant in material/structure design. Numerical examples were given to demonstrate the validity of the present method.