Topology optimization of lattices with anisotropic struts

This work presents a topology optimization method for design of architected truss lattices made of anisotropic struts. Employing anisotropic materials for the lattice struts can result in better effective properties than those that can be obtained for a lattice in which each strut is made of a single isotropic material, but different struts may be made of different materials. This work focuses on lattice struts that are either hollow or fiber-reinforced, which effectively result in transverse isotropy. The proposed method simultaneously optimizes the spatial configuration of the struts and the volume fraction of the reinforcing fibers or the holes in each strut to extremize the lattice effective properties. A parametric description of the lattice struts is projected onto a density field for analysis via the geometry projection technique. The proposed method accommodates any number of specified material symmetries by performing appropriate reflections of the projected density with respect to the symmetry planes. To ensure the size variables converge to 0 or 1, we employ an explicit penalization by imposing a discreteness constraint. To improve manufacturability, a no-cut constraint is imposed to ensure that struts are not partially cut upon reflection by the symmetry planes or by the faces of the unit cell. The smallest angle at which two struts can intersect is also constrained to avoid overlaps that are difficult to manufacture. Examples of maximization of the effective bulk modulus and minimization of the effective Poisson’s ratio of the lattice demonstrate the effectiveness of the proposed method.