Topology optimization of programmable lattices with geometric primitives

This work presents a topology optimization method for the design of programmable lattice materials whose struts can be activated/deactivated by some actuation mechanism. The proposed method simultaneously determines the spatial layout of struts in the unit cell, and two or more programs corresponding to the open/close states of the struts in order to attain desired effective properties. A high-level parametric description of the cylindrical struts in the unit cell is smoothly mapped onto a fixed mesh for analysis via the geometry projection method. Desired material symmetries are imposed by reflections with respect to the symmetry planes in the computation of the projected density. The open/close state of a strut is modeled by assigning a state variable per program to each strut, and a discreteness constraint in the optimization ensures these variables are zero or unity in the optimal design. To aid manufacturability, a no-cut constraint is imposed to preclude partial cuts of the struts by the symmetry planes or the unit cell boundaries and thus ensure that struts are whole in the optimal design. The effectiveness of the proposed method is demonstrated with examples of minimal volume design for two and three programs with target bulk moduli and for two programs with a bulk modulus target and a Poisson’s ratio target.