Topology optimization of lightweight periodic lattices under simultaneous compressive and shear stiffness constraints

This paper investigates the optimal architecture of planar micro lattice materials for minimum weight under simultaneous axial and shear stiffness constraints. A well-established structural topology optimization approach is used, where the unit cell is composed of a network of beam elements (Timoshenko beams are used instead of truss elements to allow modeling of bending-dominated architectures); starting from a dense unit cell initial mesh, the algorithm progressively eliminates inefficient elements and resizes the essential load-bearing elements, finally converging to an optimal unit cell architecture. This architecture is repeated in both directions to generate the infinite lattice. Hollow circular cross-sections are assumed for all elements, although the shape of the cross-section has minimal effect on most optimal topologies under the linear elasticity assumption made throughout this work. As optimal designs identified by structural topology optimization algorithms are strongly dependent on initial conditions, a careful analysis of the effect of mesh connectivity, unit cell aspect ratio and mesh density is conducted. This study identifies hierarchical lattices that are significantly more efficient than any isotropic lattice (including the widely studied triangular, hexagonal and Kagomé lattices) for a wide range of axial and shear stiffness combinations. As isotropy is not always a design requirement (particularly in the context of sandwich core design, where shear stiffness is generally more important than compressive stiffness), these optimal architectures can outperform any established topology. Extension to 3D lattices is straightforward.