Computational first-order homogenization theory is used for the elastic analysis of generally anisotropic lattice materials within classical continuum mechanics. The computational model is tailored for structural one-dimensional elements, which considerably reduces the computational cost comparing to previously developed models based on solid elements. The effective elastic behavior of lattice materials is derived consistently with several homogenization approaches including strain- and stress-based methods together with volume and surface averaging. Comparing the homogenization based on the Hill-Mandel Lemma and constitutive approach, a shear correction factor is also introduced. In contrast to prior studies which are usually limited to a specific class of lattice materials such as lattices with cubic symmetry or similarly situated joints, this computational tool is applicable for the analysis of any planar or spatial stretching- and bending-dominated lattices with arbitrary topology and anisotropy. Having derived the elasticity of the lattice, the homogenization is then complemented by the symmetry identification based on the monoclinic distance function. This step is essential for lattices with non-apparent symmetry. Using the computational model, nine different spatial anisotropic lattices are studied among which four are fully characterized for the first time, i.e. non-regular tetrahedron (with trigonal symmetry), rhombicuboctahedron type a (with cubic symmetry), rhombicuboctahedron type b (with transverse isotropy) and double pyramid dodecahedron (with tetragonal symmetry).

This research is focused on developing new lightweight structures for railcars based on a pre-selected material, i.e. Al 2099. The goal is to design a new sandwich structure with an octet truss lattice core for a floor panel of a hopper freight railcar designed to meet North American standards. For that, mesoscale to macroscale design of the sandwich panel was performed. In mesoscale design, relative density, elastic properties, strength properties, and failure criterion of the lattice unit cell were investigated. In the next step, these properties were used as inputs for macroscale design, i.e. design of the whole sandwich structure. Multiple failure modes associated with the lateral loading of a sandwich panel were analyzed. These equations in conjunction with the minimum weight target led to an optimization problem, and the minimum required thicknesses were obtained. Finally, the new optimized design was validated by comparing different finite element simulations with the exact analytical equations. By using this type of structure, a 53% weight reduction was achieved on the floor panel which ultimately led to an estimated 12.5% reduction in the weight of the whole freight railcar body.

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