Lattice structures, which can be fabricated by the recently developed additive manufacturing technologies, are used to have lightweight but strong components in many different areas such as aerospace, defense and biomedical industries. The relative density prediction of these lattice structures is important to have realistic designs when they are used in topology optimization. This work presents a comparison of the results of different curve fit functions of relative young moduli versus relative density of specific lattice structures. For this comparison, first, homogenized cellular mechanical properties have been calculated with a numerical homogenization method. A phyton script is prepared to calculate the homogenized properties in the commercial finite element analysis software Abaqus for various relative density values in the range between 0 and 1. Then, different fit curves are generated with different curve fit functions for the relationship between the relative density and homogenized properties. The root mean square error (RMSE) values are calculated to choose the fitting function that gives the best fit for each lattice structure. The lattice cell and the corresponding density-property curve that gives the highest homogenized properties is used in a topology optimization process to evaluate the differences of the optimized result from the regular topology optimization result.
Anahtar Kelimeler: Lattice structure, homogenization, curve fitting, topology optimization