An integrated homogenization-based topology optimization via RBF mapping strategies for additively manufactured FGLS and its application to bandgap structures

The manufacturing of lattice structures has been greatly facilitated thanks to the advances in additive manufacturing. Functionally graded lattice (FGL) structures, a major class of such structures, developed using topology optimization (TO) are known to have superior mechanical characteristics such as high stiffness to weight ratio. A new design methodology using an integrated TO process is proposed for the development of FGL structures in this research. For that purpose, a material-penalization formula derived by the application of homogenization is integrated into the TO process. As a result, relative densities of the TO are mapped directly. This approach is more advantageous compared with the alternative techniques as there is no need to post-process the optimization results. Therefore, the degradation of the optimization results from post-processing is eliminated. Then, radial basis functions (RBFs) are used to create the geometry of the FGLs efficiently. The proposed methodology is demonstrated on a case study, where a cantilever beam with a desired bandgap characteristic is designed. Numerical results using the proposed method show that the first and second bending frequencies with the resulting optimized geometry are within 3% and 12% of the original TO design, whereas using method 1 the calculated relative errors are 24% and 74% and method 2 these errors are calculated as 8% and 34%, respectively. These comparative results indicate that the geometry created by the new method is superior to other design strategies as evidenced by the improved compatibility level between the bandgap performance results of the original unpenalized TO and structures generated using alternative techniques