Generative Design of Structured Materials for Controlled Frequency Responses

Spatially varying material properties allow the dynamic response of structural systems to be almost arbitrarily tailored, far beyond the first or fundamental natural frequency. Continuing advances in manufacturing technology are making it possible to achieve the necessary range of stiffness and density variations, but the design of these property distributions is a challenging task because of the complex multidimensional nature of the problem. Generative design methods based on evolutionary optimization algorithms have been successfully used to obtain solutions based on multi-material distributions. However, the applicability of these solutions is limited by their reliance on multi-material additive manufacturing (AM), which currently only offers digitally mixed acrylic polymer options that are generally unsuitable to produce functional parts. A novel structured material solution is proposed here, in which the problem domain is divided into several volume elements (voxels), each of which contains a structure whose geometrical form is altered to adjust its effective properties to desired values. The single material structural solution will be amenable for ready fabrication by the powder-based selective laser sintering and melting processes with real engineering polymer and metal systems, thereby allowing for the realization of the benefits in real-world applications. The resulting continuous design spaces are searched using a modern evolutionary algorithm, the covariance matrix adaptation evolution strategy (CMA-ES). A MATLAB implementation of this evolutionary design method, in conjunction with finite element simulations for fitness evaluation, showed good convergence for several different cantilever beam test cases when tested against several different sets of target natural frequencies. Correlations with the multi-material solutions show that the single structured material approach is on par or even better in some cases, even though the test domain was discretized into 80% fewer voxels than for the multi-material case. Furthermore, the voxel structures can be realized using current AM technologies.