Optimal Macroscopic Structural Designs based on Microstructures
Please login to view abstract download link
Macroscopic structural designs based on microstructures can be found in technical and natural materials like metal foams and bones. Human bone, for example, consists of an outer layer of dense bone tissue (cortical bone) that is filled with highly porous bone tissue (trabecular bone) consisting of lattice-shaped and plate-shaped units. A smart combination of compact and porous materials results in a highly resilient and simultaneously lightweight structure. This exemplary observation serves as a motivation for our design paradigm: the macroscopic structural designs are defined as multi-patch geometries that are generated by tiling spline patches [1]. The geometries of the individual tiles are parameterized and can thus be optimized towards a desired mechanical behavior of the resulting macroscopic design. The cost of such an optimization is crucially determined by the total number of optimization parameters and the cost per isogeometric analysis of the current design proposal. To keep the number of optimization parameters low, the tiles’ parameters are determined by evaluating a so-called parameter spline, whose control points are then adapted during the optimization [2]. To efficiently predict the mechanical behavior of design proposals, efficient simulations of multi-patch geometries are needed. We will illustrate and evaluate the performance of our design paradigm based on applications within the context of lightweight design or structural biomechanics. REFERENCES [1] G. Elber. Precise construction of micro-structures and porous geometry via functional composition. Mathematical Methods for Curves and Surfaces, 108–125, 2017. [2] J. Zwar, G. Elber and S. Elgeti. Shape optimization for temperature regulation in extrusion dies using microstructures. Journal of Mechanical Design, 145(1):012004, 2023.