Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultra-light load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties that may be unattainable with standard cell designs. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and the number, shape, and arrangement of cell openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermo-elastic properties, however, and limitations of standard topology optimization methods prevent direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, we introduce a practical, two-stage, flexibility-based, multifunctional topology design approach for applications that require customized multifunctional properties. As part of the approach, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. The flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions, respectively, without degrading structural performance. We apply the method to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.
Algorithms in Digital Geometry Based on Cellular Topology
