@inproceedings {pub4172,
	title = {Multi-material topology optimization in LS-TaSC using ordered SIMP interpolation},
	author = {Satchit Ramnath AND Mariusz Bujny AND Nate Zurbrugg AND Stefan Menzel AND Duane Detwiler},
	year = {2020},
	month = {June},
	abstract = {The use of Topology Optimization (TO) in the automotive industry has proven to be an effective tool for developing conceptual designs capable of meeting conflicting requirements like stiffness, safety, and light weighting. Applying traditional TO method helps meet the set target, however it limits the ability to advance the development of automotive components with multiple material distribution that could enhance the performance significantly. This problem requires the ability to use multi-material optimization methods within commercially available software like LS-TaSC{\textregistered} to optimally distribute multiple materials within a single design domain. Among multi-material TO methods, approaches using ordered Solid Isotropic Material with Penalization (SIMP) interpolation [1][2] are recently gaining more attention. Similar to the standard SIMP approach, ordered SIMP is used with density-based TO methods [3], which map element densities to design variables. SIMP penalizes the intermediate densities to drive the final topology towards a design with 0-1 material distribution. In the ordered SIMP approach, a single design variable represents not only the density, but also the type of material corresponding to a given density range. As a result, ordered SIMP can be easily integrated into the standard density-based TO methods or even used together with the commercial software. One of the main advantages of this approach is that the computational costs of TO do not increase with the number of materials considered in the optimization, which is the case for other multi-material TO methods [3][4]. Finally, the computational efficiency of the method makes it applicable for TO in the industrial setting.

In this paper, a method for integration of the ordered SIMP in LS-TaSC{\textregistered} to realize multi-material TO is proposed using a solid beam that is subject to static and crash load cases. To enable the use of an ordered SIMP approach in LS-TaSC{\textregistered}, the original interpolation file for a single material that defines the discrete material cards used during optimization is replaced by a file that contains the modified material interpolation cards for multiple materials. The optimization then uses the updated distribution to assign material/density values to elements in the design domain. To demonstrate the potential of the multi-material TO and validate the results, the obtained topologies are compared to single material designs as well as to the structures optimized using the state-of-the-art gradient-based approach [1]. The results show that LS-TaSC{\textregistered} can be successfully used for deriving multi-material structures superior to the single-material designs. Finally, due to the low computational costs, the method seems to be suitable for optimization of large-scale industrial models.
},
	publisher = {ANSYS},
	booktitle = {16th International LS-DYNA Conference 2020}
}