Multi-Joint Topology Optimization: A Method for Considering Joining in Multi-Material Design

Automakers are under constant pressure to improve fuel economy and vehicle range to achieve a competitive advantage within the industry and meet government regulations. Reducing the overall weight of a vehicle contributes significantly to achieving this goal. Topology optimization (TO) has been identified within industry as a leading method to reduce weight on both a component and assembly level. With this tool, components can be redesigned to maintain structural performance requirements while also providing significant weight savings. On an assembly level, TO can be used to determine optimal loadpaths within large structures such as frames or bodies. These loadpaths can be interpreted to determine the locations of different components within the structure. To support the development of lightweight vehicle design, this paper presents a revised methodology and application of multi-joint topology optimization (MJTO). This method is an extension of multi-material topology optimization (MMTO), which is derived from the classical standard single-material problem statement (SMTO). Here, MJTO both extends topology optimization to consider multiple materials while also considering joint characteristics between material boundaries. Included here is a detailed description and demonstration of the MJTO methodology, starting with a brief overview of MMTO. Next, the derivation of MJTO element interpolation functions, sensitivities, and filtering methods are presented with the introduction of a novel mesh independent gradient approximation method. This method extends MJTO to problems with irregular mesh types and addresses issues with previously adopted approaches. Finally, a case study is presented demonstrating the MJTO method and providing a holistic comparison between SMTO and MMTO solutions.