3D decomposition optimization of topology-optimized structures considering a build volume constraint for additive manufacturing

Abstract

The integration of topology optimization and additive manufacturing (AM) offers a transformative approach to designing and fabricating complex structures across various industries. This synergy enables engineers to produce lightweight, high-performance designs with intricate, organic geometries that push the boundaries of conventional manufacturing methods. However, printing large 3D objects that exceed the allowable build volume of an AM machine poses a significant challenge. This necessity has led to the development of methodologies such as part decomposition (PD) to fit these objects within the build volume constraint. Previous studies have contributed to solving PD problems, but several limitations, such as the use of Euler angle representation and the lack of practical decomposed designs, need to be addressed. To the best of the authors’ knowledge, this is the first paper to develop a 3D decomposition optimization methodology for topology-optimized structures by establishing a novel rotational system and modeling joint mechanical properties. The novel rotational system, using a non-unit quaternion representation, is established to eliminate the singularity issue inherent in the Euler angle representation. This approach also allows for the effective optimization of partitioning cuboids, which represent the allowable AM build volume, by removing the unit-length constraint. Additionally, the joint mechanical properties at the interface between decomposed parts are modeled using geometrically represented hollow cuboids. Furthermore, analytical sensitivity expressions with respect to new design variables, including explicit variables of partitioning cuboids and rotation variables of non-unit quaternions, are derived and numerically verified to efficiently solve the decomposition optimization problem. Through practical case studies, the 3D decomposition optimization methodology demonstrates its effectiveness under various conditions, including varying maximum allowable AM build volumes, different initial partitioning cuboid layouts, and various joint mechanical properties.