Multi-Material and Multi-Joint Topology Optimization of 3D Structures

Abstract

In recent years, topology optimization has become a popular tool in automotive, aerospace and defense industries to generate novel clean slate designs. The most modern of these tools is multi-material topology optimization which is capable of simultaneously distributing material and selecting the optimum material within a design domain. However, a shortcoming of this method is that it cannot consider the practical joining of the inherently multi-component solutions. Since optimal joint design is dependent on optimal component design (and vice versa), it is argued that these aspects must be considered together to generate truly optimum multi-material designs. This limitation is addressed through multi- material and multi-joint topology optimization (MM/MJ TO) which can generate optimal joint distribution and selection at the boundary of dissimilar materials. Two different gradient-based topology optimization methods will be presented which allow for 3D MM/MJ TO structural design. These are included in the form of two manuscripts. The first manuscript expands on the current state-of- the-art MM/MJ TO algorithm and investigates its efficacy in solving 3D problems. A new concept of tooling accessibility constraints will be introduced that has yet to be discussed in literature. This constraint limits the existence of welded joints in tooling inaccessible regions to ensure manufacturability. The capabilities of the algorithm were demonstrated with three academic complexity 3D numerical examples. Through this work, it was found that the algorithm required prohibitively large computational cost while producing sub-optimal solutions. While this method was the first to achieve MM/MJ TO, it was found to have limited scalability to complex industry-driven design problems. The second manuscript introduces a novel interpolation scheme for performing coupled MM/MJ TO which addresses previous limitations. By removing the need to decouple MM and MJ TO, the algorithm can solve a new set of physically meaningful problem statements while also reducing computational time. Unlike the previous method, the new interpolation scheme enables the material interface to morph, thus capturing the mutual dependency of component and joint design. Through four numerical examples, these capabilities are demonstrated on both academic and high complexity 3D problems.