Nanomechanical resonators are used in high-precision sensing and emerging quantum experiments, where performance strongly depends on achieving a very high Quality Factor (Q), i.e., minimal energy loss. One way of achieving high Q is dissipation dilution, where tensile prestress reduces the relative losses through bending. This thesis investigates how topology optimization can be improved to design resonator geometries with enhanced dissipation dilution. A key challenge in conventional density-based optimization is the appearance of “grey” regions (intermediate volume fractions): these regions can temporarily boost performance during optimization, but are typically forced out to obtain manufacturable solid-void designs. In this work, these intermediate volume fractions are given a physical meaning by assigning them a manufacturable microstructure through homogenization, leading to designs that are not restricted to purely solid-void layouts. Using this homogenization based optimization approach, the optimized designs achieve 20% - 40% higher Q factor compared to solid-void results under comparable setting. The thesis also studies how volume and frequency constraints influence the final topology, and analyses instability issues related to localized compressive stresses, and proposes mitigation strategies. Finally, the thesis explores graphene resonators as an alternative to silicon nitride resonators, motivated by graphene’s ultra-low mass and strong tensile properties, and discusses practical design strategies to obtain a high performing resonator. ... Read more

Silicon based power semiconductors have long been used as the standard in ‘semiconductor technology in power conversion applications’. Recent developments replaces the Silicon with Silicon Carbide as it results in superior performance of the power conversion applications. However, due to the increased performance, challenges regarding heat dissipation emerge and the lifetime of the power semiconductor packaging or power module is compromised. Since this leads to an increase power density, the cooling of the power module is becoming of more importance and the heat sink becomes an interesting component to optimize. The best performance of a heat sink can be obtained when the flow through the device is turbulent. Developing turbulent flow heat sinks by using topology optimization methods can significantly improve the cooling performance compared to the current designs. This work is thus aimed towards improving methods for topology optimization of turbulent flow cooling devices. However, this work focuses on turbulent flow topology optimization only and aims to improve the accuracy of current methods. It is important that the flow physics are accurate since the thermal energy transfer is dependent on the flow field. The current state-of-the-art method based on the 𝑘−𝜔 turbulence model developed by Dilgen et al. is investigated. A design domain is subdivided into elements since the finite element method (FEM) is used, such that an optimization algorithm is able to turn every element into either fluid or solid with the goal of finding the best performing structure. This density based approach, models the solid domain as a highly impermeably porous material. To inhibit flow in the solid domain a Darcy penalization is added to the momentum equation. Moreover, in the method by Dilgen et al. boundary conditions in the other turbulent fields are also enforced using a similar penalization approach. Weaknesses and errors in the density based method are investigated by comparing solutions to ones computed on a body fitted mesh. It has been found that the largest errors in the solution, by using the state-of-the-art method, appear at the solid/fluid interface in the design. In these regions the penalizations are not applied correctly for the desired boundary conditions. Therefore, in this work it is improved on by the enforcement of the boundary condition by using the Dilation method. The Dilation method focuses on the solid/fluid region where it shifts the boundary conditions for the specific dissipation rate (𝜔) and ensures it reaches the desired value at the solid/fluid interface. Secondly, severe flow leakage is found in the “porous” solid domains using the state-of-the-art method. Flow leakage is reduced by using an improved formulation of the maximum Darcy penalization in the solid domain. Finally, the improved approach is investigated in several topology optimization cases and compared to the state-of-the-art Dilgen method. It is shown that by using the new approach, different designs with a better accuracy can be obtained. In an extreme test case, the Dilgen method resulted in an infeasible design which disconnects the flow inlets from the outlets while the new and improved method resulted in a feasible design. ... Read more