Date of Award
Doctor of Philosophy (PhD)
Aerospace Engineering Sciences
To unlock the potential of advanced manufacturing technologies like additive manufacturing, an inherent need for sophisticated design tools exists. In this thesis, a systematic approach for designing printed active structures using a combined level-set (LS) extended finite element (XFEM) density topology optimization (TO) scheme is developed. This combined scheme alleviates the downsides of both LS and density based TO approaches while building upon the advantages of either method. Thus, a superior design optimization approach is created, which, when coupled with the XFEM, yields a highly accurate physical modeling method. The unique capabilities of this combined approach include hole nucleation and minimum feature size control while retaining a crisp and unambiguous definition of the material interface. Different stabilization and regularization schemes are developed to maximize the robustness of the proposed method. Ensuring sufficient numerical stability during the TO process is especially critical when using large deformation nonlinear elasticity models. Without sufficient stabilization, divergence in the analysis or optimization process is frequently encountered. Therefore, a novel explicit LS regularization scheme, based on the construction of a signed distance field (SDF) for every design iteration, is developed in this thesis. It is also demonstrated that the obtained SDF can be used for minimum feature size control and control of the mean curvature during a TO process. Numerical design examples in 2D and 3D are presented to demonstrate the applicability of the proposed combined TO method. Physical specimens of 4D printed samples are used to validate the accuracy of the predicted structural performance by the developed thermomechanical large-strain XFEM model. Finally, conclusions and recommendations for future work are presented and the original contributions made in this thesis are summarized.
Geiss, Markus Josef, "Level-Set-XFEM-Density Topology Optimization of Active Structures: Methods and Applications" (2019). Aerospace Engineering Sciences Graduate Theses & Dissertations. 254.