Topology Optimization for Additive Manufacturing

Anders Clausen

    Research output: Book/ReportPh.D. thesis

    1835 Downloads (Pure)


    This PhD thesis deals with the combination of topology optimization and additive man-ufacturing (AM, also known as 3D-printing). In addition to my own works, the thesis contains a broader review and assessment of the literature within the field.
    The thesis first presents a classification of the various AM technologies, a review of relevant manufacturing materials, the properties of these materials in the additively manufactured part, as well as manufacturing constraints with a potential for design optimization.
    Subsequently, specific topology optimization formulations relevant for the most im-portant AM-related manufacturing constraints are presented. These constraints are di-vided into directional and non-directional constraints.
    Non-directional constraints include minimum/uniform length scale and a cavity constraint. It is shown that modified filter boundary conditions are required in order for the so-called robust formulation to ensure satisfaction of the minimum feature size in the vicinity of the design domain boundary.
    The most important directional constraint is a so-called overhang constraint. In relation to this, mainly two formulations from the literature are discussed.
    My own work has mainly been focused on better exploiting the new opportunities provided by AM. These are treated under the categories of multi-material applications, multi-scale approaches, and interface problems which incorporates elements from both of the preceding categories. It is shown how the material microstructure for a material with programmable, nearly constant Poisson’s ratio for large deformations may be designed and fabricated using direct ink writing. Structures are generated for the full interval [−0.8, 0.8], all with uniform feature size and a continuous print path, ensuring the potential for scalable manufacturing.
    In relation to interface problems it is shown how a flexible void area may be included into a standard minimum compliance problem by employing an additional design variable field and a sensitivity filter. Furthermore, it is shown how the design of coated structures may be modeled as a differentiable topology optimization problem. This is done partly by using spatial gradients of the density variable in the interpolation function between the design variable field and physical variables, partly by employing a two-step filtering scheme in order to control the gradient field. The approach is implemented for both 2D and 3D problems. A special case of this type of design problem is porous shell structures which are often used within AM. Based on numerical as well as experimental studies it is shown that such structures have a lower stiffness than fully solid structures, however, they possess significantly improved buckling properties and are less sensitive towards load perturbations. These properties are inherently ensured, that is, without the explicit definition of additional constraints.
    Original languageEnglish
    Place of PublicationKgs. Lyngby
    PublisherTechnical University of Denmark
    Number of pages154
    ISBN (Electronic)978-87-7475-466-4
    Publication statusPublished - 2016
    SeriesDCAMM Special Report


    Dive into the research topics of 'Topology Optimization for Additive Manufacturing'. Together they form a unique fingerprint.

    Cite this