Solid Mechanics

Faculty of Engineering, LTH

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Implementation of constraints for Additive Manufacturing in Topology Optimization

MSc student: Kajsa Söderhjelm

Supervisor: Mathias Wallin


Additive manufacturing permits fabrication of very complex geometry which is usually not possible with conventional manufacturing techniques. Topology optimization creates functionally optimized components where the outcome usually becomes geometrically complex solutions.  The design freedom that comes with additive manufacturing makes these two technologies a perfect match for each other.  In order to ensure manufacturability using additive manufacturing usually support material is necessary. Support material is used to overcome certain constraints, especially overhang, to prevent collapsing during fabrication. If support material is used during manufacturing it will increase the print time and material usage and resources to be able to remove it is necessary. Instead of using support structures one could modify the optimal topology to enable additive manufacturing. Langelaar (2017) proposes a method to overcome the overhang constraint that can be included in conventional density based topology optimization and is implemented with a density filter.


The aim of this master thesis is to further examine the method proposed by Langelaar (2017). The optimization problem will be solved using the optimality criteria with a density filter. It will continue with examining the possibility to alter Helmholtz PDE filter and use the density gradients to obtain a self supporting structure. The proposed method will be solved using the method of moving asymptotes with an altered Helmholtz PDE filter. Isotropic and linear elastic material will be considered.


Langelaar, M. (2017). An additive manufacturing filter for topology optimization of print-ready designs. Structural and Multidisciplinary Optimization, 55(3):871–883

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