Optimization-driven design offers advantages over traditional experience-based mechanical design. As an example, topology optimization can be a powerful tool to generate body shapes for Additive Manufacturing (AM). This is helpful, when (1) load paths are non-intuitive due to complex design domains or boundary conditions, or (2) the design process is to be automated to minimize effort associated with experience-based design. However, practically relevant boundary conditions are often difficult to put into a formal mathematical language to, for example, either feed it into a topology optimization algorithm, or provide precise quantitative criteria for CAE-supported manual design. This paper presents a survey of three industry use cases and identifies three types of requirements: the first can be directly cast into parts of an optimization problem statement (∼ 40%), the second is considered indirectly by adapting the optimization problem without explicit reference to the requirement (∼ 20%), and the third is only assessed after the design is finalized (∼ 40%). For categories 2 and 3 we propose directions of improvement to support formulating complex design tasks as unambiguous design problems.

Building structures from identical components organized in a periodic pattern is a common design strategy to reduce design effort, structural complexity and cost. However, any periodic pattern will impose certain design restrictions often leading to lower structural efficiency and heavier weight. Much research is available for periodic structures with connected components. This paper addresses minimal compliance design for periodic arrangements of unconnected components. The design problem discussed here is relevant for many applications where a tightly nested, space-saving arrangement of identical components is required. We formulate an optimal design problem for a component being part of a periodic arrangement. The orientation and position of the component relatively to its neighbours are prescribed. The component design is computed by topology optimization on a design domain possibly shared by several neighbouring components. Additional constraints prevent components from overlapping. Constraint aggregation is employed to reduce the computational cost of many local constraints. The effectiveness of the method is demonstrated by a series of 2D and 3D examples with an ever-smaller distance between the components. Moreover, problem-specific ranges with only little to no increase in compliance are reported.

Abstract3D topology optimization using a density approach with penalization usually produces truss-like, open-walled structures. The coarser the mesh, the smaller the volume fraction, and the faster the penalization is increased, the more pronounced this effect tends to be. However, closed-walled designs are often more efficient and have other beneficial properties. For instance, closed walls can contribute to achieving self-supporting designs for additive manufacturing that potentially require fewer sacrificial support structures than truss-like designs. This paper presents a two-step optimization procedure for generating closed-walled designs using coarse meshes. The first step takes the usual Eulerian approach of performing a SIMP-based topology optimization on a fixed mesh. To keep thin geometrical features, like walls with a thickness below element size, penalization is switched off deliberately where the formation of such features is detected. Adopting a Lagrangian description, intermediate densities still present in the optimized design are subsequently eliminated in a second step by shrinking each element according to its density. By analogy with volumetric thermal contraction, this is accomplished by solving a fictitious thermo-elastic problem where the temperature has been replaced by a density expression. The outcome is a morphed mesh with a somewhat smoothed surface and a volume close to the specified material volume limit. This body-fitted representation of the design considerably simplifies the final conversion into a manufacturable CAD-type geometry. The two-step optimization procedure is applied to a cantilever, a torsion rod, and a disk reinforcement benchmark problem. Optimized designs are closed-walled and show very good agreement to those found for much finer meshes. Problem-specific stiffness improvements over truss-like designs between $$6\%$$ 6 % and almost $$30\%$$ 30 % were achieved and confirmed the findings previously reported by other authors.