Abstract
Several filter approaches that introduce additive manufacturing-related overhang constraints in topology optimization exist. However, a drawback of these is that exact satisfaction of overhang constraints produces sharp inward corners resulting in stress singularities. The present paper therefore modifies such filter approaches by a penalty formulation, where the choice of penalty factor regulates how closely the overhang constraint is satisfied. By appropriately choosing certain weight factors in the penalty function, the cost of support structures is also reflected in the formulation in a simple and computationally inexpensive way. The method is demonstrated by parameter studies using the classical MBB beam, using both structured and unstructured meshes.
Highlights
Topology optimization (TO) and additive manufacturing (AM) constitute an unusually striking match of design and manufacturing method, sharing the possibility of very general shapes and forms (see Liu et al (2018) for a recent overview)
The overhang constraint, implying that the angle a surface tangent makes to the AM build direction should be below a certain value, is of prime importance
We refer to the classical paper by Duysinx and Bendsøe (1998), where it is indicated that, in case of SIMP penalization, the natural choice of local stress is obtained by scaling the standard stress by the same factor as the elasticity modulus, i.e., by ρir, r = 3, where the standard stress is calculated from the displacements without considering density scaling
Summary
Topology optimization (TO) and additive manufacturing (AM) constitute an unusually striking match of design and manufacturing method, sharing the possibility of very general shapes and forms (see Liu et al (2018) for a recent overview). The overhang free design is compared to the physical design and a penalty term is added to the objective function of the TO problem, which implies a cost for deviation between the physical design and the overhang free design This takes away the sharp corners present in original method of Langelaar, a feature that should be necessary when, e.g., stress constraints are included in TO. A certain choice of weight factors in the penalty term makes overhang far from the base plates more costly, less preferable in an optimal solution, than overhang close to the base plate It should be noted, that the method does not include a precise specification of, e.g., what length of overhang is allowed or what rounding is obtained at corners. As it is usual in TO, the suggested optimized designs should be seen as conceptual designs that need refinement and further analysis
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