There is significant interest today in integrating additive manufacturing (AM) and topology optimization (TO). However, TO often leads to designs that are not AM friendly. For example, topologically optimized designs may require significant amount of support structures before they can be additively manufactured, resulting in increased fabrication and clean-up costs.In this paper, we propose a TO methodology that will lead to designs requiring significantly reduced support structures. Towards this end, the concept of "support structure topological sensitivity" is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process.

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In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

As additive manufacturing expands into multi-material, there is a demand for efficient multi-material topology optimization, where one must simultaneously optimize the topology, and the distribution of various materials within the topology. The classic approach to multi-material optimization is to minimize compliance or stress while imposing two sets of constraints: (1) a total volume constraint, and (2) individual volume-fraction constraint on each of the material constituents. The latter can artificially restrict the design space. Instead, the total mass and compliance are treated as conflicting objectives, and the corresponding Pareto curve is traced; no additional constraint is imposed on the material composition. To trace the Pareto curve, first order element sensitivity fields are computed, and a two-step algorithm is proposed. The effectiveness of the algorithm is demonstrated through illustrative examples in 3D.

We demonstrate an approach of exploring design spaces to simultaneously satisfy kinematics-and physics-based requirements. We present a classification of constraints and solvers to enable postponing optimization as far down the design workflow as possible. The solvers are organized into two broad classes of design space 'pruning' and 'exploration' by considering the types of constraints they can satisfy. We show that pointwise constraints define feasible design subspaces that can be represented and computed as first-class entities by their maximal feasible elements. The design space is pruned upfront by intersecting maximal elements, without premature optimization. To solve for other constraints, we apply topology optimization (TO), starting from the pruned feasible space. The optimization is steered by a topological sensitivity field (TSF) that measures the global changes in violation of constraints with respect to local topological punctures. The TSF for global objective functions is augmented with TSF for global constraints, and penalized/filtered to incorporate local constraints, including set constraints converted to differentiable (in)equality constraints. We demonstrate application of the proposed workflow to nontrivial examples in design and manufacturing. Among other examples, we show how to explore pruned design spaces via TO to simultaneously satisfy physics-based constraints (e.g., minimize compliance and mass) as well as kinematics-based constraints (e.g., maximize accessibility for machining).