Bridging topology optimization and additive manufacturing

Topology optimization is a technique that allows for increasingly efficient designs with minimal a priori decisions. Because of the complexity and intricacy of the solutions obtained, topology optimization was often constrained to research and theoretical studies. Additive manufacturing, a rapidly evolving field, fills the gap between topology optimization and application. Additive manufacturing has minimal limitations on the shape and complexity of the design, and is currently evolving towards new materials, higher precision and larger build sizes. Two topology optimization methods are addressed: the ground structure method and density-based topology optimization. The results obtained from these topology optimization methods require some degree of post-processing before they can be manufactured. A simple procedure is described by which output suitable for additive manufacturing can be generated. In this process, some inherent issues of the optimization technique may be magnified resulting in an unfeasible or bad product. In addition, this work aims to address some of these issues and propose methodologies by which they may be alleviated. The proposed framework has applications in a number of fields, with specific examples given from the fields of health, architecture and engineering. In addition, the generated output allows for simple communication, editing, and combination of the results into more complex designs. For the specific case of three-dimensional density-based topology optimization, a tool suitable for result inspection and generation of additive manufacturing output is also provided.     

An additive manufacturing filter for topology optimization of print-ready designs

Additive manufacturing (AM) offers exciting opportunities to manufacture parts of unprecedented complexity. Topology optimization is essential to fully exploit this capability. However, AM processes have specific limitations as well. When these are not considered during design optimization, modifications are generally needed in post-processing, which add costs and reduce the optimized performance. This paper presents a filter that incorporates the main characteristics of a generic AM process, and that can easily be included in conventional density-based topology optimization procedures. Use of this filter ensures that optimized designs comply with typical geometrical AM restrictions. Its performance is illustrated on compliance minimization problems, and a 2D Matlab implementation is provided.     

Continuous front propagation-based overhang control for topology optimization with additive manufacturing

Additive manufacturing enables the nearly uncompromised production of optimized topologies. However, due to the overhang limitation, some designs require a large number of supporting structures to enable manufacturing. Because these supports are costly to build and difficult to remove, it is desirable to find alternative designs that do not require support. In this work, a filter is presented that suppresses non-manufacturable regions within the topology optimization loop, resulting in designs that can be manufactured without the need for supports. The filter is based on front propagation, can be evaluated efficiently, and adjoint sensitivities are calculated with almost no additional computational cost. The filter can be applied also to unstructured meshes and the permissible degree of overhang can be freely chosen. The method is demonstrated on several compliance minimization problems in which its computational efficiency and flexibility are shown. The current applications are in 2D, and the proposed method is readily extensible to 3D.     

Support structure design in additive manufacturing based on topology optimization

A support structure design technique for additive manufacturing (AM) is proposed that minimizes the deformation while using the least amount of support material, minimizes the time required to add the supports, and designs supports that are easily removed. This study presents a repulsion index (RI), which satisfies the easy removal requirement and minimizes the number of artifacts left on the specimen surface, and a weighting function, which quantifies the cost incurred by the time taken to build the supports. A multi-objective topological optimization based on the simple isotropic material with penalization method, continuous approximation of material distribution, and method of moving asymptotes is formulated that includes the proposed RI and cost formulation. Numerical simulations demonstrate that rational support layouts can be determined with the proposed cost-based formulation in the topological optimization, allowing designers to find design solutions with a compromise between specimen surface profile error and support structure costs.     

3D topology optimization for cost and time minimization in additive manufacturing

Structural and Multidisciplinary Optimization - As the frontier of modern-day engineering challenges pushes forward, the integration of multiple strategies to reduce manufacturing cost and increase...     

A new overhang constraint for topology optimization of self-supporting structures in additive manufacturing

This work falls within the scope of computer-aided optimal design, and aims to integrate the topology optimization procedures and recent additive manufacturing technologies (AM). The elimination of scaffold supports at the topology optimization stage has been recognized and pursued by many authors recently. The present paper focuses on implementing a novel and specific overhang constraint that is introduced inside the topology optimization problem formulation along with the regular volume constraint. The proposed procedure joins the design and manufacturing processes into a integrated workflow where any component can directly be manufactured with no requirement of any sacrificial support material right after the topology optimization process. The overhang constraint presented in this work is defined by the maximum allowable inclination angle, where the inclination of any member is computed by the Smallest Univalue Segment Assimilating Nucleus (SUSAN), an edge detection algorithm developed in the field of image analysis and processing. Numerical results on some benchmark examples, along with the numerical performances of the proposed method, are introduced to demonstrate the capacities of the presented approach.     

Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint

This paper presents a novel level set-based topology optimization implementation, which addresses two main problems of design-for-additive manufacturing (AM): the material anisotropy and the self-support manufacturability constraint. AM material anisotropy is widely recognized and taking it into account while performing structural topology optimization could more realistically evaluate the structural performance. Therefore, both build direction and in-plane raster directions are considered by the topology optimization algorithm, especially for the latter, which is calculated through deposition path planning. The self-support manufacturability constraint is addressed through a novel multi-level set modeling. The related optimization problem formulation and solution process are demonstrated in detail. It is proved by several numerical examples that the manufacturability constraints are always strictly satisfied. Marginally, the recently popular structural skeleton-based deposition paths are also employed to assist the structural topology optimization, and its characteristics are discussed.     

Combined optimization of part topology,support structure layout and build orientation for additive manufacturing

Additive manufacturing (AM) enables the fabrication of parts of unprecedented complexity. Dedicated topology optimization approaches, that account for specific AM restrictions, are instrumental in fully exploiting this capability. In popular powder-bed-based AM processes, the critical overhang angle of downward facing surfaces limits printability of parts. This can be addressed by changing build orientation, part adaptation, or addition of sacrificial support structures. Thus far, each of these measures have been studied separately and applied sequentially, which leads to suboptimal solutions or excessive computation cost. This paper presents and studies, based on 2D test problems, an approach enabling simultaneous optimization of part geometry, support layout and build orientation. This allows designers to find a rational tradeoff between manufacturing cost and part performance. The relative computational cost of the approach is modest, and in numerical tests it consistently obtains high quality solutions.     

Misalignment topology optimization with manufacturing constraints

Structural and Multidisciplinary Optimization - This work aims at introducing misalignment response in the design of mechanical transmission components using topology optimization. Misalignment...     

A subtractive manufacturing constraint for level set topology optimization

Structural and Multidisciplinary Optimization - We present a method for enforcing manufacturability constraints in generated parts such that they will be automatically ready for fabrication using a...     

Robust topology optimization accounting for spatially varying manufacturing errors

This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts of the structure to become thinner or thicker than intended. This type of error is modeled by means of a projection technique: a density filter is applied, followed by a Heaviside projection, using a low projection threshold to simulate under-etching and a high projection threshold to simulate over-etching. In order to simulate the spatial variation of the manufacturing error, the projection threshold is represented by a (non-Gaussian) random field. The random field is obtained as a memoryless transformation of an underlying Gaussian field, which is discretized by means of an EOLE expansion. The robust optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte Carlo simulation is performed, considering 100 random realizations of the manufacturing error. A more thorough Monte Carlo simulation with 10000 realizations is performed to verify the results obtained for the final design. The proposed methodology is successfully applied to two test problems: the design of a compliant mechanism and a heat conduction problem.     

Topology optimization of easy-removal support structures for additive manufacturing

Structural and Multidisciplinary Optimization - This paper presents a density-based topology optimization approach to design easy-removal support structures for additive manufacturing (AM). First,...     

Support optimization in additive manufacturing for geometric and thermo-mechanical constraints

Structural and Multidisciplinary Optimization - Supports are often required to safely complete the building of complicated structures by additive manufacturing technologies. In particular, supports...     

Robust multiphase topology optimization accounting for manufacturing uncertainty via stochastic collocation

Structural and Multidisciplinary Optimization - This paper presents a computational framework for multimaterial topology optimization under uncertainty. We combine stochastic collocation with...     

Optimizing supports for additive manufacturing

In additive manufacturing process, support structures are often required to ensure the quality of the final built part. In this article, we present mathematical models and their numerical implementations in an optimization loop, which allow us to design optimal support structures. Our models are derived with the requirement that they should be as simple as possible, computationally cheap, and, yet, based on a realistic physical modelling. Supports are optimized with respect to two different physical properties. First, they must support overhanging regions of the structure for improving the stiffness of the supported structure during the building process. Second, supports can help in channeling the heat flux produced by the source term (typically a laser beam) and thus improving the cooling down of the structure during the fabrication process. Of course, more involved constraints or manufacturability conditions could be taken into account, most notably removal of supports. Our work is just a first step, proposing a general framework for support optimization. Our optimization algorithm is based on the level set method and on the computation of shape derivatives by the Hadamard method. In a first approach, only the shape and topology of the supports are optimized, for a given and fixed structure. In a second and more elaborated strategy, both the supports and the structure are optimized, which amounts to a specific multiphase optimization problem. Numerical examples are given in 2D and 3D.     

Topology optimization of support structure layout in metal-based additive manufacturing accounting for thermal deformations

This paper focusses on topology optimization of support structures for metal-based additive manufacturing. Processes based on powder bed fusion are subject     

Benchmarking optimization solvers for structural topology optimization

The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.     

Stress-based topology optimization for continua

We propose an effective algorithm to resolve the stress-constrained topology optimization problem. Our procedure combines a density filter for length scale control, the solid isotropic material with penalization (SIMP) to generate black-and-white designs, a SIMP-motivated stress definition to resolve the stress singularity phenomenon, and a global/regional stress measure combined with an adaptive normalization scheme to control the local stress level.     

Parts internal structure definition using non-uniform patterned lattice optimization for mass reduction in additive manufacturing

Engineering with Computers - Today, being able to generate and produce shapes that fit mechanical and functional requirements and having as low as possible mass is crucial for aerospace and...     

Robust beam compensation for laser-based additive manufacturing

Today’s software for laser-based additive manufacturing compensates for the finite dimensions of the laser spot by insetting the contours of a solid part. However, features having smaller dimensions are removed by this operation, which may significantly alter the structure of thin-walled parts. To avoid potential production errors, this work describes in detail an algorithmic framework that makes beam compensation more reliable by computing laser scan paths for thin features. The geometry of the features can be adjusted by the scan paths by means of five intuitive parameters, which are illustrated with examples. Benchmarks show that the scan path generation comes at a reasonable cost without altering the computational complexity of the overall beam compensation framework. The framework was applied to Selective Laser Melting (SLM) to demonstrate that it can significantly improve the robustness of additive manufacturing. Besides robustness, the framework is expected to allow further improvements to the accuracy of additive manufacturing by enabling a geometry-dependent determination of the laser parameters.