Advances in additive manufacturing (AM) have drawn considerable interest due to its ability to produce geometrically complex structure, such as lattice materials. In this work, a novel methodology is ...proposed to design graded lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structure design with predictable yield performance. Instead of using the power law of material interpolation in the SIMP method, asymptotic homogenization method is employed to compute the effective elastic properties of lattice material in terms of design variable, i.e. relative density. For yield strength, a multiscale failure model is proposed to capture yield strength of microstructure with macroscopic stress. At macroscale, a modified Hill’s yield criterion is employed to describe anisotropic yield strength of lattice material. The material constants in Hill’s model are assumed to be a function of relative density, and thus a model is built up to formulate yield strength of lattice structure with macroscopic stress. The experimental verification on the printed samples demonstrates that both the homogenized elastic model and yield model can accurately describe the elasticity and plasticity of the lattice structure. Based on the proposed material interpolation for lattice structure, a lattice structure topology optimization framework is proposed for minimizing total weight of the structure under stress constraint. The sensitivity analysis is performed for the implementation of the optimization algorithm. Two three-dimensionally numerical examples are performed to demonstrate the effectiveness of the proposed optimization method, as well as accuracy of the proposed homogenization technique for graded lattice structure design. Experiment is conducted to systematically examine yielding of the optimally graded lattice structure design and compare its performance with a uniform structure. It is found that the proposed optimization framework is valid for the design examples examined and can significantly enhance mechanical performance of the structure (i.e. yield loading, stiffness, energy absorption, etc.)
A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-sensitivity method, PTO is simple to understand, easy to implement, and is also efficient ...and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing optimality criteria method which computes sensitivities. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.
Additive manufacturing technology provides a revolutional way of producing engineering structures regardless of their geometric complexity. Hence, topology optimization technique is rapidly becoming ...a promising tool to design additive manufactured structures to reduce weight and achieve optimal performance simultaneously. However, a common feature of additive manufactured materials is their anisotropy arising from the design and manufacturing process. Therefore, this viewpoint paper aims at presenting an overview of the anisotropy of additive manufactured materials and providing some insights into the role of anisotropy in topology optimization of additive manufactured load-bearing structures.
Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, for example, machining and injection molding ...or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-to-optimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors’ perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.
Laser powder bed metal additive manufacturing (AM) has been widely accepted by the industry to manufacture end-use components with complex geometry to achieve desirable performance (i.e. conformal ...cooling). However, residual stress and large deformation introduced in the laser AM process lead to severe issues, such as cracks, delamination, and large deformation. These issues result in the stoppage of powder spreading and warpage of the component. To overcome these issues, a novel optimization framework based on fast process modeling is proposed to find the optimal build orientation by minimizing the maximum residual stress and support structure volume. For support generation, a voxel-based methodology is proposed to systematically capture support surfaces from STL file, form support structure, and generate Cartesian mesh for fast process modeling. Instead of using conformal mesh, the voxel-based fictitious domain method is used to calculate the stress distribution in the design domain including the support structure, which is represented by the homogenized model. This can circumvent time-consuming mesh generation for geometrically complex geometry and its support structure during the optimization iterations, thus making it possible to minimize residual stress through orientation optimization based on process modeling. Due to its self-supporting and open-cell nature, lattice structure is employed as the support structure to anchor the overhangs to the substrate to prevent distortion resulting from residual stress. Asymptotic homogenization (AH) method is employed to compute the effective properties of lattice structure, while a multiscale model is proposed to compute the yield strength. In particular, the multi-objective optimization including both the residual stress and support volume is discussed and investigated in this work. Experimental validation is conducted on a realistic component with some geometric complexity. By comparing the component and support structure without build orientation optimization, it is found that the proposed framework can significantly reduce the influence of the residual stress on the printed part, ensure the manufacturability of the design, and decrease the material consumption for the sacrificial support structure simultaneously.
•A new voxel-based overhang detection method is proposed for AM simulation.•A fictitious domain method is developed to simulate residual stress in metal AM.•Residual stress and support volume are minimized through the optimization method.•Experiments are conducted to investigate the efficiency of the proposed framework.
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.
•This paper presents a deposition path planning-integrated structural topology optimization method for 3D additive manufacturing.•Local material anisotropy is addressed by considering the build direction and the in-plane raster directions.•The support-free manufacturability constraint is addressed through a novel multi-level set modeling.•Both the contour-offset and structural skeleton-based deposition path patterns have been considered.
This paper proposed a new topology optimization method based on geometry deep learning. The density distribution in design domain is described by deep neural networks. Compared to traditional ...density-based method, using geometry deep learning method to describe the density distribution function can guarantee the smoothness of the boundary and effectively overcome the checkerboard phenomenon. The design variables can be reduced phenomenally based on deep learning representation method. The numerical results for three different kernels including the Gaussian, Tansig, and Tribas are compared. The structural complexity can be directly controlled through the architectures of the neural networks, and minimum length is also controllable for the Gaussian kernel. Several 2-D and 3-D numerical examples are demonstrated in detail to demonstrate the effectiveness of proposed method from minimum compliance to stress-constrained problems.
Significant advance in additive manufacturing (AM) is leading to a paradigm shift in design-for-manufacturing. The manufacturability concern over geometry complexity has largely been removed by AM, ...which will greatly promote design creativity. A representative paradigm shift is the increasing focus on lattice structures which can be efficiently manufactured by AM. Specifically, lattice structures have been used to replace conventional solid materials to reduce weight and enhance multi-functional properties. Hence, lattice structure topology optimization (LSTO) has drawn remarkable interest for being an optimal lattice infill design tool. Despite the extensive investigation on LSTO, this paper addresses a novel aspect in the concurrent optimization of lattice infill and design-dependent movable features, on which boundary conditions are prescribed. This type of problem has practical importance, such as cooling channel system (forced convective boundary) design used in different thermal management applications, which is challenging to solve numerically due to the increased complexity in sensitivity calculation. In the proposed method, parametric level set function is used to represent the movable feature geometry and accordingly, the thermal boundary conditions are implicitly applied. A detailed sensitivity analysis is performed to provide the effective sensitivity information for design update. Several numerical examples are provided to prove the effectiveness of the proposed method. In particular, the proposed methodology is applied to the concurrent optimization of cooling channels and the optimized design is printed out to demonstrate the manufacturability.
Additive manufacturing (AM) eliminates many of the geometric restrictions in conventional manufacturing, and hence complex geometry, such as lattice structures, can be produced with little additional ...cost. AM designs based on lattice structuring have become increasingly popular as it possesses tunable properties and can be designed to be self-supporting easily. For these reasons, lattice infill recently has been actively studied and a variety of lattice structure topology optimization methods have been developed. On the other hand, lattice infill cannot span the design domain when there are functional features in the mechanical design (e.g. assembly holes and cooling channels). Also, the geometric form of these functional features need to be maintained and cannot be replaced by the lattice structure. Thus far, lattice structure topology optimization considers these features fixed in space without design freedom and obviously, this treatment lacks overall optimality. To fill this critical gap, this work combines the feature evolution into the variable-density lattice structure topology optimization framework, which leads to a concurrent lattice density and feature layout optimization method. Parametric level set functions are employed for the feature representation and R-functions are adopted to combine the density and level set fields. Sensitivity information is calculated on both the lattice densities and feature parameters, in order to solve the problem through a unified gradient-based approach. Several 3D numerical examples are provided to demonstrate the efficiency and robustness of the proposed method.
We study primary care physicians' prevention and monitoring technology adoption. Physicians' adoption decisions are based on benefits and costs, which depend on payment incentives, educational ...assistance, and market characteristics. The empirical study uses national Norwegian register and physician claims data between 2009 and 2014. In 2006, a new annual comprehensive checkup for Type 2 diabetic patients was introduced. A physician collects a fee for each checkup. In 2013, an education assistance program was introduced in two Norwegian counties. We estimate adoption decisions by fixed‐effect regressions, and two‐part and hazard models. We use a difference‐in‐difference model to estimate the education program impact. Fixed‐effect estimations and separate analyses of physicians who have moved between municipalities support a peer effect. The education program has a strongly positive effect, which is positively associated with a physician's number of diabetic patients, and the fraction of physician‐adopters in the same market.
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