Topology Optimization For Additive Manufacturing Research Articles

Topology optimization for additive manufacturing of CFRP structures

Combining design optimization and additive manufacturing (AM) enables the full exploitation of the potential for heightening the performance of carbon fiber reinforced plastic (CFRP) structures. This study simultaneously conducts topology optimization and fiber path design by employing the radial basis function (RBF) based level set function (LSF). Fiber paths are determined instinctively for the inherent advantages of the LSF, and fiber orientations are parameterized accordingly. Manufacturing drawbacks such as gaps and overlaps can be avoided by introducing a fast-marching method. To verify the effectiveness of the optimization method, three groups of optimized and empirical designs are fabricated by the AM technique, respectively, and the experimental tests are further carried out. Finite element (FE) models are also reconstructed based on the printing schemes, and then the FE simulation is validated by the experimental tests. With the proposed optimization method, stiffnesses for all three groups of the optimal samples are significantly improved compared with the empirical counterparts. The FE modeling technique is capable of reproducing the experimental results. This study paves a new way to develop an integrated framework of optimization, additive manufacturing, experimentation, and validation to deliver high-performance CFRP structures.

The Impact of Additive Manufacturing Constraints and Design Objectives on Structural Topology Optimization

To analyze the impact of different objective functions and additive manufacturing (AM) constraints on structural topology optimization, it is necessary to perform an in-depth comparative study. This analysis should consider specific structural design factors, such as compliance, volume, or stress minimization, and assess their effects on the topology optimization for AM. In addition, the inclusion of AM constraints can have a significant influence on various aspects, including optimal part geometry, part volume, support structure volume, and structural performance. Thus, it is essential to investigate and compare these factors to determine the optimal part design for AM. This study focuses on comparing topology optimization results obtained using compliance, stress, or multi-objective minimization, with and without AM constraints. A comparative analysis was conducted in the study, utilizing three structural design examples: cantilever beam, bridge-shaped structure, and L-shaped beam. The comparison results provide insights into the effects of build orientation, AM constraints such as overhang, and different design objectives on the structural topology optimization for AM.

Concurrent Build Direction, Part Segmentation, and Topology Optimization for Additive Manufacturing Using Neural Networks

Abstract Without an explicit formulation to minimize support structures, topology optimization may create complex shapes that require an intensive use of support material when additively manufactured. We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an optimized: (1) part segmentation, (2) the topology of each part, and (3) the build direction of each part that collectively minimize the amount of support structure. Through training, the network learns a material density and segment classification in the continuous 3D space. Given a problem domain with prescribed load and displacement boundary conditions, the neural network takes as input 3D coordinates of the voxelized domain as training samples and outputs a continuous density field. Since the neural network for topology optimization learns the density distribution field, analytical solutions to the density gradient can be obtained from the input–output relationship of the neural network. We demonstrate our approach on several compliance minimization problems with volume fraction constraints, where support volume minimization is added as an additional criterion to the objective function. We show that simultaneous optimization of part segmentation along with the topology and print angle optimization further reduces the support structure, compared to a combined print angle and topology optimization without segmentation.

Multi-material topology optimization for additive manufacturing considering dimensional constraints

Recent advances in additive manufacturing have enabled the fabrication of structures in which members made of multiple materials are placed in appropriate positions. However, dimensional constraints must be considered in such a process because of the size limitations of the 3D printer. This paper proposes a topology optimization method that considers the dimensional constraints of each material component. An extended level-set method is used to represent multiple material phases in the structural design. Constraint functions are formulated to control the size of each component. The weighted covariance matrix is used for the bounding box constraint. The sensitivity is based on the topological derivative and adjoint variable method. The proposed method was applied to solving the minimum compliance problem for two- and three-dimensional numerical examples to demonstrate its effectiveness and its potential contribution to enriching designs in additive manufacturing.

Topology optimization for additive manufacturing with strength constraints considering anisotropy

Abstract Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

Space Node Topology Optimization Design Considering Anisotropy of Additive Manufacturing

At present, a large number of scholars have conducted related research on topology optimization for additive manufacturing (AM). However, there are few relevant research reports on the impact of different directions of additive manufacturing on the optimal design and manufacturing results. In this paper, using the bidirectional evolutionary optimization (BESO) method, anisotropic optimization analysis was carried out on space nodes that are currently popular in the field of additive manufacturing and topology optimization. The elastic constants in different directions were used as anisotropic material properties for optimization research in this paper through tensile testing, which was carried out on 316L stainless-steel specimens fabricated using Selective Laser Melting (SLM) technology. In addition, SEM analyses were performed to explore the microscopic appearance of the material. The study found that additive manufacturing is affected by the printing direction in terms of both macroscopic mechanical properties and microscopic material structure; the deformation obtained by anisotropic optimization was about 1.1–2.3% smaller than that obtained by isotropic optimization.

Controlling local overheating in topology optimization for additive manufacturing

A novel constraint to prevent local overheating is presented for use in topology optimization (TO). The very basis for the constraint is the Additive Manufacturing (AM) process physics. AM enables fabrication of highly complex topologically optimized designs. However, local overheating is a major concern especially in metal AM processes leading to part failure, poor surface finish, lack of dimensional precision, and inferior mechanical properties. It should therefore be taken into account at the design optimization stage. However, including a detailed process simulation in the optimization would make the optimization intractable. Hence, a computationally inexpensive thermal process model, recently presented in the literature, is used to detect zones prone to local overheating in a given part geometry. The process model is integrated into density-based TO in combination with a robust formulation, and applied in various numerical test examples. It is found that existing AM-oriented TO methods which rely purely on overhang control do not ensure overheating avoidance. Instead, the proposed physics-based constraint is able to suppress geometric features causing local overheating and delivers optimized results in a computationally efficient manner.

Topology Optimization for Additive Manufacturing

Topology Optimization for Additive Manufacturing

On preventing the dripping effect of overhang constraints in topology optimization for additive manufacturing

This article falls within the scope of topology optimization for Additive Manufacturing processes and proposes an alternative strategy to prevent the phenomenon known as the Dripping Effect. The Dripping Effect is when an overhang constraint is imposed on topology optimization processes for Additive Manufacturing and is defined as the formation of oscillatory contour trends within the prescribed threshold angle. Although these drop-like formations constitute local minimizers of the constraint function, they do not provide a printable feature, and, therefore, they neither eliminate the need to form temporary support structures. So far, there has been no general agreement on how to prevent the Dripping Effect, so this work aims to introduce a strategy that effectively prevents it, and that at the same time may be easy to extrapolate to other types of geometric overhang restrictions. This paper provides a study of the origin of the Dripping Effect and gives detailed instructions on how the proposed prevention strategy is applied. In addition, several benchmark examples where the Dripping Effect is prevented are shown.

Topology Optimization for additive manufacturing with distortion constraints

An important cause of failure in powder bed additive manufacturing is the distortion of the part due to thermal shrinkage during printing and the relaxation of residual stresses after its release from the base plate. In this paper, Additive Manufacturing simulations are coupled with Topology Optimization in order to generate designs that are not susceptible to failure associated with distortion. Two possible causes of failure are accounted for: recoater collision and global distortion of the product. Both are considered by simulation of the build process and defined as constraints in the context of a Solid Isotropic Material with Penalization method based topological optimization. The adjoint method is used to derive the sensitivities of the additive manufacturing constraints. The method is demonstrated with the 2D and 3D optimization of a bracket. Next to global topological changes, the obtained designs show features that are aimed at facilitating the printing process. These features resemble supports that are routinely applied to powder bed additive manufacturing. The formulated constraints were found to prevent excessive part distortion and associated build failures in all cases, against a modest increase in the compliance of the bracket.

Generative adversarial network for early-stage design flexibility in topology optimization for additive manufacturing

Topology optimization has become a valuable design tool for structures to be fabricated by additive manufacturing (AM). However, during early stage design, parameters are frequently evolving, resulting in multiple similar TO runs. Especially when design for manufacturing principles expand the parameter space, this iterative process is computationally burdensome, and does not take advantage of redundant information in each study. We introduce a deep learning-based framework that learns latent similarities between runs in a training set to predict near optimal designs, enabling efficient wholistic understanding of the problem setup space, which includes both loading conditions and, for the first time in this study, manufacturing process configuration. Learning was achieved using a conditional generative adversarial network (cGAN) trained on a dataset of randomized boundary conditions, loadings, and AM build orientations, and the corresponding optimal structures obtained through overhang-filtered TO. cGAN predictions showed good agreement with true optima. For even greater accuracy, predictions can be post-processed by applying a small number of TO iterations. Manifold learning techniques were used to provide further insight, and we were able to conclude that the cGAN error generally increases with distance between the load and the boundary conditions or build plate. Interestingly, in 9% of test cases, the cGAN generated structures with compliances better than the corresponding TO-calculated structures, often by as much as 50 % with an average of 7.8 %. That some of these structures appeared qualitatively different in form suggests the potential value of the approach in other domains such as generative design, where a range of alternate near-optimal designs are used to guide the ideation process.

Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing

Multidisciplinary topology optimization (TO) for additive manufacturing (AM) exhibits unprecedented design and manufacturing freedom as an effective lightweight methodology. In order to fully utilize the AM advantages of materialized arrangement in spatial and voxel-by-voxel digitalized printing, multidisciplinary TO for AM requires a full understanding of the process-structure-property-performance (PSPP) relationship to establish the quantitative correlation of part property and multiple process factors, including laser-, process-, and material-related parameters. This study incorporates the PSPP relationships of laser sintered material with topology optimizer so as to provide a guideline for TO collaborative AM design. The proposed workflow involves mapping functions of PSPP relationships via a data-driven approach and then optimizes the multiple process parameters and structural topology by the gradient-based algorithm. Compared with conventional optimization approaches, three case-dependent optimizations demonstrate the effectiveness of the proposed approach yielding encouraging improvements of lightweight performance. The multidisciplinary TO can be generally applied to types of AM technologies, establishing a strong linkage of physical product and digital design.

Optimization of Brake Calipers Using Topology Optimization for Additive Manufacturing

The weight optimization of a structure can be conducted by using fewer and downsized components, applying lighter materials in production, and removing unwanted material. Topology optimization (TO) is one of the most implemented material removal processes. In addition, when it is oriented towards additive manufacturing (AM), it increases design flexibility. The traditional optimization approach is the compliance optimization, where the material layout of a structure is optimized by minimizing its overall compliance. However, TO, in its current state of the art, is mainly used for design inspiration and not for manufacturing due to design complexities and lack of accuracy of its design solutions. The authors, in this research paper, explore the benefits and the limitations of the TO using as a case study the housings of a front and a rear brake caliper. The calipers were optimized for weight reduction by implementing the aforementioned optimization procedure. Their housings were topologically optimized, partially redesigned, prepared for 3D printing, validated, and 3D printed in titanium using selective laser melting (SLM). The weight of the optimized calipers reduced by 41.6% compared to commercial calipers. Designers interested in either TO or in automotive engineering can exploit the findings in this paper.

Accessibility of support structures in topology optimization for additive manufacturing

AbstractAdditive manufacturing (AM) and topology optimization (TO) have a synergetic relation, as AM can produce complex TO designs, and TO provides high‐performance parts that utilize the form freedom provided by AM. Recently, TO has been tailored more toward AM with the inclusion of the minimum allowable overhang angle as a design constraint: resulting designs can be built without any support structures. This work is an extension thereof, by allowing support structures only if they are accessible, such that they can be removed after manufacturing. This is achieved by applying a conventional overhang filter twice, combined with basic operations such as geometry inversion, union, and intersection. The result is an accessibility‐aware overhang filter that can be incorporated in TO. Compared with conventional overhang filtered designs, the accessibility filter results in increased part performance and better convergence behavior. Furthermore, a modular filter structure is presented to easily construct the accessibility filter, and its effectiveness is demonstrated on several numerical cases.

Topology optimization for additive manufacturing with self-supporting constraint

Topology optimization can devise structures with superior performance, while the results produced by topology optimization are often very complex and difficult to be manufactured directly. The additive manufacturing is a free-form manufacturing technique in which the component is built in a layer-by-layer manner. The integration of topology optimization and additive manufacturing technologies has the potential to bring significant synergy benefits. However, typical topology optimization algorithms have not considered the unique manufacturing limitations of additive manufacturing. This article focuses on the topology optimization for additive manufacturing considering self-supporting constraint based on the Solid Isotropic Material with Penalization (SIMP) framework. An explicit self-supporting constraint model is constructed, and the proposed method realizes self-supported by gradual evolution of supporting structures. The corresponding sensitivity analysis is investigated, which requires less computational cost and can be solved in parallel. Besides, a directional sensitivity filter is specifically proposed to promote the evolution of supporting structures. The performance and functionality of the proposed method is illustrated with three compliance minimization problems. All cases achieve self-supported successfully, and the solutions own good manufacturability.

Fatigue Behavior of Metallic Components Obtained by Topology Optimization for Additive Manufacturing

The main goal of the present research is to propose an integrated methodology to address the fatigue performance of topology optimized components, produced by additive manufacturing. The main steps of the component design will be presented, specially the methods and parameters applied to the topology optimization and the post-smoothing process. The SIMP method was applied in order to obtain a lighter component and a suitable stiffness for the desired application. In addition, since residual stresses are intrinsic to every metallic additive manufacturing process, the influence of those stresses will be also analyzed. The Laser Powder Bed Fusion was numerically simulated aiming at evaluating the residual stresses the workpiece during the manufacturing process and to investigate how they could influence the fatigue behavior of the optimized component. The effect of the built orientation of the workpiece on the residual stresses at some selected potential critical points are evaluated. The final design solution presented a stiffness/volume ratio nearly 6 times higher when compared to the initial geometry. By choosing the built orientation, it is possible impact favorably in the fatigue life of the component.

Anisotropic Multicomponent Topology Optimization for Additive Manufacturing With Build Orientation Design and Stress-Constrained Interfaces

Abstract This paper presents a multicomponent topology optimization method for designing structures assembled from additively manufactured components, considering anisotropic material behavior for each component due to its build orientation, distinct material behavior, and stress constraints at component interfaces (i.e., joints). Based upon the multicomponent topology optimization (MTO) framework, the simultaneous optimization of structural topology, its partitioning, and the build orientations of each component is achieved, which maximizes an assembly-level structural stiffness performance subject to maximum stress constraints at component interfaces. The build orientations of each component are modeled by its orientation tensor that avoids numerical instability experienced by the conventional angular representation. A new joint model is introduced at component interfaces, which enables the identification of the interface location, the specification of a distinct material tensor, and imposing maximum stress constraints during optimization. Both 2D and 3D numerical examples are presented to illustrate the effect of the build orientation anisotropy and the component interface behavior on the resulting multicomponent assemblies.

Overhang control based on front propagation in 3D topology optimization for additive manufacturing

It is attractive to combine topology optimization (TO) with additive manufacturing (AM), due to the design freedom provided by AM, and the increased performance that can be achieved with TO. One important aspect is to include the design rules associated with the process restrictions of AM to prevent the requirement of relatively large support volumes during printing. This paper presents a TO filter that enforces a minimum overhang angle, resulting in an optimized topology that is printable without the need for support structures. The filter is based on front propagation, which, as it is described by a PDE, allows for a straightforward application on unstructured meshes, to enforce an arbitrary overhang angle. Efficient algorithms developed for front propagation are used in combination with adjoint sensitivities, in order to have a minor influence on the total computational cost. The focus of this work is on the implementation of the filter for high resolution 3D cases, which requires development of the front propagation for tetrahedral elements, and its parallelization.

Simultaneous optimization of build orientation and topology for additive manufacturing

The paper presents a method to optimize build orientation and topological layout simultaneously in density-based topology optimization for additive manufacturing. Support structures are required in additive manufacturing of parts of complex shape. To eliminate or reduce support structures during the additive processes, we constrain the lower bound of the overhang angle of the optimized design. In this method, the build orientation and the density field used to represent the part are simultaneously optimized to satisfy the overhang angle constraints for part self-support. While these angle constraints are locally defined on every material point over the design domain, they are transformed into two global constraints through the Heaviside projection-based aggregations. The first directional gradient based global constraint controls the overhang angle of the solid/void interface inside the design domain to eliminate the internal supports. The second density-based global constraint controls the angle of the design domain boundary to reduce the external supports. Numerical examples on both 2D and 3D linear elastic problems are presented to demonstrate the validity and efficiency of the proposed formulations in the build orientation optimization and in the overhang angle control.

Morphable components topology optimization for additive manufacturing

This paper addresses the issue of minimizing support material in additive manufacturing (AM) during topology optimization (TO) in order to reduce material and post-processing costs. The TO method developed in this paper utilizes the moving morphable components (MMC) approach, where a structure is composed of several building blocks. This work introduces minimum build angle constraints to eliminate overhanging edges, supplementing these with penalty functions to ensure connectivity between building blocks, such that the TO output is printable. The MMC approach uses explicit geometric entities for the morphable components that are controlled by geometric parameters, such as length, thickness, and angle. These parameters are the design variables. Using this approach enables the formulation of geometric manufacturing constraints and the construction of CAD models, which are important advantages of the MMC method. Examples of a short cantilever beam and an MBB beam demonstrate the capabilities of the TO methods.