Topology Optimization Results Research Articles

Multi-objective topology optimization and numerical investigation of heat sinks based on triply periodic minimal surface lattices

In thermal management applications, such as heat sinks (HSs) for electronic devices, cellular materials have extensively been employed. In recent years, there has been a growing attention towards employing topology optimization for enhancing hydraulic and heat transfer performance of HSs by optimizing their topology. The utilization of triply periodic minimal surface (TPMS) based structures presents distinctive prospects for customizing the design and performance of HSs. However, their potential remains unexplored in the context of customizing additively manufactured porous optimized HSs. Consequently, there is a need for research aimed at examining their coupled hydraulic and thermal performance. Density mapping approaches are used to build a variable density TPMS-based HSs from the output of topology optimization by applying the TPMS level-set equations that relate relative density and the level-set constant. In this work, a relative density mapping methodology is applied to thermo-fluid optimization problem to design a TPMS-based convective cooling system. An in-house MATLAB code was developed to perform a multi-objective topology optimization. After that, uniform and variable density (mapped from topology optimization results) TPMS-based HSs are analyzed using Star-CCM + CFD software to investigate their hydraulic and heat transfer performance. An experimental setup was established, and the numerical results were validated using uniform TPMS-based heat sinks. Results showed that incorporating TPMS with topology optimization has a great potential in thermal management applications as pressure drop across the heat sink was reduced while maintaining the performance.

Optimization on distribution of high thermal conductivity materials in metal hydride reactor for improving heat transfer performance

The poor heat transfer performance significantly limits the reaction rate of hydrogen storage and release in metal hydrides reactors. In this work, the expanded graphite was used as high thermal conductivity materials (HTCMs), its optimal distribution in metal hydrides reactor was obtained by topology optimization method to enhance the heat transfer performance. Comparative studies on the hydrogen storage and release performance were conducted for the optimal HTCMs distribution model, uniform HTCMs distribution model, reconstructed model, and unimproved model to validate the optimization results. Finally, the effect of HTCMs contents was also studied. The results show that the optimization results shorten the hydrogen storage and release time by 32.3 % and 15.9 %, respectively, compared to the uniform distribution model. Besides, the proposed optimization scheme exhibits good performance under different HTCMs contents. When the content was set to 12 %, the optimized model reduces the hydrogen storage and release time by 28.5 % and 10.8 %, compared to the results of uniform distribution. The method and results of topology optimization have high reliability, and the HTCMs distribution designed by topology optimization has better hydrogen storage and release performance compared to original designs, it is widely applicable.

Generating a Multi-Material Lattice Structure through a Modified Relative Density Mapping Algorithm

Multi-material lattice structures demonstrate superior mechanical advantages and lightweight potential, enabling it preferable in many engineering fields, especially with the rise of additive manufacturing. However, employing multi-scale topology optimization inherently involves computational complexities of designing the macromaterial distribution and microlattice geometric size simultaneously. In this paper, a modified relative density mapping (MRDM) method is proposed, which generates a multi-material lattice structure by projecting the continuum multi-material topology optimization results. The proposed method extends the standard relative density mapping (RDM) method to multi-material problem and improves the performance. To achieve such purpose, a new mapping relation considering multi-material density and stress information is introduced to generate mapping weight of materials, which is the most novel contribution. Second, to avoid intersection of different materials, two types of material mapping strategies, namely continuous mapping strategy, and discrete mapping strategy, are introduced to generate multi-material lattice structure using the mapping weight of materials. Several numerical examples are exhibited, which demonstrate that the proposed method is capable of generating a multi-material lattice structure with clear material interface and good performance.

Application of Surface-Based Smoothing Methods for Topology Optimization Results

Topology optimization (TO) is becoming an essential part of designing new or modifying current parts to improve their properties. A typical problem of TO in structural applications is minimizing compliance with volume (mass) constraints. TO is often complemented by additive manufacturing which allows the printing of complex geometries. Resulting geometries are dependent on the used method, most of the time it is the finite element method. The exported geometry from the optimization procedure, however, tends to have a lot of sharp edges, which causes problems with stress distribution, aesthetics and manufacturing (even if it is additive manufactured). The aim of this paper is to review, apply smoothing techniques on the surface of bodies, Laplacian and Taubin smoothing, and compare the results of smoothing. To fulfill this aim, we developed a smoothing procedure and evaluated the criteria of smoothed-out polymer geometries.

Numerical and Experimental Evaluation of Structured Material for Use in Multiscale Topology Optimization

Multiscale topology optimization is a powerful tool for engineers seeking a design with minimum weight and maximum stiffness, using a structured material in the form of a lattice structure. Furthermore, the current trend is to combine multiple lattice topologies in one component to achieve the best possible response to local loading conditions while minimizing weight. Therefore, herein, a numerical and experimental evaluation by compression tests in two directions is performed for six basic lattice topologies and two hypotheses are tested. The first hypothesis states that an additional weight saving of more than 30% can be achieved by a better choice of lattice topology. The second hypothesis is based on the manufacturing limitations of the laser powder bed fusion technology and the assumption that a favorable loading direction parallel to the building direction exists. The first hypothesis is only confirmed for loading in the direction parallel to the building direction and the second only for two lattice topologies. When both hypotheses are combined, the additional weight reduction of the multiscale topology optimization result is 44.5% according to the numerical results and 32.7% according to the experimental verification.

Multi-field coupling in designing embedded microchannels for three-dimensional integrated chip: A topology optimization approach

Topology optimization methods have shown promise in enhancing the heat transfer performance of microchannel structures. However, the thermal-electrical-force multi-field coupling effects in three-dimensional integrated chips present a complex heat generation scenario that necessitates their consideration in the design of embedded microchannel structures. Here, we perform topology optimization of embedded microchannels specifically tailored for three-dimensional integrated chip, with a specific focus on the multi-field coupling effects of through-silicon-via structures within the topology optimization process. A new and improved 2D microchannel structure that exhibits superior heat transfer performance was obtained by analyzing the effects of pressure drop constraints within the channel, as well as fixing the microfin diameter and local heat flux of through-silicon-via. Furthermore, the obtained topology optimization results were validated through rigorous three-dimensional numerical simulations. The findings demonstrate that the new microchannel structure, when compared to the original microfin model, yields a significant improvement in the comprehensive heat transfer performance coefficient, achieving a remarkable enhancement factor of 1.43. Furthermore, under identical flow conditions, the structural stress within the chip experiences a substantial reduction of 43.9%. These outcomes underscore the efficacy of the topology optimization approach in effectively addressing the thermal management challenges associated with three-dimensional integrated chip.

Topology optimization of labyrinth seals using interface identification techniques

Labyrinth seals are mechanical devices that reduce the leakage between moving components of rotating machines. They are crucial for determining the performance of these machines and essential for reducing greenhouse gas emissions. Therefore, mathematical optimization algorithms for labyrinth seals are of high interest. This work concerns the topology optimization of labyrinth seals, which is a challenging task because the optimizer must distribute solids at different velocities to properly model the flow in the cavity of the labyrinth seal. Also, the model must not allow the optimizer to close the fluid channel or to leave free-floating islands of solid elements in the final design. Therefore, the interface identification method based on a series of erosion-dilate projection filters is used to model the fluid channel as the interface between the rotor and stator, allowing the representation of different velocities and avoiding the channel closure. The virtual temperature method is employed as a connectivity constraint to avoid free-floating islands of solid material. Still, thin structural members appear in the optimized designs, so geometric constraints are used to impose the minimum length scale on rotor and stator components. The final topology optimization results are labyrinth seals with contorted channels constricted to the minimum allowed gap size (as expected for low Reynolds flows), showing the success of the proposed formulation. The staggered and stepped labyrinth seal configurations are optimized to show the generality of the method.

Development and assessment of a methodology for abstraction of topology optimization results to enable the substitution of optimized beams

Improving mechanical topology optimization (TO) results by substituting biomimetic beams is one possibility to achieve designs of mechanical components that are highly sustainable and show good mechanical performance. Because of their geometric complexity, such designs were found to be well-suited for production by laser additive manufacturing. One obstacle of incorporating biomimetics beams in TO designs is the lack of detailed design methodologies. Röver et al. [“Methodology for integrating biomimetic beams in abstracted topology optimization results,” in Proceedings of the ASME 2022 International Mechanical Engineering Congress and Exposition. Volume 4: Biomedical and Biotechnology; Design, Systems, and Complexity Columbus, OH, 30 October–3 November (ASME, New York, 2022)] proposed a corresponding design concept. Building on their concept, we present in this work a detailed methodology for abstraction of TO results to a design consisting of ball nodes and cylindrical beams. Using such an auxiliary design, the internal forces and moments of the beams can be evaluated to allow for the substitution of suitable biomimetic beams to generate biomimetic component designs in a next step. We present a skeletonization algorithm based on the potential field approach. Using the skeletonization and an additional analysis of the dimensions of the beams in the TO result, the algorithm develops an auxiliary design of the original TO result. The final algorithm was applied to three common TO results to obtain one auxiliary component design each. The developed algorithm was found to generate abstractions that were well-suited for use in the methodology proposed in Röver et al. [“Methodology for integrating biomimetic beams in abstracted topology optimization results,” in Proceedings of the ASME 2022 International Mechanical Engineering Congress and Exposition. Volume 4: Biomedical and Biotechnology; Design, Systems, and Complexity Columbus, OH, 30 October–3 November (ASME, New York, 2022)], because internal forces and moments in the abstracted beams could be evaluated with less effort. Therefore, our work contributes to a detailed design methodology for biomimetic mechanical components in the field of design for additive manufacturing.

Multidisciplinary collaborative topology optimization method for perforated plates

Perforated plate is a connection structure able to provide variety of functions such as load-bearing and flow-through capabilities. The current designs of perforated plate are mostly obtained by optimization after establishing an initial model empirically, ignoring the influence across different disciplines and lacking a systematic design process. In this study, we proposed a multidisciplinary topology optimization method to address the design issues of holes on perforated plates. The response states of perforated plate in structural mechanics, fluid mechanics, and vibration were determined using disciplinary analysis, and a single disciplinary topology optimization model was established based on this. A multidisciplinary topology optimization model was constructed based on the disciplinary coupling relationship and collaborative optimization method, with material retention as a shared variable. The continuous change process of materials was discretized by taking a finite number of values for shared variables, and the trend of topology optimization results with respect to material retention was obtained. The hole parameters were converted individual hollow parameters of the material by establish functional and process, and the final topology optimization result was obtained by combining partition collaboration. The method and process were used to optimize the connecting plate of top nozzle, and the results showed higher comprehensive performance compared to engineering case.

Structure Improvement and Optimization of Gantry Milling System for Complex Boring and Milling Machining Center

To enhance the efficiency and machining precision of the TX1600G complex boring and milling machining center, a study was conducted on the structure of its gantry milling system. This study aimed to mitigate the influence of factors such as structural quality, natural frequency, and stiffness. The approach employed for this investigation involved mechanism topology optimization. To initiate this process, a finite element model of the gantry milling system structure was established. Subsequently, an objective function, comprising strain energy and modal eigenvalues, was synthesized. This objective function was optimized through multi-objective topology optimization, taking into account certain mass fraction constraints and considering various factors, including processing technology. The ultimate goal of this optimization was to create a gantry milling structure that exhibited high levels of dynamic and static stiffness, a superior natural frequency, and reduced mass. To validate the effectiveness of these topology optimization results, a comparison was made between the new and previous structures. The findings of this study serve as a valuable reference for optimizing the structure of other components within the machining center.

Automatic construction method for editable CAD models of isogeometric topology optimization results

Automatic construction method for editable CAD models of isogeometric topology optimization results

Optimization of Components with Topology Optimization for Direct Additive Manufacturing by DLMS.

This paper presents a novel design methodology that validates and utilizes the results of topology optimization as the final product shape. The proposed methodology aims to streamline the design process by eliminating the need for remodeling and minimizing printing errors through process simulation. It also eliminates the repeated export and import of data between software tools. The study includes a case study involving the steering column housing of a racing car, where Siemens NX Topology Optimization was used for optimization, and verification analysis was conducted using the NX Nastran solver. The final solution was fabricated using AlSi10Mg via direct metal laser sintering on a 3D printer and successfully validated under real conditions. In conclusion, this paper introduces a comprehensive design methodology for the direct utilization of topology optimization, which was validated through a case study, yielding positive results.

Generative design of space frames for additive manufacturing technology

A generative design methodology is presented that solves for minimum volume and compliance space-frame systems, with consideration of stress and buckling constraints. The solution space is explored using formal topology optimisation routines. A parameterisation method converts voxelised topology optimisation solutions into skeletonised connectivity representations. An inequality constrained gradient descent optimisation method optimises and defines cross-sectional geometry. This enables fast and automatic solution generation, providing designers with sets of high-performing problem solutions. Skeleton representations provide an inexpensive modelling tool for parallel analysis of physical problems difficult to model using topology optimisation. Geometry is represented using traditional engineering cross-sections with well understood behaviour. This improves certainty in the performance of solutions, simplifying certification processes. The generative design of a structural aerospace bracket for additive manufacture has been used as a case study within this research. A design of experiments produced 360 topology optimisation results, altering input variables and discretisation resolution to identify their effect on solution outcomes and the performance of parameterisation. The proposed method was found to robustly generate high-performing solutions utilising low-resolution topology optimisation. Additionally, 6 high-performing topologies were identified, providing designers with a set of solutions to select from. Limitations on the parameterisation process were identified, with topology optimisation solutions with volume fractions above 0.2 not parameterising successfully, and simulations with a resolution of 5 mm element size and below generating low performing skeletonised topologies.

Free-mounted cooling plate multi-objective topology optimization method towards precision machine tool heat dissipation: An experimental and numerical study

Machining accuracy is reduced by precision machine tool thermal deformation. Currently, machine tool temperature and thermal deformation are usually controlled by optimizing original machine tool structure or using a cooling system. However, these methods are poor in generalization ability and convenience, and traditional cooling channels have shortcomings of a large flow resistance and low heat transfer efficiency. In this study, a cooling plate multi-objective topology optimization method towards precision machine tool heat dissipation is proposed. Firstly, multi-objective topology optimization model is established with maximum heat exchange and minimum fluid dissipation energy as objective function. Then effect of various design parameters on topology optimization results is investigated. Penalty factor and design Reynolds number are taken as design variables, and heat dissipation and flow performances of different topology optimization results are analyzed. Response surface model is constructed, and then an analytical model of average temperature in design domain and pressure drop generated by Pareto fronts under different working conditions are obtained. Furthermore, a full-size three-dimensional thermal-fluid interaction verification model is constructed, and cooling and flow performances of topology optimization cooling plate are compared with those of traditional spiral cooling plate. Numerical results show that cooling performance of topology optimization cooling plate is stronger than that of spiral cooling plate at high Reynolds number, and pressure drop of topology optimization cooling plate is reduced by 85.38% compared with that of spiral cooling plate. Finally, topology optimization and spiral cooling plates are manufactured, and experimental platform is built to evaluate heat dissipation and flow performances of cooling plates. For topology optimization plate, maximum deviations between simulation results and experimental data for temperature and pressure drop are 4.8% and 6.4%, respectively. The effectiveness and feasibility of the topology optimization design for cooling plate are verified.

Topology Optimization of Continuum Structures Based on Binary Hunter-Prey Optimization Algorithm

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used to solve the problems that the BESO method of topology optimization has, such as easily falling into the local optimal value and being unable to obtain the optimal topology configuration; the metaheuristic algorithm was able to solve the topology optimization model’s low computational efficiency and could easily produce intermediate elements and unclear boundaries. Firstly, the BHPO algorithm was constructed by discrete binary processing using the s-shape transformation function. Secondly, BHPO-BESO topology optimization theory was established by combining the BHPO algorithm with BESO topology optimization. Using the sensitivity information of the objective function and the updated principle of the meta-heuristic of the BHPO algorithm, a semi-random search for the optimal topology configuration was carried out. Finally, numerical simulation experiments were conducted by using the three typical examples of the cantilever beam, simply supported beam, and clamping beam as optimization objects and the results were compared with the solution results of BESO topology optimization. The experimental results showed that compared with BESO, BHPO-BESO could find the optimal topology configuration with lower compliance and maximum stiffness, and it has higher computational efficiency, which can solve the above problems.

Real-Time Structure Generation Based on Data-Driven Using Machine Learning

Topology optimization results are highly dependent on the given design constraints and boundary conditions. Moreover, small changes in initial design conditions can result in different topological configurations, which makes topology optimization time-consuming in a given design constraint domain and inefficient in structural design. To address this problem, a data-driven real-time topology optimization framework and method coupled with machine learning by using a principal component analysis algorithm combined with a feedforward neural network are developed in this paper. Meanwhile, through the offline training, the mapping relationship between initial design conditions and topology optimization results is obtained. From this mapping, we estimate the optimal topologies for novel loading configurations. Numerical examples display that the online prediction results are consistent with the results of the topology optimization method. Furthermore, the network parameters are calibrated, and accurate structure prediction is achieved based on the algorithm. In addition, this method ensures the accuracy of high-resolution structural prediction on the premise of small samples.

Computational Geometry Reconstruction from 3D Topology Optimization Results: A New Parametric Approach by the Medial Axis

Computer-Aided Design and Applications is an international journal on the applications of CAD and CAM. It publishes papers in the general domain of CAD plus in emerging fields like bio-CAD, nano-CAD, soft-CAD, garment-CAD, PLM, PDM, CAD data mining, CAD and the internet, CAD education, genetic algorithms and CAD engines. The journal is aimed at all developers and users of CAD technology to ptovide CAD solutions for various stages of design and manufacturing. The journal publishes all about Computer-Aided Design and Computer-Aided technologies.

The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures

<abstract> <p>We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples.</p> </abstract>

Application of Digital Image Correlation method for verification of topology optimization of 3D printed load-bearing element

This paper presents DIC-based experimental verification of topology optimization of the 3D printed cantilever plate load-bearing element. Test samples were 3D printed from ABS and PET-G materials using FDM technology. A 3D geometrical parametric model was created and FEA and topology optimization were performed using computer program Autodesk Inventor. In order to successfully define the optimization problem and obtain reliable results, it is extremely important to properly define the analysis input parameters, such as material parameters and boundary conditions. Young's moduli of ABS and PET-G were determined experimentally on samples which were made using 3D printing technology with identical settings as cantilever plate samples. Stresses and strains in optimized samples were determined using FEA. To verify the FEA and topology optimization results, an experimental setup for holding and loading of 3D printed samples was prepared and displacements were measured using digital image correlation system ARAMIS. Results obtained experimentally were compared with the results obtained by finite element analysis of optimized cantilever plate sample and show very good agreement for both ABS and PET-G samples, with deviation of around 4 % and 11 % respectively.

Numerical and experimental performance investigation of a heat exchanger designed using topologically optimized fins

Topology optimization for thermal-fluid problems has been successfully used to improve performance of small structures used for heat transfer. Optimization of full heat exchangers, due to analysis method limitations and computational costs, has not been able to produce manufacturable designs complex enough to satisfy heat exchanger specifications. The goal of this study is determining if a practical heat exchanger design can be obtained by the use of topology optimization. By considering a plate-fin heat exchanger, topology optimization is used to obtain a locally optimized fin pattern which is extended to form a heat exchanger core. A modification of the Number of transfer units method is presented to deal with the unique topology obtained by optimization and evaluate the performance of the exchanger. The performance, when compared to traditional serrated fin designs, show that optimization improvements extend beyond the optimized region onto the entire exchanger. The results show that the optimized design is an improvement outside optimization flow parameters. However, the limitations in 3D printer technology result in slight deviation of experiment results compared to the analysis, and prevent the manufacturing of designs with comparable total performance values to heat exchangers manufactured through traditional methods. • Design procedure obtains a heat exchanger core by localized topology optimization. • NTU method is modified to evaluate results of topology optimization. • Modified NTU, CFD and experimental evaluations are in good agreement with each other. • Performance improvements are maintained outside optimization flow parameters.