Topology Optimization Techniques Research Articles

Non-parametric geometry patching technique for MMC topology optimization

Non-parametric geometry patching technique for MMC topology optimization

Monte Carlo analysis of dosimetric issues in space exploration

The Radiation protection is of paramount importance in the planning of human exploration activities in space. The related risks must be considered with respect to two aspects: devising a proper shielding and providing answers to the requirement of an effective dosimetry evaluation in astronaut's activities. Both aspects have been considered using the Monte Carlo (MC) code MCNP 6.2 as the reference tool. As case study an application devised for the National Aeronautics and Space Administration (NASA) Artemis program has been chosen. The project aims to establish a sustainable human presence on the Moon, envisioning the realization of an outpost that will serve as a steppingstone for space exploration endeavors. A Class III shelter, in situ resource utilization (ISRU) built habitat for the Moon, has been designed through computational methods and topology optimization techniques, and analyzed in terms of radiation shielding performances and the strictly related structural behavior. The outpost must be able to withstand temperature variations, micrometeorite impacts, and the absence of a substantial atmosphere. Any solution studied to respect the constraints must devise robust and innovative materials and techniques to create habitats that have as goal the shielding from the Galactic Cosmic Rays (GCR) and from the solar flares to provide a safe and habitable environment at the time scales scheduled for the missions. Moreover, the outpost design must incorporate strategies for extracting and utilizing local resources. Overcoming such challenges will pave the way for the establishment of a sustainable human presence on the Moon and serve as a crucial leap for future space exploration missions.

On the Integrity of Large-Scale Direct-Drive Wind Turbine Electrical Generator Structures: An Integrated Design Methodology for Optimisation, Considering Thermal Loads and Novel Techniques

With the rapid expansion of offshore wind capacity worldwide, minimising operation and maintenance requirements is pivotal. Regarded as a low-maintenance alternative to conventional drivetrain systems, direct-drive generators are increasingly commonplace for wind turbines in hard-to-service areas. To facilitate higher torque requirements consequent to low-speed operation, these machines are bulky, greatly increasing nacelle size and mass over their counterparts. This paper therefore details the structural optimisation of the International Energy Agency 15 MW Reference Wind Turbine rotor through iterative Parameter and Topology Optimisation and the inclusion of additional structural members, with consideration to its mechanical, modal, and thermal performances. With temperature found to have a significant impact on the structural integrity of multi-megawatt direct-drive machines, a Computational Fluid Dynamics analysis was carried out to map the temperature of the structure during operation and inform a consequent Finite Element Method analysis. This process, novel to this paper, found that topologically optimised structures outperform parametrically optimised structures thermally and that integrated heatsinks can be employed to further reduce deformation. Lastly, generative design techniques were used to further optimise the structure, reducing its mass, deformation, and maximum stress and expanding its operating envelope. This study reaches several key conclusions, demonstrating that significant mass reductions are achievable through the removal of cylinder wall geometry areas as well as through the implementation of structural supports and iterative parametric and topology optimisation techniques. Through the flexibility it grants, generative design was found to be a powerful tool, delivering further improvements to an already efficient, yet complex design. Heatsinks were found to lower generator structural temperatures, which may yield lower active cooling requirements whilst providing structural support. Lastly, the link between the increased mass and the increased financial and environmental impact of the rotor was confirmed.

Efficient design of sandwich panels with cellular truss cores and large phononic band gaps using surrogate modeling and global optimization

Recent advancements in additive manufacturing technologies and topology optimization techniques have catalyzed a transformative shift in the design of architected materials, enabling increasingly complex and customized configurations. This study delves into the realm of engineered cellular materials, spotlighting their capacity to modulate the propagation of mechanical waves through the strategic creation of phononic band gaps. Focusing on the design of sandwich panels with cellular truss cores, we aim to harness these band gaps to achieve pronounced wave suppression within specific frequency ranges. Our methodology combines surrogate modeling with a comprehensive global optimization strategy, employing three machine learning algorithms—k-Nearest Neighbors (kNN), Random Forest Regression (RFR), and Artificial Neural Networks (ANN)—to construct predictive models from parameterized finite element (FE) analyses. These models, once trained, are integrated with Particle Swarm Optimization (PSO) to refine the panel designs. This approach not only facilitates the discovery of optimal truss core configurations for targeted phononic band gaps but also showcases a marked increase in computational efficiency over traditional optimization methods, particularly in the context of designing for diverse target frequencies.

Stiffness, strength, anisotropy, and buckling of lattices derived from TPMS and Platonic and Archimedean solids

Lattice metamaterials have gained considerable attention due to their distinctive topological structures and multifunctional properties. In this work, the effect of topology, loading conditions, and relative density on the effective mechanical properties of various novel lattice architectures is investigated numerically and experimentally. Thirteen strut-based lattices derived from triply periodic minimal surfaces (five lattices) as well as Platonic (three lattices) and Archimedean (five lattices) solids are considered for the first time, and their anisotropic mechanical properties, including uniaxial, shear, and bulk moduli and strengths as well as their total stiffness, buckling strengths, Poisson’s ratio, and anisotropy are investigated as a function of a wide range of relative densities (0.1% to 37%). Finite element analysis is employed to capture the full effective behavior of these lattices using periodic boundary conditions. Bifurcation analysis is performed to predict the threshold relative density governing their buckling vs yielding deformation behavior. Selected lattice structures of various relative densities are 3D printed using polymer selective laser sintering additive manufacturing technique and tested under quasi-static uniaxial compression where the experimental and numerical results are compared. The numerical results indicate that the deformation behavior can be altered between stretching and bending dominated mode of deformation as function of loading. Archimedean lattices are shown to outperform a wide range of strut-based lattices. This work opens the doors for more investigations of the multifunctional properties of these novel types of lattices and their engineering applications. Furthermore, the generated comprehensive data are useful in optimizing latticed structures using topology optimization techniques.

Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures

This work presents a novel approach for the design of metadevices conceived to recover a prescribed set of the natural eigenfrequencies of a structure lightened by machining arbitrary shape holes, using classical topology optimization (TO) techniques. This TO metadevice design (TOMD) is performed by minimizing the error of an eigenfrequency recovery task, using the finite element method (FEM) as an analysis tool, ensuring manufacturability via the solid isotropic material with penalization (SIMP) approach with Heaviside filtering to reduce intermediate-density areas. The spatial variation of mechanical properties derives from the macroscopically distinguishable dual material distribution obtained from the TOMD problem. The methodology was first tested on lightened thin steel plates and then extended to a real-world 3D mechanical component with additional mechanical performance testing. In all cases, the optimized metadevice yielded lower error in recovering eigenfrequencies compared to the lightened component without the metadevice. Furthermore, the metadevice generally achieved further mass reduction, demonstrating its potential for lightweight design while restoring its original eigenfrequencies.

The influence of internally architected voids in the creation of high-strength, low-weight 3D-printed cobalt-chromium prototypes

Background: The additive manufacturing technology made the topology optimization technique feasible. This technique can indefinitely reduce the weight of the printed items with a promising increase in the mechanical properties of that item. Materials and Methods: In the current experimental study, 50 samples were fabricated for a 3-point bending test. They were divided into ( n = 5) as a control Group 1 free of internal geometries, ( n = 15) for each of Groups 2-4, and they were subdivided into ( n = 5) for each percentage of reduction per volume (10%, 15%, and 20%). Spherical, ovoid, and diamond shapes were each group's fundamental geometries, respectively. Cylindrical tunnels connected the voids in each group. Radiographic images were performed to validate the created geometries, the weight was measured, and flexural strength and modulus of elasticity were calculated. Data were analyzed by one-way ANOVA and Duncan's post hoc tests at P <s 0.05. Results: The weight results showed a significant reduction in mass. The flexural strength of Group 2 at a 10% reduction per volume had the highest mean significantly without compromising the elastic modulus. In comparison, the means of group 4 at 20% reduction showed the lowest level of toughness. Conclusion: The weight was reduced according to the reduction percentage. The flexural strength of Group 2 at a 10% reduction showed the highest degree of toughness among all groups. The void shape and density influenced the mechanical properties tested.

Topology optimization of a waveguide acoustic black hole for enhanced wave focusing.

The waveguide acoustic black hole (WAB) effect is a promising approach for controlling wave propagation in various applications, especially for attenuating sound waves. While the wave-focusing effect of structural acoustic black holes has found widespread applications, the classical ribbed design of waveguide acoustic black holes (WABs) acts more as a resonance absorber than a true wave-focusing device. In this study, we employ a computational design optimization approach to achieve a conceptual design of a WAB with enhanced wave-focusing properties. We investigate the influence of viscothermal boundary losses on the optimization process by formulating two distinct cases: one neglecting viscothermal losses and the other incorporating these losses using a recently developed material distribution topology optimization technique. We compare the performance of optimized designs in these two cases with that of the classical ribbed design. Simulations using linearized compressible Navier-Stokes equations are conducted to evaluate the wave-focusing performance of these different designs. The results reveal that considering viscothermal losses in the design optimization process leads to superior wave-focusing capabilities, highlighting the significance of incorporating these losses in the design approach. This study contributes to the advancement of WAB design and opens up new possibilities for its applications in various fields.

Multiscale Topology Optimization of modulated fluid microchannels based on asymptotic homogenization

Dehomogenization techniques are becoming increasingly popular for enhancing lattice designs of compliant mechanical systems with ultra-large resolutions. Their effectiveness hinges on computing a deformed periodic grid that enable to reconstruct fine-scale designs with modulated and oriented patterns. In this paper, we propose an approach for extending dehomogenization methods to laminar fluid systems. We initiate our methodology by asymptotically deriving Darcy’s law on a periodically porous medium deformed by a diffeomorphism. Unlike the mechanical context, we reveal that the homogenized permeability matrix depends not solely on local the orientation but also on the local dilation of the deformed periodic medium. This distinction presents one of the several challenges to be tackled when adapting dehomogenization-based topology optimization techniques to porous media. To accommodate existing methodologies, we formulate a simplified “poor man’s” homogenized model, which streamlines various aspects, yet still leans on periodic cell problems to estimate the spatially varying permeability matrix. Specifically, we overlook boundary layer effects, we presume periodic grid deformations, and we neglect local dilation, solely considering the relationship with local cell orientations. Subsequently, we present a numerical approach for designing a system that redistributes an input flow across numerous regularly spaced outlets at an output interface. Leveraging the homogenized model, we deduce optimized geometric arrangements of local channel spacing parameters and orientations. We then use established methods to reconstruct grid deformations and fine-scale designs. The fidelity of these reconstructions is then validated through fine-scale simulations. Our observations indicate that while the proposed designs yield satisfactory performance when subjected to the full-scale model, discernible deviations from the homogenized model persist, appealing to future improvements.

Topology optimization and numerical analysis of cold plates for concentrating photovoltaic thermal management

Continuous advances in concentrating photovoltaic (CPV) panel efficiency are increasingly affected by cell temperature. Improving PV panel cooling performance is critical. This application optimizes the internal flow channel structure of PV panel cooling systems using topology optimization techniques like multi-objective and multi-stage optimization with penalty factors. Three-dimensional CFD simulation is used to compare the heat transfer performance of topology optimized channel cooling configuration and traditional straight channel cooling configuration for photovoltaic panel systems. Effects of inlet flow rates, concentration ratios, and other parameters on cooling performance are investigated. Results show the topology optimized flow channel configuration has better cooling than the straight channel. At different concentration ratios, the solar cell temperature reduces 13.85%–23.45%. The optimized application also has lower inlet and outlet pressure drops for the same operating conditions, requiring less external power. Compared to the straight channel, the topology optimized flow channel increases net PV system output power 3.00%–19.37% at different concentration ratios. Applying topology optimization provides new ideas for optimizing PV cooling system designs.

DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks

AbstractWe propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration.

Design and Analysis of a Topology-Optimized Quadcopter Drone Frame

This study focuses on the analysis and optimization of a drone frame design to enhance its performance characteristics. The design underwent drop testing, stress analysis, displacement analysis, and flow simulation to evaluate its structural integrity, deformation resistance, and aerodynamic performance. Furthermore, topology optimization techniques were employed to achieve a 30% weight reduction while maintaining the structural integrity of the drone frame. The results of the drop test analysis revealed that Design 2 exhibited lower stress levels compared to Design 1, indicating improved load distribution and structural integrity. However, Design 1 demonstrated lower displacement values, suggesting better resistance to deformation. The flow analysis indicated that Design 1 achieved lower flow velocities, indicating superior propulsion and aerodynamic performance. Through topology optimization, the mass of the drone frame was successfully reduced by 30% without compromising structural integrity. The optimized design exhibited improved stress management, reduced displacement, and slightly higher flow velocities compared to the initial design. These improvements contribute to enhanced agility, maneuverability, and energy efficiency of the drone. The findings of this study highlight the importance of considering stress distribution, displacement, and aerodynamic performance in drone design and optimization. The results provide valuable insights for the development of efficient and reliable drones.

Practical application of multi-material topology optimization to performance-based architectural design of an iconic building

With the rapid development of architectural design methods and structural analysis techniques, structural performance-based design approaches have become increasingly important in architectural design. Among these approaches, topology optimization is a significant design method. However, most existing topology optimization research and related applications are based on single-material topology optimization techniques, which have limitations when applied to the design of complex and challenging structures. Building upon our previously proposed multi-material bi-directional evolutionary structural optimization (multi-material BESO) method, this paper presents the approaches for achieving diverse and competitive structural designs and then presents a practical application of the multi-material BESO method to the structural design of the core structure of a long-cantilevered building project called “Xiong’an Wings”. After an evolutionary design process based on the multi-material BESO method, an efficient frame with lower overall material costs, better static and dynamic performance compared to the initial design by experienced engineers is achieved. As the first practical application of the multi-material BESO method to a large-scale architectural design, the example of the “Xiong’an Wings” building demonstrates the tremendous prospects for the application of multi-material topology optimization technology to the generative design of innovative and efficient building structures.

The Updated Properties Model (UPM): A topology optimization algorithm for the creation of macro–micro optimized structures with variable stiffness

The design and manufacturing of high value industrial components is suffering a change of paradigm with 3D printing, where a macro–micro structural optimization of architected metamaterials is pursued to endow the material and the component of customized mechanical properties. Topology optimization techniques facilitate the design of both the microstructures and the overall component topology. However, current techniques do not operate directly with the mechanical properties of the material, but through density intermediates. We propose a novel topology optimization algorithm that aims to homogenize the strain level by minimizing its standard deviation across the domain with no other constraint than the imposed limits on the design space, deriving in an iterative update formula for the stiffness. Despite that the pursued objectives are different, we show that the proposed methodology can reach similar results as the current techniques, but without imposing constraints and reducing the number of external parameters, thus increasing the easy of use and its robustness. Working directly with moduli, the proposed technique is specially suitable for two-level concurrent material-component design using functionally graded metamaterials, and can be extended to materials other than linear isotropic.

Optimizing fin design for enhanced melting performance in latent heat thermal energy storage systems

The addition of fins to phase change material (PCM) in latent heat thermal energy storage (LHTES) systems is a widely employed technique to enhance thermal performance and significantly improve energy storage efficiency. This research focuses on a two-dimensional numerical model investigating heat transfer within a shell-and-tube structure of LHTES. Various combinations of fin number and fin height were explored to assess their influence on melting performance while maintaining the consistent fin volume. Subsequently, a topology optimization technique was developed to determine the most effective fin configuration. The optimized fins exhibited dendritic distributions and outperformed other fin designs in terms of heat transfer performance. The topology-optimized design resulted in a remarkable 74 % increase in melting performance compared to the structure without fins. Furthermore, we introduced a simplified model that takes into account manufacturing feasibility. We verified that a fin volume fraction of 6 % resulted in a significantly reduced melting time of 36 min, in stark contrast to the 249 min observed without fins.

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network.

Topology optimization techniques are essential for manufacturing industries, such as designing fiber-reinforced polymer composites (FRPCs) and structures with outstanding strength-to-weight ratios and light weights. In the SIMP approach, artificial intelligence algorithms are commonly utilized to enhance traditional FEM-based compliance minimization procedures. Based on an effective generalized regression neural network (GRNN), a new deep learning algorithm of compliance prediction for structural topology optimization is proposed. The algorithm learns the structural information using a fourth-order moment invariant analysis of the structural topology obtained from FEA at different iterations of classical topology optimization. A cantilever and a simply supported beam problem are used as ground-truth datasets, and the moment invariants are used as independent variables for input features. By comparing it with the well-known convolutional neural network (CNN) and deep neural network (DNN) models, the proposed GRNN model achieves a high prediction accuracy (R2 > 0.97) and drastically shortens the training and prediction cost. Furthermore, the GRNN algorithm exhibits excellent generalization ability on the prediction performance of the optimized topology with rotations and varied material volume fractions. This algorithm is promising for the replacement of the FEA calculation in the SIMP method, and can be applied to real-time optimization for advanced FRPC structure design.

Low-resistance local components design method based on topology optimization: A case study of a duct tee

The widespread local components in ventilation and air conditioning systems lead to severe energy losses and resistance effects during system operation. In this study, a method based on an improved topology optimization method for the low-resistance design of local components is proposed, and a modified Brinkman equation based on the topology optimization method is given by considering the inertia effect in flows with a high Reynolds number (Re > 2300). A tee is an important local component for airflow branching and conversion in ventilation and air conditioning systems, which has complex flow resistance characteristics. In this study, the duct tee is used as an optimization case, and the flow path layout of the tee is successfully obtained with the improved topology optimization technique. The flow resistance characteristics and resistance reduction mechanism of the topological tee are verified and analyzed by numerical simulation method, full-scale experimental verification, and the energy dissipation. The results show that the resistance reduction rate is 17–165% in the straight direction and -19-118% in the branch direction at different flow ratios. The curved form of the topological tee wall significantly weakens the fluid deformation and reduces energy dissipation in the flow process. Previous design optimization problems have focused on low Reynolds number flow, while high Reynolds number flow is widely available in the engineering field. This study extends the Reynolds number to 2300, which provides an effective method and direction to guide the optimal design of low-resistance local components in the engineering field.

A topology-based in-plane filtering technique for the combined topology and discrete fiber orientation optimization

This work proposes a filtering technique for the concurrent and sequential finite element-based topology and discrete fiber orientation optimization of composite structures. The proposed filter is designed to couple the morphology with the topology of the structural domain throughout the optimization process in a way such that it suppresses the impact of the close-to-void finite elements’ morphology on the overall morphology of the structure while steering at the same time the local fiber orientation towards the neighboring topologically dense areas of the geometry. The functionality of the filter becomes crucial at the boundaries of the optimized structure, where the fiber orientation is forced to conform to the morphology of the local boundaries. The developed filtering technique is incorporated into both the concurrent and sequential finite element-based topology and discrete fiber orientation optimization problem, and the respective optimization problems are formulated for the compliance minimization of the composite structure. To assess the efficacy of the filter, it is demonstrated in the benchmark academic case studies of the 2D Messerschmitt-Bölkow-Blohm and cantilever beams when different state-of-art interpolation techniques are employed for modeling the discrete fiber orientation optimization problem.

Topology optimization design of inner fins in spherical phase change capsules

With the development of thermal storage stacking beds, the research application of spherical phase change capsules has become a hot topic. However, the low thermal conductivity of the phase change material makes the thermal response time of spherical phase change capsules slow and the thermal storage/exhaust efficiency is poor. In order to solve this problem, this paper proposes a method for designing the inner fins of spherical phase change capsules by applying topology optimization techniques. In a two-dimensional hemispherical model, the density method is used to calculate the topology optimization results for different objective functions and to construct models to simulate the melting and solidification of a spherical phase change capsule. The results show that the fin models have a large Nusselt number, which effectively speeds up the heat transfer inside the capsule and reduces the melting and solidification time. On balance, the topology optimization fin model with minimized dissipation of thermal conductivity as the objective function has the best performance, being able to reduce the melting time by 34.22 % compared to the No Fins model and shorten the solidification time by 24.34 % compared to the straight fin model. In addition, this paper finds that the fins can influence the generation of natural convection, splitting the large vortices and accelerating the melting rate on both sides inside the capsule. This paper can provide a new idea for the fins optimal design inside the spherical phase change capsule.

Topology and Size Optimized Design and Laser Welding of the U-Frame for Free-Space Laser Communication Telescopes

The success of laser communications heavily relies on the stiffness, dynamic properties, static performance, and manufacturability of the U-frame. The U-frame is a fundamental element in satellite-to-ground laser communication telescopes. However, there is currently a lack of research on the optimal design of U-frames, leading to a significant gap between ideal construction and practical manufacturability. To address these concerns, this study proposes a comprehensive approach that combines multi-objective topology optimization and multi-start size optimization techniques. This approach considers the multidisciplinary constraints imposed by mechanical, control, and optical systems. The objective is to achieve both the conceptual and detailed design of a novel U-frame, while also ensuring thorough consideration of the structure’s manufacturability during the optimization process. The prototype of the optimized U-frame was successfully fabricated using laser welding processes. The tensile test conducted on the prototype supported the idea that laser welding can enhance the micro-grain size of the joint, leading to improved overall mechanical properties. In particular, the joint strength achieved through laser welding was found to be 1.5 times greater than that achieved through TIG (Tungsten Inert Gas) welding. Additionally, the results obtained from the free vibration experiment closely aligned with the simulation, confirming the feasibility of manufacturing the optimized structure. The optimized structure demonstrated an improvement of 7.13% in dynamic performance and 29.61% in static performance compared to the first-generation structure. Additionally, there was a reduction of 29.89% in mass without affecting the remaining performance aspects. The successful fabrication of the prototype validates the feasibility of the proposed welding process and highlights the superiority of the new U-frame.