Application Of Topology Optimization Research Articles

Design and optimization of a novel patient-specific subperiosteal implant additively manufactured in yttria-stabilized zirconia

ObjectiveTo design a patient-specific subperiosteal implant for a severely atrophic maxillary ridge using yttria-stabilized additively manufactured zirconia (3YSZ) and evaluate its material properties by applying topology optimization (TO) to replace bulk material with a lattice structure. MaterialsA contrast-based segmented skull model from anonymized computed tomography data of a patient was used for the initial anatomical design of the implant for the atrophic maxillary ridge. The implant underwent finite element analysis (FEA) and TO under different occlusal load-bearing conditions. The resulting implant designs, in bulk material and lattice, were evaluated via in-silico tensile tests and 3D printed. ResultsThe workflow produced two patient-specific subperiosteal designs: a) an anatomically precise bulk implant, b) a TO lattice implant. In-silico tensile tests revealed that the Young’s modulus of yttria-stabilized zirconia is 205 GPa for the bulk material and 83.3 GPa for the lattice. Maximum principal stresses in the implant were 61.14 MPa in bulk material and 278.63 MPa in lattice, both tolerable, indicating the redesigned implant can withstand occlusal forces of 125–250 N per abutment. Furthermore, TO achieved a 13.10 % mass reduction and 208.71 % increased surface area, suggesting improved osteointegration potential. SignificanceThe study demonstrates the planning and optimization of ceramic implant topology. A further iteration of the implant was successfully implanted in a patient-named use case, employing the same fabrication process and parameters.

Topology Optimization of Structural Drive-Train Component of an Electric Driven Vehicle for Additive Manufacturing

Additive Manufacturing (AM) is an emerging technology and an important alternative to conventional manufacturing methods as it enables the production of lighter parts that are potentially more durable. In this context, the design for additive manufacturing (DFAM) has been drawing a considerable amount of attention mainly in the aerospace, and automotive industries as well as in academia. On the other hand, the ability of additive manufacturing to manufacture complex topology is often the outcome of topology optimization, which makes topology optimization a good design tool for additive manufacturing. The main objective of the present work is to redesign a structural component of the drivetrain of the Shell Eco-Marathon vehicle, with the use of Altair Inspire™, an industrial generative design tool, by application of Topology Optimization for Additive Manufacturing aiming mass reduction and does not cover the print process.

Dynamically configured physics-informed neural network in topology optimization applications

The integration of physics-informed neural network (PINN) and topology optimization (TO) is an attractive issue because PINN can avoid the prohibitive data acquisition of solving forward problems compared to traditional machine learning. To enhance the efficiency of this integrated optimization framework, a dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed in conjunction with an active sampling strategy. The DCPINN comprises two sub-networks with distinct training costs, capable of dynamically adjusting the trainable parameters based on the optimization state of TO. Moreover, the active sampling strategy selectively samples collocations based on the pseudo-densities, which can significantly reduce training costs by decreasing the number of input collocations. Additionally, the Gaussian integral is used to calculate the strain energy of elements to decouple the mapping of the material at the collocations. The proposed method is extended to various scenarios, including those with high resolution, multiple loads, and displacement constraints. Its efficiency and generalization are validated by several illustrative examples. Furthermore, the accuracy of DCPINN versus finite element analysis-based TO (FEA-TO) was also investigated.

A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method

In this paper, a novel quasi-smooth tetrahedral numerical manifold method (NMM) and its two-dimensional (2D) counterpart are proposed. A new topology optimization method is established by combining the quasi-smooth manifold element (QSME) with the parameterized level set method (PLSM). The QSME introduces an innovative displacement function characterized by high accuracy and high-order continuity, effectively addressing the “linear dependence” (LD) issue inherent in traditional high-order NMM. To integrate QSME and PLSM, the corresponding optimization formulations and sensitivity analyses are provided. In order to fully utilize advantages of this novel quasi-smooth NMM and the PLSM, an element subdivision technique based on model recognition is proposed to accurately capture the physical boundaries. Additionally, a volume fraction update method based on element refinement is proposed. Taking advantage of the characteristics of the PLSM, a structure visualization method based on the sign distance function is developed to accurately describe curve boundary. This method allows for precise visualization of optimized structures. This study verifies high efficiency of the QSME-based PLSM for minimum compliance topology optimization problems in both 2D and 3D structures. Some representative structural optimization examples are tested to demonstrate effectiveness of the proposed method in both 2D and 3D problems, especially in complex design domain.

Finite Elements Analysis and Topology Optimization of Parking Brake Lever and Ratchet

Topology optimization is known as one of the basic categories of structural optimization. Topology optimization is received increasing attention in many engineering disciplines. Topology optimization contributes to minimizing emissions and environmental effects by increasing material utilization efficiency and manufacturing sustainability. The mechanical parking brake is still used in many vehicles. This study aims to contribute to the reduction in vehicle weight by applying topology optimization. In addition, it also purposes to promote sustainability in manufacturing by reducing material usage and energy consumption. A CAD model was created by considering the existing mechanism element dimensions. The parking brake lever mechanism component was evaluated using topology optimization and finite element analysis methods. Static analyses were performed using a finite element analysis program. The results of this analysis were used as input data for topology optimization. In the topology optimization, the response constraint mass was increased by 5 increments from 50% to 95%. As a result, the maximum equivalent (von Mises) stress for the parking brake lever is 230,29 MPa, and for the ratchet is 11,559 MPa. The maximum total deformation value for the brake lever is 0,95853 mm and for the ratchet is 0,0079482 mm. The parking brake lever mass decreased by 18,48% from 0.27751 kg to 0.22622 kg. The ratchet mass decreased from 0.095042 kg to 0.061911 kg by 34.85%.

A limit analysis-based topology optimisation method for geostructure design

Geostructures, vital for the progress of civilisation, often face inefficiencies and suboptimal performance due to the lack of optimisation in current designs. Achieving cost-efficiency in geostructure design involves optimising material usage while considering practical construction aspects. While size and shape optimisations are common in geostructure design, the application of topology optimisation remains underexplored. This paper addresses this gap by introducing a novel topology optimisation method for three-dimensional geostructure design. The method integrates mixed limit analysis and density-based topology optimisation theories, allowing for two-material design focused on the ultimate bearing capacity of the geostructure. The innovation resides in aligning the applied external load in the topology optimisation process with the ultimate load that the designed geostructure can sustain. The robustness of the proposed method is exemplified through its application to the design of an embankment and soil foundation, showcasing its potential to enhance the efficiency and performance of geostructures. This research contributes to the advancement of geostructure design practices, ultimately promoting sustainable and resilient infrastructure development.

Topology optimization for rigid and compliant hybrid mechanisms

This paper proposes a topology optimization method integrating the variable trajectory constraints to design rigid and compliant hybrid mechanisms. The variable trajectory constraints are distributed in the design domain and are uniformly modeled by nonlinear spring model. Each of the variable trajectory constraints has an active or inactive state and different states map various mechanical properties of the nonlinear springs. The nonlinear relation between force and displacement of the spring is formulated. A new group of design variables denoting the states of the springs is introduced into the traditional density-based topology optimization model. The design variables representing the element density of the continuum structure and the states of the variable trajectory constraints are uniformly penalized to avoid intermediate values in order to obtain a physically realizable mechanism. Sensitivity analysis is performed by the adjoint equation method. To demonstrate the versatility and the generality of the proposed method, the typical numerical examples including linear, spline and circular trajectory constraints were implemented. The numerical comparisons between the nonlinear spring model and the actual trajectory constraints verify the accuracy. The proposed method expands the application of topology optimization and can be extensively employed to design the mechanisms integrating both the compliant members and rigid parts.

Application of Topology Optimization as a Form-Finding Method in Architectural Design, A Case Study: Pardisan Urban Footbridge

This paper proposes a framework to integrate Topology Optimization (TO) techniques into the architectural design by presenting a case study for the design of an urban footbridge. TO methods have gained popularity in several industrial sectors thanks to manufacturing and computational technology advancements. However, their applicability in architectural design could be improved by the indeterminacy of the final shapes produced by TO and their correlation with the initial design parameters. The unique form of the footbridge and its structural elements make it a suitable candidate for this study. The paper further outlines the design and implementation of the framework, including the application of TO and the subsequent refinement of the resulting form to meet the project’s functional and aesthetic requirements.

Topology optimization of modular structures with multiple assemblies and applications to airborne shelves

This work is devoted to the aeronautical application of topology optimization for modular structures with multiple assemblies that consist of repeated standard modules and optional reinforcements. These kinds of structures are widely used owing to their transportability, reconfigurability, low manufacturing and service costs. In this work, the design of airborne shelves with modular structures characterized by the standard module configuration is formulated for the first time as a topology optimization problem of multiple assemblies and multiple load cases subjected to the volume constraint. It is shown that the weighted compliance design of multiple assemblies is a compromising solution compared to the optimization result of each individual assembly of standard modules. Meanwhile, the performance of optimized airborne shelves with the modular structures can effectively be ameliorated with the help of reinforcements.

Blended structural optimization of steel joints for Wire-and-Arc Additive Manufacturing

Metal Additive Manufacturing, and in particular Wire-and-Arc Additive Manufacturing (WAAM) has proved to be a great and efficient alternative to the common subtractive manufacturing processes to realize complex-shape members and connections for construction. With reference to complex spatial structures such as gridshells, the connections play a crucial role both in the design and the construction processes. Novel computational design tools allow designers to conceive optimized joint solutions while minimizing the material use, resulting in difficult geometries to be fabricated with conventional methods. The present work aims at providing an innovative integrated design and fabrication framework to efficiently apply topology optimization algorithms to improve the efficiency of steel joints in complex spatial structures. The framework is based on the so-called “blended” structural optimization approach aimed at incorporating manufacturing constraints, basic principles of conceptual structural design and structural requirements into topology optimization to design ready-to-fabricate complex steel joints. The designs are suitable for fabrication with the WAAM process. The approach is applied to a case study to re-design the joint connections of the world’s renowned British Museum gridshell rooftop structure. From a catalogue of various designs for each unique joint, one selected design is optimized and then checked for structural requirements in terms of strengths and stiffness. Then the optimized joint is validated for fabrication with WAAM process.

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.

Lightweight design of Knee-Ankle-Foot Orthotic Devices using Voronoi patterns for Additive Manufacturing

Traditionally fabricated knee-ankle-foot orthosis (KAFO) device that is used to aid in the mobility user is uncomfortable. Problems such as weight and enclosure in almost all the part of the leg make it strenuous and humid for the user to wear for a long time. Furthermore, in the traditional production method, it can take up to a week to fabricate. The aim of this study is to redesign the knee-ankle-foot-orthosis by using the application of topology optimization in order to reduce the material used on the product and to make it lightweight. The parameters of the KAFO were determined by using indirect method; similar to traditional method. The modelling and analysis of the KAFO is completed by using CAD and CAE software. Optimization of the product is performed by redesigning the shape and applying topology optimization function. It is able to reduce the maximum stress of the product by 22.56% and the volume by 4.33%. Application of the Voronoi pattern further reduces the mass of the KAFO and produces more organic looks to the product. SLS Lisa Pro 3D printer is used to produce the KAFO in a period of less than a week. This prove to be a viable alternative for producing customized KAFO.

Topology optimization of Superhydrophobic Surfaces to delay spatially developing modal laminar–turbulent transition

Super-Hydrophobic Surfaces (SHSs) have been shown to reduce skin friction of an overlying fluid as a consequence of gas pockets trapped within the surface’s microstructure. More recently, they have also been shown capable of delaying laminar–turbulent transition. This article investigates the applicability of topology optimization in designing the macroscopic layout of SHSs in a channel that are able to further delay K-type transition in a spatial setting. Unsteady direct numerical simulations are performed to simulate the transition scenario. This is coupled with adjoint–based sensitivity analysis and gradient based optimization. The optimized designs found through this procedure are capable of moving the transition location further downstream compared to a homogeneous counterpart by inhibiting the growth of secondary instability modes. This article provides the first application of topology optimization to a spatially developing transition scenario.

Effective thermal conductivity estimation using a convolutional neural network and its application in topology optimization

Topology optimization of heterogeneous structures can find significant use in a wide range of applications, and its fabrication has been made possible by recent advances in additive manufacturing. However, the optimization procedure is computationally expensive, as each structural update requires the re-evaluation of the properties. The computational time is the major limiting factor in large-scale and complex structural optimization. In this study, a convolutional neural network (CNN) model for predicting effective thermal conductivity inspired by the VGG networks is proposed. Trained using 130,000 unique binary images, the model achieves high predictive accuracy. Specifically, it shows a mean absolute percent error (MAPE) of 0.35% in testing when the thermal conductivity of the solid is ten times larger than the fluid, and when the thermal conductivities assigned are that of aluminum and water, the MAPE is 2.35%. The prediction time is 15 ms for a single image with 128 × 128 pixels, which is 3 to 5 orders of magnitude faster than a finite volume simulation. When employed in topology optimization, the CNN retains a MAPE between 0.67% and 11.8% for different cases. The CNN model correctly predicts trends in effective thermal conductivity and improves the structure to close proximity of a theoretical maximum in all cases.

Topology optimization of HCM/PCM composites for thermal energy storage

In this paper, we have applied topology optimization (TO) to the latent heat based thermal energy storage (LHTES) device design. The high conductivity materials (HCM) are added to the phase change materials (PCM) to increase the overall thermal conductivity. Distribution of HCM in PCM is optimized by the TO method to maximize the charging speed of the LHTES device at the different charging periods. The time-dependent Navier–Stokes (NS) equations, involving natural convection and PCM phase change, are chosen as the governing equations of fluid motion. The energy equation including latent heat is strongly coupled with the NS equation. The adjoint method is utilized to derive and calculate the sensitivity. Several 2D numerical examples with different charging periods and different HCM volume fractions have been studied with this TO method. The charging period showed a huge influence on the optimized TO structures. The short charging period designs exhibit more conductive structures while the long charging period designs show convective structures. A pareto front of the topologically optimized designs has been constructed, which shows up to 110.7% of improvement in the charging speed over the parallel-fin design with the same root fin width.

A complete Physics-Informed Neural Network-based framework for structural topology optimization

Physics-Informed Neural Networks (PINNs) have recently gained increasing attention in the field of topology optimization. The fusion of deep learning and topology optimization has emerged as a prominent area of insightful research, where minimization of the loss function in neural networks can be comparable to minimization of the objective function in topology optimization. Inspired by concepts of PINNs, this paper proposes a novel framework, ‘Complete Physics-Informed Neural Network-based Topology Optimization (CPINNTO)’, to address various challenges in topology optimization, particularly related to structural optimization. The key innovation of the proposed framework lies in introducing the first complete machine-learning-based topology optimization framework through integration of two distinct PINNs. Herein, the Deep Energy Method (DEM) PINN is implemented to determine the deformation state of corresponding structures numerically. In addition, derivation of the objective function with respect to design variables is replaced with automatic differentiation in sensitivity-analysis PINN (S-PINN). The feasibility and potential of the CPINNTO framework have been assessed through several case studies while highlighting strengths and limitations of utilizing PINNs in topology optimization. Subsequent findings indicate that CPINNTO can achieve optimal topologies without labeled data nor FEA. The numerical examples demonstrate that CPINNTO is capable of stably obtaining optimal structures for various topology optimization applications, including compliance minimization problems, multi-constrained problems, and three-dimensional problems. Resulting designs exhibit favorable compliance values comparable to the designs obtained via density-based topology optimization. In summary, the proposed CPINNTO framework opens up novel and interesting possibilities for structural topology optimization.

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.

Transmissive Pancharatnam-Berry metasurfaces with stable amplitude and precise phase modulations using dartboard discretization configuration.

Metasurfaces are ultra-thin artificial structures capable of flexibly manipulating electromagnetic (EM) waves. Among various applications, phase modulation of electromagnetic (EM) waves using metasurfaces holds great significance. The Pancharatnam-Berry (P-B) metasurfaces provides a complete 2π phase modulation by simply rotating the meta-atom. However, the fixed lattice in rotation employed by traditional P-B metasurfaces often results in unstable amplitude and imprecise P-B phase, leading to performance degradation. In this work, we demonstrate transmissive P-B metasurfaces with stable amplitude and precise phase modulation. To ensure stable amplitude and precise P-B phase, we adopt a dartboard discretization configuration with a hexagonal lattice for the meta-atom design. By applying topology optimization to the encoding sequence formed by surface pixels and dimensions, we significantly enhancing the high transmissive bandwidth of the optimized meta-atom. Furthermore, the optimized meta-atom exhibits a stable amplitude and precise P-B phase for each rotation angle. As proof-of-concept demonstrations, two metasurfaces for single and multiplexed vortex beams generating are designed utilizing the optimized meta-atom. Both the simulated and measured results indicate high mode purity of generated vortex beams. The design method can also be readily extended to other high performance metasurfaces with stable amplitude and precise phase manipulations, which can enhance the efficiency and capacity of metasurface-assisted holographic imaging and 6 G wireless communication systems.

Performance analysis on the structure of the bracket mounting for hybrid converter kit: Finite-element approach

Abstract An electric motor mounting bracket is used in electric vehicles, especially hybrid ones using a parallel hybrid configuration. This study aims to analyze the strength and performance of the initial design and topology optimized design. This study uses the finite-element method (FEM) in the bracket design modeling by applying topology optimization. The topology optimization results show a mass reduction of 50% from the initial design mass. In the case of static loading, the results of optimized design 2 have a stress of 142.19 MPa and a safety factor of 3.09. While optimized design 1 has a stress of 313.8 MPa and a safety factor of 1.4. In terms of dynamic loading, the initial design, optimized design 1, and optimized design 2 have the first natural frequency, which is higher than the operating frequency of the electric motor, respectively, 100.49, 69.043, and 74.864 Hz. Optimized design 1 has the lowest natural frequency and the highest amplitude compared to the initial design, and optimized design 2 has lower damping characteristics. The study results conclude that optimized design 2 is superior in static and dynamic loading.

Effect of inlet and outlet positions on heat dissipation performance of lithium-ion battery cold plates: An analysis based on topology optimization

This study applied topology optimization methods to design a cold plate with topology channels for a square battery. With maximum heat transfer as the optimization objectives of the cold plate channel, and the performance of the cold plate at different inlet and outlet positions was systematically analyzed, effectively harnessing the potential of topology optimization. Based on the results of the topology analysis, a simplified three-dimensional cooling model was established and numerically investigated. The optimized design was explored considering different inlet and outlet arrangements, channel depths, and mass flow rates. The results demonstrated that a channel depth of 4 mm, an inlet temperature of 25 °C, and a mass flow rate of 12 g·s−1 was the ideal choice for a 1 C discharge cooling system. The different inlet and outlet positions had a greater impact on the performance of the cold plate at this time. The parallel diagonal structure (Case A-6) could lower the pressure drop by a maximum of 16.41% and improve the heat transfer efficiency by 6.10%, and the pumping power was only 0.003 W, which could obtain high heat transfer efficiency with low pump consumption; The straight-in and straight-out structure (Case B-6) was the most superior in maximum temperature and temperature deviation, with a maximum temperature of only 33.11 °C and a temperature deviation of 1.28 °C, which could decrease by 1.25 and 0.35 °C respectively compared with other structures, improving the upper limit of working temperature and the uniformity of temperature distribution. Finally, the optimized cold plates were experimentally validated. The experimental error was within 4%, proving the simulation analysis's accuracy.