Shape Optimization Research Articles

Improving the performance of room temperature rotary magnetic refrigerators via magnet shape optimization

A magnetic structure intended for use in a room-temperature rotary active magnetic regenerator (AMR) is presented, under construction at the University of Genoa. Given the overall size of the regenerator and the thickness of the gap, the magnet design is optimized to produce the highest possible magnetic field difference between two adjacent regions. Magnet shape optimization is obtained by introducing a geometry with four degrees of freedom corresponding to the position of the edges of each magnet, plus the remanence angle. This approach serves two main purposes: the primary is to increase the magnetic induction and, to follow, some effort is made to minimize the volume and weight of the expensive NdFeB magnets, while preserving the cooling performance. So, a balance between these two goals must be achieved. After a rough preliminary sizing, a parametric investigation is performed toward these targets and some shapes are presented. The magnetic flux density in the gap, and other consolidated and novel performance indices, are evaluated and compared to those found in the literature for similar devices. The final design achieves, in the air gap, a maximum induction value of 1.045 T, and an average flux density of 0.83 T in a volume per unit length of 0.00268 m3/m in the high induction region. This is accomplished by using 0.00606 m3/m of magnetic material (N50, NdFeB). The magnet designs presented here exhibit a well-balanced performance (in terms of greater cooling for the same magnet weight) compared to earlier designs for similar AMR devices.

Gold-nanoparticle-embedded membrane (GEM) for highly sensitive multiplexed sandwich immunoassays

For early disease diagnostics, highly sensitive biosensing methods are required to detect disease-related biomolecules in biofluids at low concentrations. Further, for complex diseases such as cancer, multiplexed detection is required to simultaneously measure multiple analytes in a single assay. Current technologies either lack sensitivity, multiplexing capabilities, or require complicated micro/nano-fabrication processes and specialized instrumentation, limiting their broader use in the biomedical research community as well as in clinical diagnostic applications. In this work, we have developed a gold-nanoparticle-embedded membrane (GEM) platform that consists of 3D nitrocellulose membranes preloaded with gold nanoparticles in microliter compartments for highly sensitive, multiplexed metal enhanced fluorescence (MEF)-based detection. After the development of the compartmentalized GEM and the optimization of size, shape, and concentration of the gold nanoparticles to achieve optimal MEF, we demonstrated its application for scalable multiplexed sandwich immunoassays in a microarray format for the quantification of three cancer-related proteins in blood plasma. In PBS buffer solution, the limit of detection for GM-CSF, TNF-α, and EGFR were improved by 287-folds, 949-folds, and 9.8-folds, respectively, when using the GEM compared to conventional ELISA. When spiked in pooled human plasma, low pg/mL sensitivity was also achieved for each protein, demonstrating its application for complex samples. Long-term storage was demonstrated for potential distribution of the GEM for wide availability among the biomedical and clinical community, facilitating technology dissemination. This technology offers simple, highly sensitive, and multiplexed detection capabilities with low reagent and sample consumption, suitable for accurate and early disease diagnostics.

전기자동차 배터리 냉각 플레이트의 유동 형상에 따른 냉각 성능에 관한 연구

The performance of lithium-ion batteries in electric vehicles is significantly affected by temperature. To ensure battery stability and extend its lifespan, an effective cooling system must be developed for heat dissipation. Therefore, researchers are focusing on liquid-cooled systems that use fluids with higher thermal conductivities compared with conventional air-cooling systems. However, studies regarding the flow shapes of crucial cooling plates in indirect liquid-cooling systems are scarce. In this study, the optimal flow shape of cooling plates with high cooling performance for dissipating heat generated during battery charging and discharging is determined. Four models with different structural features are analyzed via computational fluid dynamics simulations and then validated experimentally. Model 1, which features a small stagnation region, exhibits better cooling performance compared with Model 2, which features smoother curved flow paths. Models with large stagnant regions demonstrate inferior cooling performance, which is attributed to the effect of heat absorption, based on the residence time of the coolant in the cooling plate. Improvement in cooling efficiency is confirmed, which implies the feasibility of applying the model to enhance the performance of electric vehicles in the future.

The boundary Harnack principle on optimal domains

We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.

Shape Sensing for Continuum Robotics Using Optoelectronic Sensors with Convex Reflectors

Three-dimensional shape sensing in soft and continuum robotics is a crucial aspect for stable actuation and control in fields such as minimally invasive surgery, engine repairs and search and rescue operations, as the estimation of complex curvatures while using continuum robotic tools is required to manipulate through fragile paths. This challenge has been addressed using a range of different sensing techniques, for example, Fibre Bragg grating (FBG) technology, inertial measurement unit (IMU) sensor networks, or stretch sensors. Previously, an optics-based method using optoelectronic sensors was explored, offering a simple and cost-effective solution for shape sensing in a flexible tendon-actuated manipulator in two orientations. This was based on proximity-modulated angle estimation and has been the basis for the shape sensing method addressed in this paper. The improved and miniaturised technique demonstrated in this paper is based on the use of a convex shaped reflector with optoelectronic sensors integrated into a tendon-actuated robotic manipulator. Upgraded sensing capability is achieved using optimisation of the convex reflector shape in terms of sensor range and resolution, and improved calibration is achieved through the integration of spherical bearings for friction-free motion. Shape estimation is achieved in two orientations upon calibration of sensors, with a maximum Root-Mean-Square Error (RMS) of 3.37°.

A T-splines-oriented isogeometric topology optimization for plate and shell structures with arbitrary geometries using Bézier extraction

Recently, the non-uniform rational B-splines (NURBS) have been considerably employed in modeling plate and shell structures, or developing the related size, shape or topology optimization methods for their design. However, the NURBS with the tensor product feature strongly hinders the effectiveness of the optimization on complex structures. The primary intention of the current research is to propose a new T-splines-oriented Isogeometric Topology Optimization (T-ITO) method and then address the critical design problem of plate and shell structures with arbitrary shapes in practical applications. Firstly, the Bézier extraction is utilized in the T-splines to map the geometrical model into a family of Bézier elements, each of which is presented by a local Density Distribution Function (DDF) for elementary topology. A global DDF is constructed by an assembly of all local DDFs with a natural connection to the present structural topology. Secondly, the T-splines-based IsoGeometric Analysis (T-IGA) formulation with the Bézier extraction for complex plate and shell structures is developed using the Kirchhoff-Love theory, where a universal numerical implementation framework is constructed, including the Rhino, MATLAB, export modules with all geometric information and import modules for the analysis. Thirdly, a mathematical formulation for plate and shell structures with arbitrary geometries is developed using the T-ITO method to improve structural loading-capability, and the sensitivity analysis with respect to design variables is rigorously derived in detail. Finally, several numerical examples of plate and shell structures with both regular and elaborate geometries are tested to demonstrate the validity, effectiveness, superiorities and indispensability of the T-ITO method.

Generative vs. Non-Generative Models in Engineering Shape Optimization

Generative models offer design diversity but tend to be computationally expensive, while non-generative models are computationally cost-effective but produce less diverse and often invalid designs. However, the limitations of non-generative models can be overcome with the introduction of augmented shape signature vectors (SSVs) to represent both geometric and physical information. This recent advancement has inspired a systematic comparison of the effectiveness and efficiency of generative and non-generative models in constructing design spaces for novel and efficient design exploration and shape optimization, which is demonstrated in this work. These models are showcased in airfoil/hydrofoil design, and a comparison of the resulting design spaces is conducted in this work. A conventional generative adversarial network (GAN) and a state-of-the-art generative model, the performance-augmented diverse generative adversarial network (PaDGAN), are juxtaposed with a linear non-generative model based on the coupling of the Karhunen–Loève Expansion and a physics-informed shape signature vector (SSV-KLE). The comparison demonstrates that, with an appropriate shape encoding and a physics-augmented design space, non-generative models have the potential to cost-effectively generate high-performing valid designs with enhanced coverage of the design space. In this work, both approaches were applied to two large foil profile datasets comprising real-world and artificial designs generated through either a profile-generating parametric model or a deep-learning approach. These datasets were further enriched with integral properties of their members’ shapes, as well as physics-informed parameters. The obtained results illustrate that the design spaces constructed by the non-generative model outperform the generative model in terms of design validity, generating robust latent spaces with no or significantly fewer invalid designs when compared to generative models. The performance and diversity of the generated designs were compared to provide further insights about the quality of the resulting spaces. These findings can aid the engineering design community in making informed decisions when constructing design spaces for shape optimization, as it has been demonstrated that, under certain conditions, computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.

New Computerized Planning Algorithm and Clinical Testing of Optimized Nuss Bar Design for Patients with Pectus Excavatum.

BACKGROUND Computer-aided design (CAD) has been used in the Nuss procedure to determine the bar length and shape. Despite computer aid, the shape and design remain quite intuitive. We tested a new algorithm to determine the optimal bar shape. MATERIAL AND METHODS The normal sterno-vertebral distance was defined on computed tomography (CT) scans of patients without pectus excavatum (PEx) at the same level where the deepest depression was found on CT scans of 97 patients with PEx. Four points were marked on the CT scan of 60 patients with PEx at the deepest deformity: P1: edge of the vertebra; P2: edge of the deformity; P3: the expected contact point of the bar and the rib; and P4: the expected end of the bar. The algorithm generated 3 circles upon these points, and the fusion of the arcs drew the line of the ideal bar. Corrected and normal sterno-vertebral distance values were compared with the Mann-Whitney U test. Ten bars were bent manually guided by a 1: 1 printout of the designed bar and were implanted in 10 adolescents. RESULTS The shortest sterno-vertebral distance was 3 cm below the intermammillary line in PEx patients. The normal mean sterno-vertebral distance at this level was 10.16±1.35 cm in non-PEx patients. The mean virtually corrected sterno-vertebral distance was 10.28±1.27 cm. No significant difference was found (P=0.44). The bars were seamless and were successfully implanted. No bar needed adjustment, the operation time was shorter, and the patient satisfaction score was 9.4/10. CONCLUSIONS With our new algorithm, an optimal Nuss bar can be designed.

Parametric Design Method and Lift/Drag Characteristics Analysis for a Wide-Range, Wing-Morphing Glide Vehicle

The parametric design method is widely utilized in the preliminary design stage for hypersonic vehicles; it ensures the fast iteration of configuration, generation, and optimization. This study proposes a novel parametric method for a wide-range, wing-morphing glide vehicle. The whole configuration, including a waverider fuselage, a rotating wing, a blunt leading edge, rudders, etc., can be easily described using 27 key parameters. In contrast to the typical parametric method, the new method takes internal payloads into consideration during the shape optimization process. That is, the vehicle configuration can be flexibly adjusted depending on the internal payloads; these payloads may be of random amounts and have different shapes. The code for the new parametric design method is developed using the secondary development tools of UG (UG 10.0) commercial software. The lift and drag characteristics over a wide operational range (H = 6–25 km, M = 2.5–8.5, AOA = 0–10°) were numerically investigated, as was the influence of the retracting angle of the morphing wings. It was found that, for the mode of the fully deployed wings, the lift-to-drag ratio (L/D) remained at a high level (≥4.7) over a Mach range of 4.0–8.5 and an AOA range of 4–7°. For the mode of the fully retracted wings, the drag coefficient remained smaller than 0.02 over a Mach range of 4.0–8.5 and an AOA range of 0–5°. A wide L/D of 0.3–4.7 could be achieved by controlling the retracting angle of the wings, thus demonstrating a good potential for flight maneuverability. The flexible change in L/D proved to be a combined result of varying pressure distribution and edge-flow spillage. This will aid in the further optimization of lift/drag characteristics.

Optimization design of forebody shape of an underwater axisymmetric body for transition delay using a genetic algorithm

The forebody shape of an underwater vehicle significantly influences the transition position of the boundary layer, which, in turn, impacts the flow-induced noise that can interfere with the sonar in the head. Typically, underwater vehicle forebodies are axisymmetric. Optimizing the forebody shape of an axisymmetric body can effectively delay the boundary layer transition and reduce the interference caused by flow noise on the sonar. This study applies an artificial intelligence algorithm for the optimization of the forebody shape. Specifically, a genetic algorithm is adopted to establish the optimization design method. The non-uniform rational B-spline (NURBS) method is used to parameterize the forebody shape, and the eN method based on linear stability theory is employed to predict the transition position. The optimization is conducted at the scale of a real vehicle and at a fixed velocity. After 45 generations, the genetic algorithm converges to an optimized shape. The transition position of the optimized shape is significantly delayed in comparison to that of the optimal original shape, with the relative delay amounting to an impressive 20.8%. Furthermore, the optimized shape effectively suppresses wall pressure fluctuation (WPF) in the unstable laminar region, also contributing to a reduction in flow-induced noise.

Numerical Investigation and Optimization of a Morphing Airfoil Designed for Lower Reynolds Number

A novel concept of morphing airfoils, capable of changing camber and thickness, is proposed. A variable airfoil shape, defined by six input parameters, is achieved by allowing the three spinal points (at fixed axial positions) to slide vertically, while the upper and lower surfaces are determined by the lengths of the three corresponding ribs that are perpendicular to the spine. Thus, it is possible to find the most appropriate geometric configuration for a wide range of possible operating conditions often present with contemporary unmanned aerial vehicles. Shape optimizations for different Reynolds numbers and different cost functions are performed by coupling a genetic algorithm with simple panel method flow calculations. The obtained airfoils are presented and compared, whereas the proposed concept is validated by more advanced flow simulations. It appears that improvements in aerodynamic performance of nearly 20% can be expected at Re ranging from 0.05 × 106 to 0.1 × 106. The proposed methodology shows promise and can be applied to different types of lifting surfaces, including wing, tail or propeller blade segments. To check the viability of this method for producing airfoils that can be used in a practical sense, structural analysis of one of the obtained geometries using a simplified 1D finite element method as well as a more detailed 3D analysis are performed. The model is then 3D-printed on a fused deposition modeling (FDM) printer with a polyethylene terephthalate glycol (PETG) filament, and the capability of the airfoil to adequately morph between the two desired geometries is experimentally shown.

Multi-objective optimization of assembly free-form cable-stiffened reticulated shell considering the influence of initial states

In this study, we propose a geometric model of free-form grid structures based on the sliding translation method. Furthermore, an end-flattened inserted-plate joint could be applied to a quadrilateral free-form grid structure. The height of the control point was considered as the optimization variable, while the strain energy, geometric integrated index, and ultimate bearing capacity were considered as the optimization objectives. The results demonstrated the influence of the initial prestress and joint stiffness using multi-objective optimization. Based on the effects of the initial prestress, joint stiffness, and initial geometric imperfections, we propose a multi-objective optimization method for the assembly of a free-form cable-stiffened reticulated shell. The feasibility of the optimization method was verified using examples. Compared with the results of the shape optimization, structures having superior mechanical properties and mesh quality were obtained via the combined method for optimizing the shape and initial prestress, which verified the necessity and effectiveness of the combined optimization method. The mechanical properties of the optimized structures were improved by increasing the joint stiffness; in particular, the ultimate bearing capacity was improved. On using the multi-objective optimization method while considering the initial geometric imperfections, the properties of the structure were improved effectively, and the mechanical properties can be guaranteed even after geometric imperfections are applied.

An efficient and robust shape optimization framework for gridshell designs based on node shifting method

In this paper, a novel and efficient shape optimization framework for freeform gridshell designs, especially for cantilevering structures, is proposed based on the node shifting method. The nodal coordinates are directly chosen as the design variables without any extra parameterization, and are iteratively updated to minimize the structural compliance. The distributed load filter is introduced for a smoother and more efficient shape updating scheme, where the negative sensitivity numbers are applied as the virtual external load for the shape updating analysis to guarantee both the smoothness of surfaces and the sustained reduction of structural compliance at each step. The penalized volume adjustment subroutine is then applied to satisfy the volume constraint and to improve the uniformity of grids. Compared to the conventional nodal shifting methods, it is observed that a much more stable and faster convergence is achieved. A variety of examples are presented to demonstrate the improved effectiveness and the efficiency of the proposed algorithm.

Topology Optimization Design Method for Acoustic Imaging Array of Power Equipment.

Acoustic imaging technology has the advantages of non-contact and intuitive positioning. It is suitable for the rapid positioning of defects such as the mechanical loosening, discharge, and DC bias of power equipment. However, the existing research lacks the optimization design of microphone array topology. The acoustic frequency domain characteristics of typical power equipment are elaborately sorted out. After that, the cut-off frequencies of acoustic imaging instruments are determined, to meet the needs of the full bandwidth test requirements. Through a simulation calculation, the circular array is demonstrated to be the optimal shape. And the design parameters affect the imaging performance of the array to varying degrees, indicating that it is difficult to obtain the optimal array topology by an exhaustive method. Aimed at the complex working conditions of power equipment, a topology optimization design method of an acoustic imaging array for power equipment is proposed, and the global optimal solution of microphone array topology is obtained. Compared with the original array, the imaging performance of the improved LF and HF array is promoted by 54% and 49%, respectively. Combined with the simulation analysis and laboratory test, it is verified that the improved array can not only accurately locate the single sound source but also accurately identify the main sound source from the interference of the contiguous sound source.

The Shape Effect of Acoustic Micropillar Array Chips in Flexible Label-Free Separation of Cancer Cells.

The precise isolation of circulating tumor cells (CTCs) from blood samples is a potent tool for cancer diagnosis and clinical prognosis. However, CTCs are present in extremely low quantities in the bloodstream, posing a significant challenge to their isolation. In this study, we propose a non-contact acoustic micropillar array (AMPA) chip based on acoustic streaming for the flexible, label-free capture of cancer cells. Three shapes of micropillar array chips (circular, rhombus, and square) were fabricated. The acoustic streaming characteristics generated by the vibration of microstructures of different shapes are studied in depth by combining simulation and experiment. The critical parameters (voltage and flow rate) of the device were systematically investigated using microparticle experiments to optimize capture performance. Subsequently, the capture efficiencies of the three micropillar structures were experimentally evaluated using mouse whole blood samples containing cancer cells. The experimental results revealed that the rhombus microstructure was selected as the optimal shape, demonstrating high capture efficiency (93%) and cell activity (96%). Moreover, the reversibility of the acoustic streaming was harnessed for the flexible release and capture of cancer cells, facilitating optical detection and analysis. This work holds promise for applications in monitoring cancer metastasis, bio-detection, and beyond.

Optimization of fin parameters in cooling systems for temperature uniformity enhancement in battery module applications with offset strip fins

The efficient thermal management of Lithium-ion batteries (LIBs) stands as a critical factor in ensuring the reliable operation of electric vehicles. For managing multiple LIB modules, a common approach involves utilizing a cold plate for mounting. It has been suggested that this interspersed design proves more effective, especially for large-scale battery packs, in achieving smoother overall cooling performance and temperature uniformity. Consequently, we need a new cold plate design that not only enhances thermal performance for batteries emitting higher thermal loads but also ensures more uniform temperature distributions across battery surfaces, all while maintaining simplicity in manufacturability. In this study, we introduce a new cold plate design employing offset strip fins (OSFs) cores. We assess its thermal and hydraulic performance using objective functions such as the Colburn factor ( j ) and Fanning friction factor ( f ). Through optimization techniques, we determine the optimal shape parameters that maximize heat transfer rates on the cold plate, with only a marginal increase in pressure drop. This optimized configuration is then compared with both the baseline common cold plate and a reference OSFs cold plate. The results show a significant reduction of up to 32.3% in maximum temperature differences, signifying an improved temperature uniformity achieved with this new design.

Physics-informed shape optimization using coordinate projection

The rapid growth of artificial intelligence is revolutionizing classical engineering society, offering novel approaches to material and structural design and analysis. Among various scientific machine learning techniques, physics-informed neural network (PINN) has been one of the most researched subjects, for its ability to incorporate physics prior knowledge into model training. However, the intrinsic continuity requirement of PINN demands the adoption of domain decomposition when multiple materials with distinct properties exist. This greatly complicates the gradient computation of design features, restricting the application of PINN to structural shape optimization. To address this, we present a novel framework that employs neural network coordinate projection for shape optimization within PINN. This technique allows for direct mapping from a standard shape to its optimal counterpart, optimizing the design objective without the need for traditional transition functions or the definition of intermediate material properties. Our method demonstrates a high degree of adaptability, allowing the incorporation of diverse constraints and objectives directly as training penalties. The proposed approach is tested on magnetostatic problems for iron core shape optimization, a scenario typically plagued by the high permeability contrast between materials. Validation with finite-element analysis confirms the accuracy and efficiency of our approach. The results highlight the framework’s capability as a viable tool for shape optimization in complex material design tasks.

Multiobjective optimization of Vortex Generators for heat transfer enhancement in turbulent flows

Convective heat transfer can be enhanced by streamwise vortices and coherent flow structures produced downstream Vortex Generators (VGs). The thermal performance depends on the VG shape which controls the intensity and topology of the vortices. Thus, VG shape optimization is a major challenge in designing sustainable and efficient heat exchangers. In the present study, a multi-objective optimization is performed through large space exploration design to find optimal VG shapes that adapt to different flow regimes. Simulations are carried out in parallel plate turbulent flow for three different Reynolds numbers; Re1=4600,Re2=9920, and Re3=30050. The present numerical results are first validated against numerical and experimental data from the open literature. Then, and for the first time, seven design parameters are investigated, based on VG shape dimensions. The new optimized VG show a thermal enhancement factor between 11 and 35%, relative to a smooth channel case, and between 3 and 14%, relative to different VG shapes from the recent open literature. The present results are analyzed in details by focusing on the physics of the flow structure and its correlation to the convective heat transfer enhancement using local criteria for flow visualization and vortex intensity quantification.

Effects of Limiting the Number of Different Cross-Sections Used in Statically Loaded Truss Sizing and Shape Optimization.

This research aims to show the effects of adding cardinality constraints to limit the number of different cross-sections used in simultaneous sizing and shape optimization of truss structures. The optimal solutions for sizing and shape optimized trusses result in a generally high, and impractical, number of different cross-sections being used. This paper presents the influence of constraining the number of different cross-sections used on the optimal results to bring the scientific results closer to the applicable results. The savings achieved using the cardinality constraint are expected to manifest in more than just the minimization of weight but in all the other aspects of truss construction, such as labor, assembly time, total weld length, surface area to be treated, transport, logistics, and so on. It is expected that the optimal weight of the structures would be greater than when not using this constraint; however, it would still be below conventionally sized structures and have the added benefits derived from the simplicity and elegance of the solution. The results of standard test examples for each different cardinality constraint value are shown and compared to the same examples using only a single cross-section on all bars and the overall optimal solution, which does not have the cardinality constraint. An additional comparison is made with results of just the sizing optimization from previously published research where authors first used the same cardinality constraint.

A stacking-based ensemble prediction method for multiobjective aerodynamic optimization of high-speed train nose shape

A stacking-based ensemble prediction method is proposed in order to improve the efficiency and accuracy of aerodynamic shape optimization. This can be divided into a two-level model. The first-level model uses various base learners to predict the training dataset and obtain various combinations of predictions. In the second-level model, the meta-learner is trained using various combinations of predictions as inputs and the true response values as outputs. The RMSE and R-Square metrics results show that the performance metrics of the stacked models are significantly better than those of the original surrogate models, except for the stacked RBFNN model. The stacked Kriging model and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0039 and 0.8418 for aerodynamic drag coefficient, respectively. The stacked Kriging model, RBFNN model, and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0024 and 0.76 for aerodynamic lift coefficient, respectively. Four state-of-the-art multiobjective optimization algorithms are used to perform the optimization process. The results of hypervolume and Pareto fronts demonstrate the effectiveness of the selected FDV-NSGAII algorithm. After optimization, the drag and lift coefficients before and after optimization are reduced by 1.9% and 12.7%, respectively.