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Keywords = NURBS-based model

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23 pages, 5585 KB  
Article
NURBS Morphing Optimization of Drag and Lift in a Coupe-Class Vehicle Using Symmetry-Plane Comparison of Aerodynamic Performance
by Sohaib Guendaoui, Abdeslam El Akkad, Ahmed El Khalfi, Sorin Vlase and Marin Marin
Symmetry 2025, 17(9), 1571; https://doi.org/10.3390/sym17091571 - 19 Sep 2025
Viewed by 383
Abstract
This study presents a morphing Non-Uniform Rational B-Spline (NURBS) optimization method for enhancing sports car aerodynamics, with performance evaluation conducted in the vehicle’s symmetry plane. The morphing approach enables precise, smooth deformations of rear-end and spoiler geometries while preserving shape continuity, allowing controlled [...] Read more.
This study presents a morphing Non-Uniform Rational B-Spline (NURBS) optimization method for enhancing sports car aerodynamics, with performance evaluation conducted in the vehicle’s symmetry plane. The morphing approach enables precise, smooth deformations of rear-end and spoiler geometries while preserving shape continuity, allowing controlled aerodynamic modifications suitable for comparative analysis. Flow simulations were carried out in ANSYS Fluent 2022 using the Reynolds-Averaged Navier–Stokes (RANS) equations with the standard k-ε turbulence model, selected for its stability and accuracy in predicting boundary-layer evolution, wake behavior, and flow separation in external automotive flows. Three configurations were assessed: the baseline model, a spoiler-equipped version, and two NURBS-morphed designs. The symmetry-plane evaluation ensured bilateral balance across all variants, enabling direct comparison of drag and lift performance. The results show that the proposed morphing strategy achieved notable lift reduction and favorable drag-to-lift ratios while maintaining manufacturability. The findings demonstrate that combining NURBS-based morphing with symmetry-plane aerodynamic assessment offers an efficient, reliable framework for vehicle aerodynamic optimization, bridging geometric flexibility with robust computational evaluation. Full article
(This article belongs to the Section Mathematics)
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15 pages, 4368 KB  
Article
On the Construction of Freeform Volumetric 3D Puzzles
by Gershon Elber
Modelling 2025, 6(3), 90; https://doi.org/10.3390/modelling6030090 - 25 Aug 2025
Viewed by 562
Abstract
We present a simple algorithm for synthesizing volumetric 3D puzzles from a 3D freeform geometric model represented volumetrically as trivariate NURBs functions, M. The construction algorithm is based on the functional composition of puzzle elements, positioned in the domain of M, [...] Read more.
We present a simple algorithm for synthesizing volumetric 3D puzzles from a 3D freeform geometric model represented volumetrically as trivariate NURBs functions, M. The construction algorithm is based on the functional composition of puzzle elements, positioned in the domain of M, with M. The puzzle elements can be (heterogeneous) freeform polygonal models or freeform surface or trivariate functions and of arbitrary shape, and can include added joints to neighboring puzzle elements. The proposed approach is demonstrated via several examples of such volumetric puzzles, 3D printed and assembled. Full article
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18 pages, 15177 KB  
Article
Optimization-Driven Reconstruction of 3D Space Curves from Two Views Using NURBS
by Musrrat Ali, Deepika Saini, Sanoj Kumar and Abdul Rahaman Wahab Sait
Mathematics 2025, 13(14), 2256; https://doi.org/10.3390/math13142256 - 12 Jul 2025
Viewed by 528
Abstract
In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight [...] Read more.
In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight optimization. This study introduces an enhanced iterative strategy that leverages the geometric significance of NURBS weights to incrementally refine curve fitting. By formulating an inverse optimization problem guided by model deformation principles, the proposed method progressively adjusts weights to minimize reprojection error. Experimental evaluations confirm the method’s convergence and demonstrate its superiority in fitting accuracy when compared to conventional optimization techniques. Full article
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23 pages, 2527 KB  
Article
Application of Machine Learning for Bulbous Bow Optimization Design and Ship Resistance Prediction
by Yujie Shen, Shuxia Ye, Yongwei Zhang, Liang Qi, Qian Jiang, Liwen Cai and Bo Jiang
Appl. Sci. 2025, 15(6), 2934; https://doi.org/10.3390/app15062934 - 8 Mar 2025
Cited by 2 | Viewed by 1159
Abstract
Resistance is a key index of a ship’s hydrodynamic performance, and studying the design of the bulbous bow is an important method to reduce ship resistance. Based on the ship resistance sample data obtained from computational fluid dynamics (CFD) simulation, this study uses [...] Read more.
Resistance is a key index of a ship’s hydrodynamic performance, and studying the design of the bulbous bow is an important method to reduce ship resistance. Based on the ship resistance sample data obtained from computational fluid dynamics (CFD) simulation, this study uses a machine learning method to realize the fast prediction of ship resistance corresponding to different bulbous bows. To solve the problem of insufficient accuracy in the single surrogate model, this study proposes a CBR surrogate model that integrates convolutional neural networks with backpropagation and radial basis function models. The coordinates of the control points of the NURBS surface at the bulbous bow are taken as the design variables. Then, a convergence factor is introduced to balance the global and local search abilities of the whale algorithm to improve the convergence speed. The sample space is then iteratively searched using the improved whale algorithm. The results show that the mean absolute error and root mean square error of the CBR model are better than those of the BP and RBF models. The accuracy of the model prediction is significantly improved. The optimized bulbous bow design minimizes the ship resistance, which is reduced by 4.95% compared with the initial ship model. This study provides a reliable and efficient machine learning method for ship resistance prediction. Full article
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23 pages, 8962 KB  
Article
A Parametric Design Method for Unstepped Planing Hulls Using Longitudinal Functions and Shape Coefficients
by Junjie Chen, Yongpeng Ou, Guo Xiang, Qing Ye and Wei Wang
Appl. Sci. 2025, 15(5), 2667; https://doi.org/10.3390/app15052667 - 1 Mar 2025
Viewed by 1159
Abstract
This paper proposes a specifically parametric design method for planing hulls using longitudinal functions and shape coefficients in order to meet the requirements for optimizing the hydrodynamic performance of planing hulls. To fully define the geometry of the planing hull, a series of [...] Read more.
This paper proposes a specifically parametric design method for planing hulls using longitudinal functions and shape coefficients in order to meet the requirements for optimizing the hydrodynamic performance of planing hulls. To fully define the geometry of the planing hull, a series of design parameters and a set of longitudinal functions and shape coefficients are introduced to define key geometric features. The main frame curves of the hull are designed from bottom to top to ensure the priority and independence of parameters related to the planing surface. The mathematical equations of the control points of the keel curve, chine curve, sheer curve, and surface station curve of the hull framework are established and solved based on B-spline theory. This configures the basis for generating a continuous smooth surface of the hull. Finally, based on the frame curves, the hull surface was generated by using NURBS surface interpolation. The design parameters, especially the longitudinal functions and shape coefficients, can intuitively and independently control the key features of the hull form, which allow control over key geometric features that are highly relevant to the hydrodynamics of the planing hull. By utilizing this approach, rapid production of deep-V and radial planing hulls is achievable, resulting in closed and smooth hull surfaces. Case studies have provided evidence that the modeling of monohull unstepped planing hulls with diverse characteristics can be effectively accomplished through the definition of these parameters. Full article
(This article belongs to the Section Marine Science and Engineering)
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21 pages, 5267 KB  
Article
Research on a Fully Parameterized Geometric Modeling Method for an Air Cavity Planing Hull
by Junjie Chen, Yongpeng Ou, Guo Xiang, Wei Wang and Hao Wu
J. Mar. Sci. Eng. 2025, 13(3), 476; https://doi.org/10.3390/jmse13030476 - 28 Feb 2025
Viewed by 602
Abstract
An air-lubricated planing hull with integrated air channels presents a transformative approach for enhancing marine vessel performance by significantly reducing hydrodynamic resistance. Within the framework of air-layer drag reduction research, the precise definition and optimization of geometric design parameters are critical, as they [...] Read more.
An air-lubricated planing hull with integrated air channels presents a transformative approach for enhancing marine vessel performance by significantly reducing hydrodynamic resistance. Within the framework of air-layer drag reduction research, the precise definition and optimization of geometric design parameters are critical, as they directly influence the formation and stability of the air layer and the hydrodynamic characteristics of the hull. Applying a fully parameterized modeling approach to the air-lubricated planing hull is highly relevant and pivotal for advancing systematic, performance-driven hull design and optimization in modern naval architecture. This study proposes a fully parameterized modeling method specifically designed for such crafts. The method utilizes B-spline curves to represent the planar projections of the primary hull contours and the sectional lines of key hull surfaces. The hull surfaces are fitted using non-uniform rational B-Spline (NURBS) surfaces, and the design parameters are smoothed according to the principle of minimum strain energy, leading to fair and smooth hull surfaces. A dedicated program is developed based on this method. It facilitates the rapid generation of smooth hull forms for an air-lubricated planing hull solely from design parameters without depending on parent hull forms. This approach provides geometric hull samples for optimizing the hydrodynamic performance of the air-lubricated planing hull. Full article
(This article belongs to the Section Ocean Engineering)
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26 pages, 1133 KB  
Article
Adaptive CT XIGA Using LR B-Splines for Efficient Fracture Modeling
by Fei Gao, Cancan Ge, Zhuochao Tang, Jiming Gu and Rui Meng
Materials 2025, 18(5), 920; https://doi.org/10.3390/ma18050920 - 20 Feb 2025
Viewed by 520
Abstract
This paper presents a novel adaptive crack-tip extended isogeometric analysis (adaptive CT XIGA) framework based on locally refined B-splines (LR B-splines) for efficient and accurate fracture modeling in two-dimensional solids. The XIGA method facilitates crack modeling without requiring the specific locations of crack [...] Read more.
This paper presents a novel adaptive crack-tip extended isogeometric analysis (adaptive CT XIGA) framework based on locally refined B-splines (LR B-splines) for efficient and accurate fracture modeling in two-dimensional solids. The XIGA method facilitates crack modeling without requiring the specific locations of crack faces and enables crack propagation simulation without remeshing by employing localized enrichment functions. LR B-splines, as an advanced extension of B-splines and NURBS, offer high-order continuity, precise geometric representation, and local refinement capabilities, thereby enhancing computational accuracy and efficiency. Various local mesh refinement strategies, designed based on crack and crack-tip locations, are investigated. Among these strategies, the crack-tip topological refinement strategy is adopted for local refinement in the adaptive CT XIGA framework. Stress intensity factors (SIFs) are evaluated using the contour interaction integral technique, while the maximum circumferential stress criterion is adopted to predict the crack growth direction. Numerical examples demonstrate the accuracy, efficiency, and robustness of adaptive CT XIGA. The results confirm that the proposed framework achieves superior error convergence rates and significantly reduces computational costs compared to a-posteriori-error-based adaptive XIGA methods, particularly in crack propagation simulations. These advantages establish adaptive CT XIGA as a powerful and efficient tool for addressing complex fracture problems in solid mechanics. Full article
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36 pages, 12291 KB  
Article
Skill-Learning-Based Trajectory Planning for Robotic Vertebral Plate Cutting: Personalization Through Surgeon Technique Integration and Neural Network Prediction
by Heqiang Tian, Xiang Zhang, Yurui Yin and Hongqiang Ma
Biomimetics 2024, 9(12), 719; https://doi.org/10.3390/biomimetics9120719 - 21 Nov 2024
Viewed by 1114
Abstract
In robotic-assisted laminectomy decompression, stable and precise vertebral plate cutting remains challenging due to manual dependency and the absence of adaptive skill-learning mechanisms. This paper presents an advanced robotic vertebral plate-cutting system that leverages patient-specific anatomical variations and replicates the surgeon’s cutting technique [...] Read more.
In robotic-assisted laminectomy decompression, stable and precise vertebral plate cutting remains challenging due to manual dependency and the absence of adaptive skill-learning mechanisms. This paper presents an advanced robotic vertebral plate-cutting system that leverages patient-specific anatomical variations and replicates the surgeon’s cutting technique through a trajectory parameter prediction model. A spatial mapping relationship between artificial and patient vertebrae is first established, enabling the robot to mimic surgeon-defined trajectories with high accuracy. The robotic system’s trajectory planning begins with acquiring point cloud data of the vertebral plate, which undergoes preprocessing, Non-Uniform Rational B-Splines (NURBS) fitting, and parametric discretization. Using the processed data, a spatial mapping method translates the surgeon’s cutting path to the robotic coordinate system, with simulation validating the trajectory’s adherence to surgical requirements. To further enhance the accuracy and stability of trajectory planning, a Backpropagation(BP) neural network is implemented, providing predictive modeling for trajectory parameters. The analysis and training of the neural network confirm its effectiveness in capturing complex cutting trajectories. Finally, experimental validation, involving an artificial vertebral body model and cutting trials on patient vertebrae, demonstrates the proposed method’s capability to deliver enhanced cutting precision and stability. This skill-learning-based, personalized trajectory planning approach offers significant potential for improving the safety and quality of orthopedic robotic surgeries. Full article
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26 pages, 14206 KB  
Article
The Heritage Building Information Modeling Methodology for Structural Diagnosis: An Integrated System of Digital Models for the Baptistery of San Giovanni in Pisa
by Giada Bartolini, Anna De Falco, Lorenzo Gianfranceschi, Massimiliano Martino and Laura Vignali
Heritage 2024, 7(11), 6366-6391; https://doi.org/10.3390/heritage7110298 - 15 Nov 2024
Viewed by 1269
Abstract
The structural diagnosis of monumental buildings necessitates organizing diverse cross-disciplinary data. The H-BIM procedure employs 3D digital models to create a comprehensive virtual repository, offering advantages in documentation access, interoperability, intervention design, cost evaluation, and maintenance management. This work proposes an approach to [...] Read more.
The structural diagnosis of monumental buildings necessitates organizing diverse cross-disciplinary data. The H-BIM procedure employs 3D digital models to create a comprehensive virtual repository, offering advantages in documentation access, interoperability, intervention design, cost evaluation, and maintenance management. This work proposes an approach to combining different models while addressing interoperability challenges by best exploiting their positive characteristics. After evaluating the advantages and limitations of textured-mesh and NURBS-based models, and virtual reality environments based on specific comparison criteria, an integrated system of these models within the H-BIM framework is proposed. The latter is applied to study the relevant case of the Baptistery of San Giovanni in Pisa, Italy. The integrated H-BIM model is designed primarily to facilitate the structural diagnosis of the monument, and illustrates how combining different 3D representations, each providing multiple information with different levels of detail, enhances its capabilities. This integration results in a more effective tool for the multidisciplinary conservation of cultural heritage, accommodating a wide range of data beyond structural aspects, thus fostering collaboration among professionals from various fields of expertise. Full article
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16 pages, 8484 KB  
Article
Stochastic Dynamic Buckling Analysis of Cylindrical Shell Structures Based on Isogeometric Analysis
by Qingqing Yu, Xiaojun Liu, Fei Xue, Zhenyu Guan, Yujie Guo and Jianjiang Zeng
Mathematics 2024, 12(17), 2742; https://doi.org/10.3390/math12172742 - 3 Sep 2024
Cited by 1 | Viewed by 1362
Abstract
In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified [...] Read more.
In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis. Full article
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21 pages, 20296 KB  
Article
Isogeometric Topology Optimization of Multi-Material Structures under Thermal-Mechanical Loadings Using Neural Networks
by Yi Qiu, Cheng Xu, Jiangpeng Peng and Yanjie Song
Mathematics 2024, 12(15), 2350; https://doi.org/10.3390/math12152350 - 27 Jul 2024
Cited by 3 | Viewed by 1186
Abstract
An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and [...] Read more.
An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and computational models. Neural networks replace the optimization algorithms of traditional topology optimization to update the relative densities of multi-material structures. The weights and biases of neural networks are taken as design variables and updated by automatic differentiation without derivation of the sensitivity formula. In addition, the grid elements can be refined directly by increasing the number of refinement nodes, resulting in high-resolution optimal topology without extra computational costs. To obtain comprehensive performance from ITO for multi-material structures, a weighting coefficient is introduced to regulate the proportion between thermal compliance and compliance in the loss function. Some numerical examples are given and the validity is verified by performance analysis. The optimal topological structures obtained based on the proposed model exhibit both excellent heat dissipation and stiffness performance under thermal-mechanical loadings. Full article
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24 pages, 11966 KB  
Article
Evaluation of Denoising and Voxelization Algorithms on 3D Point Clouds
by Sara Gonizzi Barsanti, Marco Raoul Marini, Saverio Giulio Malatesta and Adriana Rossi
Remote Sens. 2024, 16(14), 2632; https://doi.org/10.3390/rs16142632 - 18 Jul 2024
Cited by 10 | Viewed by 3136
Abstract
Proper documentation is fundamental to providing structural health monitoring, damage identification and failure assessment for Cultural Heritage (CH). Three-dimensional models from photogrammetric and laser scanning surveys usually provide 3D point clouds that can be converted into meshes. The point clouds usually contain noise [...] Read more.
Proper documentation is fundamental to providing structural health monitoring, damage identification and failure assessment for Cultural Heritage (CH). Three-dimensional models from photogrammetric and laser scanning surveys usually provide 3D point clouds that can be converted into meshes. The point clouds usually contain noise data due to different causes: non-cooperative material or surfaces, bad lighting, complex geometry and low accuracy of the instruments utilized. Point cloud denoising has become one of the hot topics of 3D geometric data processing, removing these noise data to recover the ground-truth point cloud and adding smoothing to the ideal surface. These cleaned point clouds can be converted in volumes with different algorithms, suitable for different uses, mainly for structural analysis. This paper aimed to analyse the geometric accuracy of algorithms available for the conversion of 3D point clouds into volumetric models that can be used for structural analyses through the FEA process. The process is evaluated, highlighting problems and difficulties that lie in poor reconstruction results of volumes from denoised point clouds due to the geometric complexity of the objects. Full article
(This article belongs to the Special Issue New Perspectives on 3D Point Cloud II)
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23 pages, 26729 KB  
Article
A Parameter-Driven Methodology of Wheel Flat Modeling for Wheel–Rail Impact Dynamics
by Guangwei Zhao, Nan Li, Yuxin Sun and Changxin Chi
Appl. Sci. 2024, 14(13), 5956; https://doi.org/10.3390/app14135956 - 8 Jul 2024
Viewed by 1630
Abstract
A wheel flat is a typical wheel defect that significantly impacts the wheel–rail system, posing substantial challenges to vehicle operation safety. In the existing literature, the wheel flat plane model does not account for the contribution of the width direction to the impact [...] Read more.
A wheel flat is a typical wheel defect that significantly impacts the wheel–rail system, posing substantial challenges to vehicle operation safety. In the existing literature, the wheel flat plane model does not account for the contribution of the width direction to the impact response and thus cannot accurately reveal the wheel–rail contact state with a flat. This paper systematically proposes a three-dimensional analytical model that considers multiple worn stages and constructs a spatial complex surface reconstruction model for flats based on NURBS technology. A vehicle–track coupled dynamics model, considering the geometry of the flat, is established to investigate the effects of flat geometry on the wheel–rail impact response and contact relationship in detail. The results show that in the subcritical regime, the wear degree of the flat predominantly affects the impact force, while in the transcritical regime, both the wear degree and velocity together determine the magnitude of the wheel–rail impact force. As the wear degree increases, the moment of wheel lateral jump occurs earlier. The spatial modeling method for flats proposed in this paper offers a novel technical approach for accurately simulating the dynamic behavior of wheel–rail contact when a flat is present. Full article
(This article belongs to the Topic Vehicle Dynamics and Control)
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20 pages, 9501 KB  
Article
Inverse Geometric Reconstruction Based on MW-NURBS Curves
by Musrrat Ali, Deepika Saini and Sanoj Kumar
Mathematics 2024, 12(13), 2071; https://doi.org/10.3390/math12132071 - 2 Jul 2024
Cited by 2 | Viewed by 1467
Abstract
Currently, rational curves such as the Non-Uniform Rational B-Spline (NURBS) play a significant role in both shape representation and shape reconstruction. NURBS weights are often real in nature and are referred to as challenging to assign, with the exception of conics. ‘Matrix Weighted [...] Read more.
Currently, rational curves such as the Non-Uniform Rational B-Spline (NURBS) play a significant role in both shape representation and shape reconstruction. NURBS weights are often real in nature and are referred to as challenging to assign, with the exception of conics. ‘Matrix Weighted Rational Curves’ are the expanded form of rational curves that result from replacing these real weights with matrices, or matrix weights. The only difference between these curves and conventional curves is the geometric definition of the matrix weights. In this paper, MW-NURBS curves are used to reconstruct space curves from their stereo perspectives. In particular, MW-NURBS fitting is carried out in stereo views, and the weight matrices for the MW-NURBS curves are produced using the normal vectors provided at the control points. Instead of needing to solve a complicated system, the MW-NURBS model can reconstruct curves by choosing control points and control normals from the input data. The efficacy of the proposed strategy is verified by using many examples based on both synthetic and real images. The various error types are compared to those of conventional methods like point-based and NURBS-based approaches. The results demonstrate that the errors acquired from the proposed approach are much fewer than those obtained from the point-based method and the NURBS-based method. Full article
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15 pages, 9215 KB  
Article
Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach
by Sanjay Rajni Vejanand, Alexander Janushevskis and Ivo Vaicis
Computation 2024, 12(5), 90; https://doi.org/10.3390/computation12050090 - 2 May 2024
Viewed by 1655
Abstract
While there are multiple methods to ventilate protective clothing, there is still room for improvement. In our research, we are using ventilation elements that are positioned at the ventilation holes in the air space between the body and clothing. These ventilation elements allow [...] Read more.
While there are multiple methods to ventilate protective clothing, there is still room for improvement. In our research, we are using ventilation elements that are positioned at the ventilation holes in the air space between the body and clothing. These ventilation elements allow air to flow freely while preventing sun radiation, rain drops, and insects from directly accessing the body. Therefore, the shape of the ventilation element is crucial. This led us to study the shape optimization of ventilation elements through the utilization of metamodels and numerical approaches. In order to accomplish the objective, it is crucial to thoroughly evaluate and choose suitable criteria for the optimization process. We know from prior research that the toroidal cut-out shape element provides better results. In a previous study, we optimized the shape of this element based on the minimum pressure difference as a criterion. In this study, we are using different criteria for the shape optimization of ventilation elements to determine which are most effective. This study involves a metamodeling strategy that utilizes local and global approximations with different order polynomials, as well as Kriging approximations, for the purpose of optimizing the geometry of ventilation elements. The goal was achieved by a sequential process. (1) Planning the position of control points of Non-Uniform Rational B-Splines (NURBS) in order to generate elements with a smooth shape. (2) Constructing geometric CAD models based on the design of experiments. (3) Compute detailed model solutions using SolidWorks Flow Simulation. (4) Developing metamodels for responses using computer experiments. (5) Optimization of element shape using metamodels. The procedure is repeated for six criteria, and subsequently, the results are compared to determine the most efficient criteria for optimizing the design of the ventilation element. Full article
(This article belongs to the Section Computational Engineering)
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