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Keywords = plate stiffness properties

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17 pages, 3469 KiB  
Article
Performance Characteristics of a New Aerostatic Thrust Bearing with Poro-Elastic Restrictor
by Alin Mărgineanu, Alice Marinescu, Aurelian Fatu, Traian Cicone and Yann Henry
Lubricants 2025, 13(8), 346; https://doi.org/10.3390/lubricants13080346 - 3 Aug 2025
Viewed by 50
Abstract
Aerostatic bearings were proven to be an optimal choice in situations where low friction, cleanliness, and high motion accuracy are required. Their functionality relies heavily on flow restrictors, which are responsible for regulating and controlling the supply flow, and consequently, the thickness and [...] Read more.
Aerostatic bearings were proven to be an optimal choice in situations where low friction, cleanliness, and high motion accuracy are required. Their functionality relies heavily on flow restrictors, which are responsible for regulating and controlling the supply flow, and consequently, the thickness and stiffness of the fluid film. A diverse range of restrictors with varying characteristics is used, among which are the porous restrictors. The current work introduces a novel solution involving a porous, highly compressible restrictor, whose element of novelty compared to its predecessors consists of its variable thickness and corresponding permeability, regulated by the load on the bearing. The gas is supplied through an annular, elastic, deformable, porous disc, which is compressed by a metal plate, subjected to compression by the recess pressure on one side and by the supply pressure on the other side. One or more springs are used in parallel with the porous disc to obtain the optimum elastic response. The objective of this study is to evaluate the performance characteristics and compare them to a conventional restrictor. A parametric analysis is performed to define the size and properties of the porous restrictor. Full article
(This article belongs to the Special Issue Advances in Lubricated Bearings, 2nd Edition)
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22 pages, 9506 KiB  
Article
The Influence of Plate Geometry on the Cyclic Bearing Behavior of Single Helical Piles in Silty Sand
by Faxiang Gong, Wenni Deng, Xueliang Zhao, Xiaolong Wang and Kanmin Shen
J. Mar. Sci. Eng. 2025, 13(8), 1416; https://doi.org/10.3390/jmse13081416 - 25 Jul 2025
Viewed by 221
Abstract
Helical piles are widely used in geotechnical engineering, and their rapid installation and service reliability have attracted significant interest from the offshore wind industry. These piles are frequently subjected to cyclic loading in complex marine environments. Although the cyclic bearing behavior of helical [...] Read more.
Helical piles are widely used in geotechnical engineering, and their rapid installation and service reliability have attracted significant interest from the offshore wind industry. These piles are frequently subjected to cyclic loading in complex marine environments. Although the cyclic bearing behavior of helical piles has been studied, most research has focused on soil properties and loading conditions, with a limited systematic analysis of plate parameters. Moreover, the selection of plate parameters is not explicitly defined. As a crucial preliminary step in the capacity calculation, it is vital for the design of helical piles. To address this gap, the present study combines physical modeling tests and finite element simulations to systematically evaluate the influence of plate parameters on their cyclic bearing behavior. The parameters investigated include the plate depth, the plate diameter, plate spacing, and the number of plates. The results indicate that, under the same embedment conditions, cumulative displacement increases with the plate depth, with a critical embedment depth ratio of Hcr/D = 6 under cyclic loading conditions, but decreases with the number of plates. Axial stiffness increases with the plate depth, diameter, and number of plates, with an increase ranging from 0.5 to 3.0. However, the normalized axial stiffness decreases with these parameters, reaching a minimum value of 1.63. The plate spacing has a minimal influence on cyclic bearing behavior. Additionally, this study examines the evolution of displacement and stiffness parameters over repeated cycles in numerical simulations, as well as the post-cyclic pullout capacity of the helical pile foundation, which varies between −5% and +12%. Full article
(This article belongs to the Section Coastal Engineering)
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20 pages, 917 KiB  
Article
Numerical Investigation of Buckling Behavior of MWCNT-Reinforced Composite Plates
by Jitendra Singh, Ajay Kumar, Barbara Sadowska-Buraczewska, Wojciech Andrzejuk and Danuta Barnat-Hunek
Materials 2025, 18(14), 3304; https://doi.org/10.3390/ma18143304 - 14 Jul 2025
Viewed by 258
Abstract
The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that [...] Read more.
The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that ensure the parabolic shear stress profile and zero shear stress boundary condition at the upper and lower surface of the plate, hence removing the need for a shear correction factor. The plate is made up of carbon fiber bounded together with polymer resin matrix reinforced with MWCNT fibers. The mechanical properties are homogenized by a Halpin–Tsai scheme. The MATLAB R2019a code was developed in-house for a finite element model using C0 continuity nine-node Lagrangian isoparametric shape functions. The geometric nonlinear and linear stiffness matrices are derived using the principle of virtual work. The solution of the eigenvalue problem enables estimation of the critical buckling loads. A convergence study was carried out and model efficiency was corroborated with the existing literature. The model contains only seven degrees of freedom, which significantly reduces computation time, facilitating the comprehensive parametric studies for the buckling stability of the plate. Full article
(This article belongs to the Special Issue Mechanical Behavior of Advanced Composite Materials and Structures)
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23 pages, 6745 KiB  
Article
Crushing Modeling and Crushing Characterization of Silage Caragana korshinskii Kom.
by Wenhang Liu, Zhihong Yu, Aorigele, Qiang Su, Xuejie Ma and Zhixing Liu
Agriculture 2025, 15(13), 1449; https://doi.org/10.3390/agriculture15131449 - 5 Jul 2025
Viewed by 356
Abstract
Caragana korshinskii Kom. (CKB), widely cultivated in Inner Mongolia, China, has potential for silage feed development due to its favorable nutritional characteristics, including a crude protein content of 14.2% and a neutral detergent fiber content below 55%. However, its vascular bundle fiber structure [...] Read more.
Caragana korshinskii Kom. (CKB), widely cultivated in Inner Mongolia, China, has potential for silage feed development due to its favorable nutritional characteristics, including a crude protein content of 14.2% and a neutral detergent fiber content below 55%. However, its vascular bundle fiber structure limits the efficiency of lactic acid conversion and negatively impacts silage quality, which can be improved through mechanical crushing. Currently, conventional crushing equipment generally suffers from uneven particle size distribution, high energy consumption, and low processing efficiency. In this study, a layered aggregate model was constructed using the discrete element method (DEM), and the Hertz–Mindlin with Bonding contact model was employed to characterize the heterogeneous mechanical properties between the epidermis and the core. Model accuracy was enhanced through reverse engineering and a multi-particle-size filling strategy. Key parameters were optimized via a Box–Behnken experimental design, with a core normal stiffness of 7.37 × 1011 N·m−1, a core shear stiffness of 9.46 × 1010 N·m−1, a core shear stress of 2.52 × 108 Pa, and a skin normal stiffness of 4.01 × 109 N·m−1. The simulated values for bending, tensile, and compressive failure forces had relative errors of less than 10% compared to experimental results. The results showed that rectangular hammers, due to their larger contact area and more uniform stress distribution, reduced the number of residual bonded contacts by 28.9% and 26.5% compared to stepped and blade-type hammers, respectively. Optimized rotational speed improved dynamic crushing efficiency by 41.3%. The material exhibited spatial heterogeneity, with the mass proportion in the tooth plate impact area reaching 43.91%, which was 23.01% higher than that in the primary hammer crushing area. The relative error between the simulation and bench test results for the crushing rate was 6.18%, and the spatial distribution consistency reached 93.6%, verifying the reliability of the DEM parameter calibration method. This study provides a theoretical basis for the structural optimization of crushing equipment, suppression of circulation layer effects, and the realization of low-energy, high-efficiency processing. Full article
(This article belongs to the Section Agricultural Technology)
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19 pages, 3945 KiB  
Article
Static Analysis of a Composite Box Plate with Functionally Graded Foam Core
by Andrejs Kovalovs
J. Manuf. Mater. Process. 2025, 9(7), 209; https://doi.org/10.3390/jmmp9070209 - 22 Jun 2025
Viewed by 455
Abstract
In functionally graded polymer foam, mechanical properties and chemical composition vary in a prescribed direction according to a power law distribution. However, most manufacturing methods lack precise control over pore size, limiting their application. In this case, the graded foam structure can be [...] Read more.
In functionally graded polymer foam, mechanical properties and chemical composition vary in a prescribed direction according to a power law distribution. However, most manufacturing methods lack precise control over pore size, limiting their application. In this case, the graded foam structure can be formed from separate layers, with each layer assigned unique values in terms of mechanical properties or chemical composition based on the power law distribution. The hypothesis of the work is that the application of functionally graded (FG) foam materials inside the rotor blades or wings of an unmanned aerial vehicle can provide the ability to vary their stiffness properties. The aim of this work is to conduct an investigation of the static behaviour of a composite box plate with constant and variable heights that simulate the dimensions and changing profile of a helicopter rotor blade. In the numerical analysis, two models of composite box plate are considered and the material properties of graded polymeric foam core are assumed to vary continuously by the power law along the width of cross-sectional structures. It is not possible to model the continuous flow of graded properties through the foam in construction; therefore, the layers of foam are modelled using discontinuous gradients, where the gradient factor changes step by step. The numerical results are obtained using ANSYS software. The results of the numerical calculation showed that the use of graded foam affects the parameters under study. The stiffness of a structure significantly decreases with an increase in the power law index. Full article
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26 pages, 1080 KiB  
Review
Toward Integrative Biomechanical Models of Osteochondral Tissues: A Multilayered Perspective
by Bruna Silva, Marco Domingos, Sandra Amado, Juliana R. Dias, Paula Pascoal-Faria, Ana C. Maurício and Nuno Alves
Bioengineering 2025, 12(6), 649; https://doi.org/10.3390/bioengineering12060649 - 13 Jun 2025
Viewed by 413
Abstract
Understanding the complex mechanical behavior of osteochondral tissues in silico is essential for improving experimental models and advancing research in joint health and degeneration. This review provides a comprehensive analysis of the constitutive models currently used to represent the different layers of the [...] Read more.
Understanding the complex mechanical behavior of osteochondral tissues in silico is essential for improving experimental models and advancing research in joint health and degeneration. This review provides a comprehensive analysis of the constitutive models currently used to represent the different layers of the osteochondral region, from articular cartilage to subchondral bone, including intermediate regions such as the tidemark and the calcified cartilage layer. Each layer exhibits unique structural and mechanical properties, necessitating a layer-specific modeling approach. Through critical comparison of existing mathematical models, the viscoelastic model is suggested as a pragmatic starting point for modeling articular cartilage zones, the tidemark, and the calcified cartilage layer, as it captures essential time-dependent behaviors such as creep and stress relaxation while ensuring computational efficiency for initial coupling studies. On the other hand, a linear elastic model was identified as an optimal starting point for both the subchondral bone plate and the subchondral trabecular bone, reflecting their dense and stiff nature, and providing a coherent framework for early-stage multilayer integration. This layered modeling approach enables the development of physiologically coherent and computationally efficient representations of osteochondral region modeling. Furthermore, by establishing a layer-specific modeling approach, this review paves the way for modular in silico simulations through the coupling of computational models. Such an integrative framework supports scaffold design, in vitro experimentation, preclinical validation, and the mechanobiological exploration of osteochondral degeneration and repair. These efforts are essential for deepening our understanding of tissue responses under both physiological and pathological conditions. Ultimately, this work provides a robust theoretical foundation for future in silico and in vitro studies aimed at advancing osteochondral tissue regeneration strategies. Full article
(This article belongs to the Section Biomechanics and Sports Medicine)
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17 pages, 4191 KiB  
Article
Calcium Supplement Combined with Dietary Supplement Kidtal Can Promote Longitudinal Growth of Long Bone in Calcium-Deficient Adolescent Rats
by Haosheng Xie, Mingxuan Zhang, Zhengyuan Zhou, Hongyang Guan, Kunmei Shan, Shiwei Mi, Xinfa Ye, Zhihui Liu, Jun Yin and Na Han
Nutrients 2025, 17(12), 1966; https://doi.org/10.3390/nu17121966 - 10 Jun 2025
Viewed by 934
Abstract
Objective: Growth retardation in adolescents caused by nutritional deficiency requires effective intervention. A novel dietary supplement containing bamboo shoot extract, amino acids, and calcium citrate (Kidtal + Ca, KDTCa) was evaluated for its growth-promoting effects. Methods: After acclimatization, sixty-three 3-week-old male Sprague-Dawley (SD) [...] Read more.
Objective: Growth retardation in adolescents caused by nutritional deficiency requires effective intervention. A novel dietary supplement containing bamboo shoot extract, amino acids, and calcium citrate (Kidtal + Ca, KDTCa) was evaluated for its growth-promoting effects. Methods: After acclimatization, sixty-three 3-week-old male Sprague-Dawley (SD) rats were randomly divided into a normal control group and model groups. Growth retardation was induced in the modeling groups through calcium-deficient feeding, followed by administration of KDTCa, bamboo shoot extract and amino acids (Kidtal), or calcium citrate (CC). After 6 weeks of intragastric administration, the mechanical properties, microstructure, and growth plate development of bone were evaluated using three-point bending, micro-CT, and H&E staining, respectively. Bone calcium/phosphorus distribution and fecal calcium apparent absorption rate were measured by ICP-MS. Results: All inter-group differences were analyzed using one-way analysis of variance and checked using the Tuckey test. KDTCa treatment dose-dependently enhanced bone development in calcium-deficient rats. Compared to the model group, H-KDTCa significantly restored naso-anal length (p < 0.05) and body weight (p < 0.01). KDTCa supplementation significantly restored calcium and phosphorus levels in blood and bone. Three-point bending experiments showed that the stiffness and bending energy were increased by 142.58% and 384.7%. In bone microarchitecture, both bone mineral density (BMD) and microstructural parameters were significantly improved. These findings were consistent with the increased long bone length (p < 0.05) and decreased serum BALP/TRACP levels (p < 0.001). Dose-dependent IGF-1 elevation (p < 0.01) potentially mediated growth plate elongation by 35.34%. Notably, KDTCa increased calcium apparent absorption by 6.1% versus calcium-only supplementation at equal intake. Conclusions: KDTCa improves bone microstructure and strength, restores bone metabolism, and enhances growth plate height via promoting IGF-1 secretion to facilitate bone development. Further studies are needed to determine whether the components and calcium in Kidtal have a synergistic effect. Full article
(This article belongs to the Section Micronutrients and Human Health)
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28 pages, 5048 KiB  
Article
Voxel-Based Finite Element Investigation of Micromechanics Models for Stiffness Prediction of Cross-Ply Laminates
by Darya Forooghi and Yunhua Luo
J. Compos. Sci. 2025, 9(6), 288; https://doi.org/10.3390/jcs9060288 - 4 Jun 2025
Viewed by 435
Abstract
Laminate plate and shell structures with symmetric cross-ply configurations are widely used due to their high stiffness-to-weight ratio. However, conventional lamination theories rely on simplifying assumptions that may introduce inaccuracies. This study evaluates the predictive capability of such theories by integrating multiple micromechanics [...] Read more.
Laminate plate and shell structures with symmetric cross-ply configurations are widely used due to their high stiffness-to-weight ratio. However, conventional lamination theories rely on simplifying assumptions that may introduce inaccuracies. This study evaluates the predictive capability of such theories by integrating multiple micromechanics models with First-Order Shear Deformation Theory (FSDT), and comparing the results against voxel-based finite element modeling (VB-FEM), which serves as a high-fidelity numerical reference. A range of models—including Voigt–Reuss, Chamis, Halpin–Tsai, Bridging, and two iterative isotropized formulations—are assessed for unidirectional laminae with fiber volume fractions from 40% to 73%. Quantitative comparison reveals that while all models predict the longitudinal modulus accurately, significant deviations arise in predicting transverse and shear properties. The Bridging Model consistently yields the closest agreement with VB-FEM across all five elastic constants, maintaining accuracy even at high volume fractions where the modified Halpin–Tsai model begins to fail. Discrepancies in micromechanics-based lamina properties propagate to laminate-level stiffness predictions, highlighting the critical role of model selection. These findings establish VB-FEM as a valuable tool for validating analytical models and guide improved modeling strategies for laminated composite design. Full article
(This article belongs to the Special Issue Characterization and Modeling of Composites, 4th Edition)
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25 pages, 12314 KiB  
Article
Optimization and Analysis of Plates with a Variable Stiffness Distribution in Terms of Dynamic Properties
by Łukasz Domagalski and Izabela Kowalczyk
Materials 2025, 18(9), 2150; https://doi.org/10.3390/ma18092150 - 7 May 2025
Viewed by 563
Abstract
This study investigates the optimization of thickness distribution in simply supported and cantilever plates to maximize gaps between adjacent natural frequencies. The research employs a genetic algorithm (GA) as the primary optimization tool, with the finite element method (FEM) integrated for structural dynamics [...] Read more.
This study investigates the optimization of thickness distribution in simply supported and cantilever plates to maximize gaps between adjacent natural frequencies. The research employs a genetic algorithm (GA) as the primary optimization tool, with the finite element method (FEM) integrated for structural dynamics analysis. The optimization process focuses on tailoring the plate thickness (stiffness) while maintaining fixed overall dimensions. The study considers square and rectangular plates with two boundary conditions: simply supported and cantilever. The optimization targets gaps between the first three natural frequencies. The GA-based optimizer demonstrates effectiveness in increasing the relative separation between neighboring natural frequencies, as defined by the fitness function. Compared to the reference individuals, the optimized individuals achieve objective function values from 0.25 to 2.5 times higher. The GA optimization tool is also compared with an alternative optimization tool achieving up to 35% better results. This research contributes to the field of structural dynamics by demonstrating the potential of genetic algorithms in optimizing plate designs for enhanced vibrational characteristics. Such optimization is particularly relevant in civil engineering, where plate elements are widely used, and where controlling dynamic properties can improve serviceability and reduce the risk of resonance under operational or environmental loads. The findings have implications for various engineering applications where controlling dynamic properties of plate structures is crucial. Full article
(This article belongs to the Section Materials Simulation and Design)
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15 pages, 3014 KiB  
Article
Biomechanical Performance and Handling of Mineral–Organic Adhesive Bone Cements Based on Magnesium Under Clinical Test Conditions
by Stefanie Hoelscher-Doht, Alexandra Fabian, Lasse Bögelein, Eva Kupczyk, Rainer H. Meffert, Uwe Gbureck and Tobias Renner
J. Clin. Med. 2025, 14(9), 3081; https://doi.org/10.3390/jcm14093081 - 29 Apr 2025
Viewed by 625
Abstract
Background/Objectives: Biomineral adhesive bone adhesives composed of phosphoserine combined with magnesium oxides or phosphates exhibit exceptional adhesive properties. This study evaluates two experimental mineral–organic cementitious adhesives in a clinical test setup, investigating their potential for fracture reduction and simultaneous defect filling. Methods [...] Read more.
Background/Objectives: Biomineral adhesive bone adhesives composed of phosphoserine combined with magnesium oxides or phosphates exhibit exceptional adhesive properties. This study evaluates two experimental mineral–organic cementitious adhesives in a clinical test setup, investigating their potential for fracture reduction and simultaneous defect filling. Methods: The two experimental adhesives (Groups B and C) and a standard hydroxyapatite cement (Group A, reference) underwent compressive strength testing, shear strength testing, and screw pullout tests as part of a first biomechanical characterization. Furthermore, all materials were tested in a porcine tibial split depression fracture model, where they served both for fracture reduction and for filling the metaphyseal bone defect, supplementary to plate osteosynthesis. Fracture stability was assessed under cyclic loading in a materials testing machine. Results: The OPLS (O-phospho-L-serine) containing adhesive (Group B) demonstrated the highest compressive strength as well as the highest shear strength. All three materials showed comparable maximum pullout forces. Both experimental adhesives (Groups B and C) exhibited higher pullout stiffness compared to the standard cement (Group A). In the fracture model, no significant differences in displacement under cyclic loading were observed between groups. Conclusions: The biomineral adhesive bone adhesives (Groups B and C) demonstrated biomechanical advantages in axial compression, adhesive (shear) strength, and screw fixation compared to the standard hydroxyapatite cement (Group A). Furthermore, they achieved comparable stabilization of metaphyseal fractures under clinically relevant dynamic loading conditions. Full article
(This article belongs to the Special Issue Advances in Trauma and Orthopedic Surgery: 2nd Edition)
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26 pages, 12184 KiB  
Article
A Study on the Seismic Performance of Steel H-Column and T-Beam-Bolted Joints
by Hongtao Ju, Wen Jiang, Xuegang Hu, Kai Zhang, Yan Guo, Junfen Yang and Kaili Hao
Appl. Sci. 2025, 15(9), 4643; https://doi.org/10.3390/app15094643 - 23 Apr 2025
Viewed by 457
Abstract
The finite-element model was developed using ABAQUS to investigate the hysteretic properties of space joints. This study examined the effects of axial compression ratio, T-plate stiffness, column wall thickness, and bolt-preload on the joint’s hysteretic behavior. The model was verified by comparing the [...] Read more.
The finite-element model was developed using ABAQUS to investigate the hysteretic properties of space joints. This study examined the effects of axial compression ratio, T-plate stiffness, column wall thickness, and bolt-preload on the joint’s hysteretic behavior. The model was verified by comparing the failure modes, hysteresis curves, and skeleton curves of the specimens with the test results of the relevant literature, ensuring the reliability of the research. The results reveal three primary failure modes: beam flange buckling, T-plate buckling, and column-wall buckling; increasing the thickness of the T-plate web or column wall significantly enhances joint stiffness and mitigates brittle failure. Specifically, the stiffness of T-plate 1 has a substantial impact on joint performance, and it is recommended that its web thickness be no less than 18 mm. In contrast, variations in the thickness of T-plate 2 have negligible effects on seismic performance. Increasing the column wall thickness improves the bearing capacity and stiffness of the joint, with a recommended minimum thickness of 12 mm, which should not be less than the flange thickness of the steel beam. While an increase in the axial compression ratio reduces the bearing capacity and stiffness, it enhances the energy dissipation capacity and ductility of the joint. Notably, variations in bolt-preload were found to have minimal influence on joint performance. These findings provide valuable insights for optimizing the design of unilateral bolted joints in steel structures to improve seismic resilience. Full article
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18 pages, 9531 KiB  
Article
Experimental Validation of Clamping-Type Mesh Fastening Method Using Thin Plates and Push-Button Rivets for Deployable Mesh Antennas
by Jae-Seop Choi, Bong-Geon Chae and Hyun-Ung Oh
Aerospace 2025, 12(3), 248; https://doi.org/10.3390/aerospace12030248 - 17 Mar 2025
Viewed by 425
Abstract
Deployable mesh antennas offer advantages such as high gain, ultra-light weight, and high packaging efficiency. However, the mesh that constitutes the reflection surface is prone to deformation due to its low stiffness, which directly affects the performance of the antenna. Therefore, it is [...] Read more.
Deployable mesh antennas offer advantages such as high gain, ultra-light weight, and high packaging efficiency. However, the mesh that constitutes the reflection surface is prone to deformation due to its low stiffness, which directly affects the performance of the antenna. Therefore, it is essential to minimize the mechanical deformation of the mesh caused by external forces in order to achieve the target performance. In particular, the fastening interface between the mesh and the antenna structure is a critical area where high tensile forces are incurred due to the dynamic behavior of the antenna structure during ground tests, launch environments, and on-orbit operation. This causes degradation in the precision of the reflection surface. Therefore, an important part of the antenna development process is researching mesh fabric fastening methods that minimize the deformation of the reflection surface. Nevertheless, existing studies have only briefly mentioned mesh fastening methods, with limited systematic analysis of their impact on the mechanical properties of mesh fabric. In this paper, we propose a clamping-type mesh fastening method that combines push-button rivets and thin plates, which have high workability during mesh assembly, and conduct experimental validation. The characteristics of each fastening method were analyzed through tensile strength tests conducted at the mesh fabric level, and the results of the repeated tensile tests verified the effectiveness of the proposed fastening method. Full article
(This article belongs to the Section Astronautics & Space Science)
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16 pages, 5970 KiB  
Article
Advanced Vibration of Functionally Graded Material Coupled Plates and Circular Shells with Four Layers
by Chih-Chiang Hong
Fibers 2025, 13(3), 32; https://doi.org/10.3390/fib13030032 - 12 Mar 2025
Viewed by 516
Abstract
This study is based on typical thermal studies on thick, functionally graded material (FGM)-coupled plates and circular shells. Numerical studies have been previously published by researchers on the linear first-order shear deformation theory (FSDT) model for thin-thickness and two-layer materials. The present relationship [...] Read more.
This study is based on typical thermal studies on thick, functionally graded material (FGM)-coupled plates and circular shells. Numerical studies have been previously published by researchers on the linear first-order shear deformation theory (FSDT) model for thin-thickness and two-layer materials. The present relationship was further studied by the author on the nonlinear third-order shear deformation theory (TSDT) model for thick-thickness and four-layer FGMs. The material properties of FGM layers deal with the effect of temperature. The novelty of this study is in its further consideration of four layers of FGMs and the non-dimensional shear coefficient. The stiffness and stiffness integrals of the four layers are studied. The material properties in the power law expression of the functions of the four layers are assumed for the first time. Under the conditions of a time sinusoidal, varied thermal loads and simply supported conditions for four layers are studied. Parametric case studies involving temperature, the standard power law form of the index, and the nonlinear term of the displacement theory and shear coefficient for the dynamic stresses and displacements are obtained and presented. Full article
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12 pages, 2115 KiB  
Article
Longitudinal Bending Stiffness Analysis of Composite Carbon Plates and Shoe Sole, Based on Three-Point Bending Test
by Yangyu Guo, Yunlong Jia, Yusen Wu and Xiaolan Zhu
Appl. Sci. 2025, 15(5), 2785; https://doi.org/10.3390/app15052785 - 5 Mar 2025
Viewed by 1623
Abstract
The forefoot longitudinal bending stiffness of shoe soles, measured through the widely used three-point bending test, is a key factor influencing running economy and lower-limb biomechanics. This study utilizes the finite element method to simulate three-point bending, examining the influence of different loading [...] Read more.
The forefoot longitudinal bending stiffness of shoe soles, measured through the widely used three-point bending test, is a key factor influencing running economy and lower-limb biomechanics. This study utilizes the finite element method to simulate three-point bending, examining the influence of different loading rates on stiffness and analyzing the impact of various plate thicknesses and forefoot curvature radii on the stiffness of plates and the ‘plate-sole’ system. The results indicate that within the same displacement range, varying the loading rates did not affect stiffness. However, increased thickness significantly enhanced both the stiffness of the plate and the ‘plate-sole’, while a larger curvature radius of the plate resulted in a modest 5–10% stiffness increase for both. To conclude, the present study provides a theoretical foundation for further exploring the mechanical properties of carbon plate configurations in footwear. Plate stiffness is affected by both thickness and curvature radius, with thickness having a greater impact. The same applies to the ‘plate-sole’. The stiffness of the ‘plate-sole’ is not a simple sum of the individual contributions from the shoe and the plate. This non-additive response emphasizes the significant role of the shoe material in altering the plate’s mechanical properties, which is an important consideration for optimizing shoe design. Full article
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16 pages, 4655 KiB  
Proceeding Paper
A Combined Approach of Experimental Testing and Inverse FE Modelling for Determining Homogenized Elastic Properties of Membranes and Plates
by Christian Iandiorio, Riccardo Serenella and Pietro Salvini
Eng. Proc. 2025, 85(1), 27; https://doi.org/10.3390/engproc2025085027 - 23 Feb 2025
Cited by 1 | Viewed by 343
Abstract
Accurately determining the mechanical properties of complex materials is a key challenge in structural analysis, especially when using the finite element method (FEM). While homogeneous materials can be modeled with relative ease, heterogeneous materials such as composites or biological tissues with multiphase compositions [...] Read more.
Accurately determining the mechanical properties of complex materials is a key challenge in structural analysis, especially when using the finite element method (FEM). While homogeneous materials can be modeled with relative ease, heterogeneous materials such as composites or biological tissues with multiphase compositions pose significant difficulties due to the variability in their internal structures. The most used approach is numerical homogenization, which allows for the estimation of effective material properties by combining the characteristics of individual phases; however, this technique may not always be feasible, especially for materials with irregular or unknown phase distributions. This paper proposes an original methodology that combines non-destructive experimental testing with an inverse finite element modeling to extract the anisotropic elastic properties of quasi two-dimensional structures such as membranes and plates. The method involves modeling the component using membrane or plate finite elements, but managing a global stiffness matrix expressed analytically. While geometric information is incorporated in the global stiffness matrix, the material properties, specifically the components of the anisotropic elasticity matrix, remain unknown. The experimental data, comprising force and displacement measurements, are used to solve a nonlinear system, allowing for the identification of the material’s constitutive properties via numerical computation. To validate this approach, two experimental setups were conducted. The first involved a hyperelastic neoprene membrane, subjected to various biaxial preloading conditions, while the second focused on PLA plates produced through additive manufacturing including both homogeneous and reinforced variants. In both cases, the method successfully captured the full anisotropic elastic response, yielding accurate estimates of Young’s moduli, Poisson’s ratios, shear modulus, and orthotropy system orientation, in agreement with independent mechanical tests. This combined approach offers a practical and efficient solution for determining the elastic properties of complex materials, particularly in cases where traditional homogenization techniques are impractical or inadequate. Furthermore, this method can be a versatile tool for evaluating the damaging and aging effects on materials subjected to cyclic loading or those with irregular and complex internal structures. Full article
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