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Keywords = shell–spring model

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22 pages, 3552 KB  
Article
Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance
by Liangzheng Huang, Jinhao Zhang, Chao Shang, Dongshuo Yang and Xin Fang
Mathematics 2026, 14(11), 1876; https://doi.org/10.3390/math14111876 - 28 May 2026
Viewed by 291
Abstract
Dynamic vibration absorbers (DVAs) serve as critical passive control devices. However, their conventional designs are characterized by high directional sensitivity and large additional mass, failing to meet the rigorous demands of modern equipment for multi-directional coupled vibration suppression and lightweighting. To address these [...] Read more.
Dynamic vibration absorbers (DVAs) serve as critical passive control devices. However, their conventional designs are characterized by high directional sensitivity and large additional mass, failing to meet the rigorous demands of modern equipment for multi-directional coupled vibration suppression and lightweighting. To address these challenges, this study establishes an isotropic dynamic model of coupling spring and shell stiffnesses. This model shows that the isotropy degrades with the lightweight design due to a failure mode of shear deformation. Then, by constraining the shear stiffness, a collaborative design framework integrating topology optimization and parameter optimization is constructed to lighten the DVA. Using a 50 Hz DVA as a case study, prototype designs, simulations, and experiments are conducted. The results indicate that the isotropic natural frequencies agree well with the design targets. The shell mass is reduced by 79.8% compared to the conventional rigid shell design. Moreover, in vibration reduction simulations under the same total mass, the optimized absorber further reduces the vibration response by 7.4 dB compared to the rigid shell design. Full article
(This article belongs to the Special Issue Advanced Mathematical Models in Engineering Design Optimization)
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14 pages, 2763 KB  
Article
A Semi-Analytical Legendre–Ritz Method to Dynamically Analyze a Stepped Functionally Graded Cylindrical Shell
by Yanbin Shen, Lijia Yang, Diming Guo and Luyue Xi
Vibration 2026, 9(2), 37; https://doi.org/10.3390/vibration9020037 - 22 May 2026
Viewed by 888
Abstract
This study introduces the dynamic characteristics of stepped functionally graded (FG) cylindrical shells under general boundary conditions using the Legendre–Ritz method. The calculated model is established based on the first-order shear deformation theory and the domain decomposition method, and the artificial spring is [...] Read more.
This study introduces the dynamic characteristics of stepped functionally graded (FG) cylindrical shells under general boundary conditions using the Legendre–Ritz method. The calculated model is established based on the first-order shear deformation theory and the domain decomposition method, and the artificial spring is introduced to simulate the boundary conditions and ensure segment continuity. The Legendre polynomials and the Fourier series are used to form the admissible displacement function. The Rayleigh–Ritz method is employed to determine the free and forced vibration characteristics of stepped FG cylindrical shells. Results are presented for various boundary conditions, material parameters and geometric dimensions, and comparisons with published studies are performed. The method demonstrates good accuracy, providing a basis for analyzing the vibration behavior of stepped FG cylindrical shells. Full article
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20 pages, 1102 KB  
Article
Evaluation of Formulation-Dependent Antimicrobial Activity and Plant Compatibility of Chitosan-Based Silver Nanoparticles
by Ahmed Hosney, Neringa Matelionienė, Donata Drapanauskaitė, Sana Ullah and Karolina Barčauskaitė
Mar. Drugs 2026, 24(5), 183; https://doi.org/10.3390/md24050183 - 19 May 2026
Viewed by 951
Abstract
Chitosan-based silver nanoparticles (Ch-AgNPs) are emerging as promising antimicrobial materials with potential applications in crop protection. This study evaluated the formulation-dependent antimicrobial activity and plant compatibility of Ch-AgNPs synthesized from chitosan extracted via different routes from shrimp shells. Antibacterial activity was assessed against [...] Read more.
Chitosan-based silver nanoparticles (Ch-AgNPs) are emerging as promising antimicrobial materials with potential applications in crop protection. This study evaluated the formulation-dependent antimicrobial activity and plant compatibility of Ch-AgNPs synthesized from chitosan extracted via different routes from shrimp shells. Antibacterial activity was assessed against representative Gram-negative and Gram-positive model bacteria (Escherichia coli and Staphylococcus aureus), as well as phytopathogenic bacteria (Xanthomonas campestris, Pseudomonas syringae), using disk diffusion assays. Antifungal activity was evaluated against Fusarium graminearum in vitro and in a controlled growth chamber. All formulations exhibited concentration-dependent antibacterial activity, with L10 and L20 formulations derived from optimized lactic acid-based extraction routes and DP4 derived from an inorganic deproteinization-based extraction route showing the highest efficacy at 1.0 mg/mL. Strong antifungal activity was observed, particularly for L10 and DP4, achieving mycelial growth inhibition of 92% and 84%, respectively, at 1.0 mg/mL. Seed germination and seedling growth assays confirmed that all formulations were non-phytotoxic at 1.0 mg/mL, with L10 and DP4 significantly enhancing germination parameters and early plant growth. Under controlled conditions, these formulations also reduced the incidence and severity of crown and root rot in spring wheat caused by F. graminearum. These findings demonstrate that optimized Ch-AgNP formulations combine antimicrobial activity with plant compatibility, highlighting their potential for crop protection, pending further environmental safety and agronomic validation under field conditions. Full article
(This article belongs to the Special Issue Marine-Derived Chitin and Chitosan: From Extraction to Applications)
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21 pages, 2489 KB  
Article
Simulation of Post-Tensioned CLT Rocking Wall and Platform Structure Response Under Earthquake Lateral Loads with Simplified Equivalent Model
by Yunxiang Ma, Qingli Dai, Da Huang, Miaomiao Li and Xiang Zhao
Buildings 2026, 16(10), 1948; https://doi.org/10.3390/buildings16101948 - 14 May 2026
Viewed by 475
Abstract
The post-tensioned cross-laminated timber (CLT) rocking wall is a recently developed resilient CLT lateral force-resisting system with a self-centering feature. The structural responses of the systems with different designs need to be determined and evaluated efficiently to promote the development and standardization of [...] Read more.
The post-tensioned cross-laminated timber (CLT) rocking wall is a recently developed resilient CLT lateral force-resisting system with a self-centering feature. The structural responses of the systems with different designs need to be determined and evaluated efficiently to promote the development and standardization of industrial applications. This study developed a computationally efficient, component-assembled numerical model for post-tensioned cross-laminated timber (PT CLT) rocking walls that captures decompression, post-tension self-centering, and energy dissipation within a framework. The single wall model was assembled using nonlinear zero-length springs for the compression at the CLT bottom, truss bar element for the PT tendon, and elastic shell element for the CLT panel deformation. The energy dissipation device, the UFP, was modeled with nonlinear one-dimensional springs between the wall panels in the coupled wall model. The wall models were separately calibrated considering the wall designs of single-panel walls and coupled walls. Both single and coupled wall models predicted the initial stiffness, decompression, yielding, post-yield stiffness, and reloading/unloading stiffness. The residual drift and nonlinear unloading captured with the PT model were also validated with the test data. A two-story platform structure model was established based on the NHERI Tallwood project, assembled with the coupled wall model and CLT slab in shell elements and columns in Euler beam elements. With recorded ground acceleration signals from the test, the platform structure’s peak story displacement and inter-story drift were simulated with less than 30% differences for most cases. Unlike existing detailed contact-based models, the proposed approach balances local damage fidelity and computational efficiency. The validated model provides a framework for evaluating PT CLT wall design parameters considering their influence on full structures. Full article
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30 pages, 7153 KB  
Article
Assessment of Integral Abutment Retrofit Performance for Steel Bridges Subjected to Thermal Loading
by Jawad H. Gull, Sana Amir and Qasim Shaukat Khan
Infrastructures 2026, 11(5), 163; https://doi.org/10.3390/infrastructures11050163 - 7 May 2026
Viewed by 493
Abstract
Integral abutment bridges (IABs) eliminate deck joints by rigidly connecting the superstructure to the abutments, reducing maintenance costs but introducing thermal restraint forces. When only one abutment is made integral, all thermally induced longitudinal movement concentrates at the remaining non-integral end, overloading bearings [...] Read more.
Integral abutment bridges (IABs) eliminate deck joints by rigidly connecting the superstructure to the abutments, reducing maintenance costs but introducing thermal restraint forces. When only one abutment is made integral, all thermally induced longitudinal movement concentrates at the remaining non-integral end, overloading bearings and concrete elements not designed for this condition. This paper investigates IAB behavior and evaluates two repair options for two, three-span continuous steel bridges on Interstate 635 in Kansas City, Kansas, which sustained progressive abutment damage following a unilateral integral conversion in 2005. A 2D finite element model was developed in LARSA 4D, incorporating composite superstructure elements, shell element abutments, beam element piles, and soil-structure interaction via distributed lateral springs. The model was analyzed under dead, live, braking, and thermal load combinations in accordance with AASHTO LRFD. Full integral conversion generates thermal restraint moments of approximately 813.5 kN-m (600 kip-ft) at the abutments, and pile stresses of 383.9 MPa (55.68 ksi) under Service I and 497.4 MPa (72.14 ksi) under Strength I combinations, both exceeding allowable limits. Elastomeric bearing pads at the non-integral abutment satisfied all stress limits without foundation modification and are recommended as a practical repair strategy for bridges in similar conditions. Full article
(This article belongs to the Section Infrastructures and Structural Engineering)
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22 pages, 23312 KB  
Article
From Past to Future: Assessing Ria Formosa’s Suitability for Grooved Carpet Shell Aquaculture
by Humberto Pereira, Ana Picado, Ines Alvarez, Magda C. Sousa, Ana C. Brito, David Carvalho and João M. Dias
Sci 2026, 8(5), 100; https://doi.org/10.3390/sci8050100 - 28 Apr 2026
Viewed by 824
Abstract
Most Portuguese aquaculture farms are located in estuaries and coastal lagoons, which are highly productive, nutrient-rich transition zones that are also among the most vulnerable to anthropogenic pressures and climate change. This study assesses Ria Formosa’s suitability for grooved carpet shell (Ruditapes [...] Read more.
Most Portuguese aquaculture farms are located in estuaries and coastal lagoons, which are highly productive, nutrient-rich transition zones that are also among the most vulnerable to anthropogenic pressures and climate change. This study assesses Ria Formosa’s suitability for grooved carpet shell (Ruditapes decussatus) aquaculture, accounting for projected climate change and a potential increase in clam farming production. The methodology involved implementing a numerical modeling system to map key physico-chemical variables under historical (1995–2014) and future (2081–2100) conditions. Model outputs were then used to compute a suitability index (SI), which was converted into aquaculture suitability maps for this species. Results indicate that the hydrodynamic and transport components reproduced tidal propagation and the transport of salinity and heat effectively. In contrast, simulations of water quality variables were less accurate, reflecting the greater complexity and uncertainty in representing biochemical processes. Across both time periods, environmental conditions were generally less favorable in winter and more favorable in spring. Water temperature and chlorophyll-a concentration emerged as the dominant drivers of seasonal suitability. Projections suggest that Ria Formosa may become increasingly suitable for grooved carpet shell aquaculture by the end of the century. However, expanding production could compromise ecological balance, reduce resilience, and constrain the system’s long-term sustainable development. Full article
(This article belongs to the Special Issue Advances in Coastal Ecosystem Structure, Function and Dynamics)
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20 pages, 5655 KB  
Article
Semi-Analytical Modeling and Free Vibration Analysis of Joined Conical–Cylindrical Shells with Axially Stepped Thickness
by Lin Lu, Zhe Zhao, Ting Li, Cong Gao and Jiajun Zheng
Vibration 2026, 9(1), 13; https://doi.org/10.3390/vibration9010013 - 13 Feb 2026
Cited by 2 | Viewed by 1384
Abstract
This study develops a semi-analytical method for free vibration analysis of joined conical–cylindrical shell with axially stepped thickness. The computational framework is built through the domain decomposition method, artificial spring technology and shear deformation shell theory. Kinematic admissible functions are constructed via superposition [...] Read more.
This study develops a semi-analytical method for free vibration analysis of joined conical–cylindrical shell with axially stepped thickness. The computational framework is built through the domain decomposition method, artificial spring technology and shear deformation shell theory. Kinematic admissible functions are constructed via superposition of Chebyshev orthogonal polynomials and trigonometric series. Subsequently, the Rayleigh–Ritz method is employed to solve for the system’s characteristic frequencies. The accuracy of the method is further verified by the excellent agreement between the current results and those from published studies and finite element simulations. Ultimately, the influence of boundary conditions, structural parameters and stepped thickness distribution on the free vibration characteristics of conical–cylindrical shells are systematically discussed. These findings reveal the critical methodological constraints in free vibration modeling of stepped thickness shell systems, thereby advancing vibration design optimization for the stepped thickness structures. Full article
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13 pages, 2688 KB  
Article
Three-Dimensional Numerical Simulation for Mechanical Performance of Semi-Prefabricated Second Lining of Highway Tunnels
by Yangyang Bao, Haitao Bao, Yeongbin Yang and Yazhou Liu
Buildings 2025, 15(18), 3425; https://doi.org/10.3390/buildings15183425 - 22 Sep 2025
Viewed by 881
Abstract
To align with the development trends of green construction and industrialized building, prefabricated assembly technology has been widely applied in highway tunnel lining structures. However, when used in large-section highway tunnels, this technology faces challenges not only due to the large size of [...] Read more.
To align with the development trends of green construction and industrialized building, prefabricated assembly technology has been widely applied in highway tunnel lining structures. However, when used in large-section highway tunnels, this technology faces challenges not only due to the large size of the components but due to the high demands in the working space. In response to the limitations of traditional assembly methods, this paper proposes a semi-prefabricated secondary lining structure for highway tunnels. The mechanical performance of the second lining constructed by various segmentation schemes under surrounding rock pressure is analyzed using a 3D shell-spring finite element model, considering both the continuous and staggered seam layouts. This study provides technical support for the design of assembled secondary lining structures in large-section highway tunnels. Full article
(This article belongs to the Section Building Structures)
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18 pages, 4221 KB  
Article
Dynamics Modeling and Control Method for Non-Cooperative Target Capture with a Space Netted Pocket System
by Wenyu Wang, Huibo Zhang, Jinming Yao, Wenbo Li, Zhuoran Huang, Chao Tang and Yang Zhao
Actuators 2025, 14(7), 358; https://doi.org/10.3390/act14070358 - 21 Jul 2025
Cited by 3 | Viewed by 992
Abstract
The space flexible netted pocket capture system provides a flexible and stable solution for capturing non-cooperative space objects. This paper investigates the control problem for the capture of non-cooperative targets undergoing motion. A dynamic model of the capturing net is established based on [...] Read more.
The space flexible netted pocket capture system provides a flexible and stable solution for capturing non-cooperative space objects. This paper investigates the control problem for the capture of non-cooperative targets undergoing motion. A dynamic model of the capturing net is established based on the absolute nodal coordinate formulation (ANCF) and equivalent plate–shell theory. A contact collision force model is developed using a spring–damper model. Subsequently, a feedforward controller is designed based on the estimated collision force from the dynamic model, aiming to compensate for the collision effects between the target and the net. By incorporating the collision estimation data, an extended state observer is designed, taking into account the collision estimation errors and the flexible uncertainties. A sliding mode feedback controller is then designed using the fast terminal sliding mode control method. Finally, simulation analysis of target capture under different motion states is conducted. The results demonstrate that the spacecraft system’s position and attitude average flutter amplitudes are less than 102 m and 102 deg. In comparison to standard sliding mode control, the designed controller reduces the attitude jitter amplitude by an order of magnitude, thus demonstrating its effectiveness and superiority. Full article
(This article belongs to the Section Control Systems)
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21 pages, 7487 KB  
Article
Free- and Forced-Vibration Characteristic Analysis of a Double-Layered Cylindrical Shell with General Boundary Conditions
by Jianghai Wu, Hongzhen Zhu and Yong Duan
J. Mar. Sci. Eng. 2025, 13(4), 641; https://doi.org/10.3390/jmse13040641 - 24 Mar 2025
Cited by 4 | Viewed by 1611
Abstract
The double-layered cylindrical shell represents a key structural configuration for underwater vehicles, where its vibration behavior remains a primary concern in engineering design and analysis. This study develops a spectral element method (SEM) for dynamic modeling of multi-component shell systems by extending the [...] Read more.
The double-layered cylindrical shell represents a key structural configuration for underwater vehicles, where its vibration behavior remains a primary concern in engineering design and analysis. This study develops a spectral element method (SEM) for dynamic modeling of multi-component shell systems by extending the vibrational governing equations of conical shells. The methodology is validated through finite element method (FEM) case studies on both conical shells and double-layered cylindrical configurations. Parametric investigations examine ribbed substructures and solid rib plates within the cylindrical shell assembly, while artificial spring techniques model arbitrary boundary conditions—with validation against classical benchmarks confirming their effectiveness for elastic constraints. Numerical demonstrations reveal the following: rib and plate thickness variations exhibit a negligible impact on low-frequency vibrational responses; the natural frequency sensitivity peaks when the elastic boundary stiffness approaches the inherent dynamic stiffness of the shell’s base configuration, while extreme stiffness values approximate clamped or free boundary conditions with engineering significance. The proposed SEM framework demonstrates a superior computational efficiency and accuracy compared to conventional FEM approaches. These findings deliver practical guidance for marine structural engineering, particularly in the boundary condition specifications and performance optimization of composite shell systems. Full article
(This article belongs to the Section Ocean Engineering)
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14 pages, 3837 KB  
Article
Solar Irradiance Mitigation in LEO Optical Inter-Satellite Links via Inter-Shell Based Path Optimization
by Jae Seong Hwang, Ji-Yung Lee and Hyunchae Chun
Appl. Sci. 2025, 15(6), 3364; https://doi.org/10.3390/app15063364 - 19 Mar 2025
Cited by 3 | Viewed by 2877
Abstract
Solar irradiance is a critical factor influencing the reliability of optical inter-satellite links (O-ISLs). Despite its significance, limited research has focused on addressing this challenge. This work investigates the impact of solar irradiation on the optimal path configuration. A multi-directional field-of-view (FoV) model [...] Read more.
Solar irradiance is a critical factor influencing the reliability of optical inter-satellite links (O-ISLs). Despite its significance, limited research has focused on addressing this challenge. This work investigates the impact of solar irradiation on the optimal path configuration. A multi-directional field-of-view (FoV) model is used to practically accommodate the solar irradiance imposed on each optical transceiver module in a single satellite. The effectiveness of the optimal path configurations is evaluated through detour mitigation strategies, comparing inter-plane and inter-shell link alternatives in intercontinental scenarios within the northern hemisphere. In the scenarios, it is found that there is a tradeoff between the FoV and the level of the signal-to-noise ratio (SNR) required to overcome the effects of solar irradiance. Also, seasonal alterations in the sun’s incident direction significantly influence the link availability, with unusable link rates nearly doubling in summer compared to spring because of orbital inclinations tending to be aligned more closely with the solar direction toward Earth. The proposed inter-shell-based path optimization reduces the total link distance by up to 2500 km compared to those of the inter-plane configurations, demonstrating superior performance in mitigating impairment due to solar irradiance. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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32 pages, 7060 KB  
Article
Vibration Analysis of Functionally Graded Material (FGM) Double-Layered Cabin-like Structure by the Spectro-Geometric Method
by Dongze He, Rui Zhong, Qingshan Wang and Bin Qin
Materials 2025, 18(6), 1231; https://doi.org/10.3390/ma18061231 - 10 Mar 2025
Cited by 2 | Viewed by 1648
Abstract
This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation [...] Read more.
This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh–Ritz method, and the corresponding vibration solutions are computed. The model’s reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell’s inherent characteristics and steady-state response. Full article
(This article belongs to the Special Issue Mechanical Behavior of Advanced Composite Materials and Structures)
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18 pages, 3194 KB  
Article
Ritz Solution of Vibration Analysis of Functionally Graded Porous Elliptic Shells and Panels Under Various Arbitrary Boundary Types
by Qingtao Gong, Tao Liu, Yao Teng, Binjie Ma and Xin Li
Materials 2025, 18(5), 1101; https://doi.org/10.3390/ma18051101 - 28 Feb 2025
Cited by 2 | Viewed by 1183
Abstract
This paper seeks to establish a generalized numerical model to examine the free vibration behavior of functionally graded porous (FGP) elliptical shells and panels with various boundary types. The model is built on first-order shear deformation theory (FSDT) to express structural displacements. A [...] Read more.
This paper seeks to establish a generalized numerical model to examine the free vibration behavior of functionally graded porous (FGP) elliptical shells and panels with various boundary types. The model is built on first-order shear deformation theory (FSDT) to express structural displacements. A segmentation technique is used to maintain continuity between shell elements, and virtual spring boundary techniques are employed to simulate arbitrary boundaries. Variable-coefficient Jacobi polynomials are introduced as admissible functions for displacement. Finally, the Ritz variational method, combined with the least-squares weighted residual method (LSWRM), is used for constructing the energy functional and solving the energy equations. Validation of the numerical model against finite element and literature results confirms its reliability and convergence properties. This study also explores the effects of geometric parameters and boundary conditions on FG elliptical shells and panels, providing a theoretical basis for future research. Full article
(This article belongs to the Special Issue Numerical Analysis of Sandwich and Laminated Composites)
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22 pages, 9939 KB  
Article
A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process
by Xuezhi Wang, Kelin Chen, Yanli Lin and Zhubin He
Materials 2024, 17(15), 3739; https://doi.org/10.3390/ma17153739 - 28 Jul 2024
Cited by 3 | Viewed by 1625
Abstract
A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by [...] Read more.
A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. Full article
(This article belongs to the Special Issue Nonconventional Technology in Materials Processing-3rd Edition)
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20 pages, 761 KB  
Article
Dynamic Response of the Tunnel Lining with a Circumferential Crack Subjected to a Harmonic Point Load
by Jianwei Yang, Changdong Liu, Peishan Liu and Yue Zhao
Appl. Sci. 2024, 14(7), 3072; https://doi.org/10.3390/app14073072 - 5 Apr 2024
Cited by 4 | Viewed by 2191
Abstract
Cracks are one of the most common diseases of tunnel lining, and the structural dynamic response can be used to assess the health of a tunnel. Hence, this paper investigates the dynamic response of shield tunnel lining with a partly circumferential crack. The [...] Read more.
Cracks are one of the most common diseases of tunnel lining, and the structural dynamic response can be used to assess the health of a tunnel. Hence, this paper investigates the dynamic response of shield tunnel lining with a partly circumferential crack. The shield tunnel lining is regarded as a thin cylindrical shell and analyzed independently. The research methodology integrates the wave propagation method, the local flexibility matrix, the line spring model and the wave superposition principle. The results show that the position and depth of a partly circumferential crack can influence the natural frequency of the shield tunnel lining. Under the fixed-position load, as the distance from the monitoring point to the crack increases, the difference in displacement response amplitude between the undamaged and cracked linings diminishes. Moreover, deepening cracks enlarge the magnitude of amplitude differences. When the load approaches the crack, the radial amplitude difference first increases and then decreases as the monitor moves away from the crack. This finding helps determine the required monitor position. The displacement response of the selected monitor indicates that the closer the load position is to the crack, the larger the amplitude difference. The results aid in identifying the crack position and selecting corresponding load and monitor locations. Full article
(This article belongs to the Section Civil Engineering)
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