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  • Research Progress on Ultrasonic Testing of Manufacturing Defects of Aerospace Composite Structures
    ZHANG Zhen, XU Haorun, NI Fupeng, XU Haifeng, YANG Weidong, LI Yan
    2025, 46(1): 1-19. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.001
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    With the continuous advancement of composite manufacturing technology and the requirements of civil aviation for economy, the application of lightweight and high-strength composite structures in the aerospace field has gradually expanded from thin-walled secondary load-bearing structures to large-thickness, variable-section main load-bearing structures. The wide application of these complex composite structural parts has raised higher requirements for their manufacturing reliability verification. However, due to the anisotropy of the composite materials and the complexity of the shape of the aviation structure, defects such as delamination, pores, fiber waviness, and resin-rich layers are prone to occur during the manufacturing process of the main load-bearing composite structure. These microstructural anomalies significantly degrade the macro-mechanical performance of the composite components. Ultrasonic testing has become an important technology of defect detection in aerospace composite structures due to its high penetration, high sensitivity and good applicability. In this paper, we first introduce the types and characteristics of manufacturing defects in aerospace composite structures, focusing on the analysis of the causes of defects such as pores, delamination, fiber waviness and resin-rich layers and their effects on the mechanical properties of the structure. Then, the research progress of ultrasonic testing in the detection of single-type manufacturing defects and mixed-type defects in thin laminate and thick composite structures in recent years is reviewed. Subsequently, the application of artificial intelligence technology in the defect diagnosis of composite structure is discussed. Finally, the challenges faced by the current ultrasonic testing of aviation composite structures are analyzed, and the future development trend is prospected.
  • Analysis of Stresses at Two-Dimensional Rough Interface Between Lithium Electrode and Solid-State Electrolyte
    GUO Zijian, ZHAO Ying, NIE Guohua
    2025, 46(1): 20-27. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.002
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    During the charge and discharge processes of solid-state lithium metal batteries, the stress generated at the interface between the rough surfaces of the lithium electrode and solid-state electrolyte plays a crucial role in the formation of lithium dendrites. In this paper, a mechanical model is established by considering the electrode and electrolyte as elastic bodies. Specifically, the stress at the interface of a two-dimensional sinusoidal rough interface is investigated for isotropic linear elastic materials. Using a two-dimensional Fourier transform, the relationship between stress and displacement at the interface in the transform domain is obtained. By applying the inverse transform and incorporating boundary conditions and interface continuity conditions, an analytical solution for the interfacial stress in two dimensional conditions is derived. When the wavenumber of surface roughness in one direction of the interface is zero, the two-dimensional interfacial stress solution degrades to the one-dimensional case. Subsequently, the analytical solution is used to analyze the influences of the material parameters of the electrolyte and electrode on the magnitude of the interfacial stress.
  • Nonlinear Interface Vibro-Acoustic Model and Localization Method for Delamination in Laminated Beams
    YANG Yuchen, LI Qiushi, JI Mincong, QIU Ling
    2025, 46(1): 28-38. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.003
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    Laminated beams are widely used in engineering structures due to their enhanced strength and stiffness. However, delamination, a barely visible form of damage, can occur during manufacturing or service. Accurate localization of delamination in laminated beams is essential for maintaining structural integrity. While the existing linear interface vibration model has been proposed to represent the absence of linear interface forces in the debonding region of open delamination, it fails to capture the opening-closing contact behavior of "breathing" debonding under nonlinear vibro-acoustic excitation. To address this problem, this study proposes a new nonlinear interface vibro-acoustic model, in which the nonlinear interface forces appear exclusively in the "breathing" debonding region, acting as multi-tone harmonic excitation sources to produce sideband harmonics. Moreover, this study emphasizes the use of nonlinear interface forces for the localization of delamination due to this inherent merit of localization. The nonlinear interface forces are reconstructed from nonlinear operating deflection shapes of a laminated beam. Nonlinear damage indices are established relying on nonlinear interfaces associated with multiple neighbouring sideband harmonics. The capability of the approach for localizing "breathing" debonding in laminated beams is experimentally validated through non-contact measurements using a scanning laser vibrometer. The results demonstrate that the approach is capable of predicting the occurrence of delaminations in laminated beams and accurately identifying their locations and sizes.
  • A CPG Gait Control of Hexapod Robot Based on Time-Delay Coupling
    WANG Hongxiang, WU Kaijun, SONG Zigen
    2025, 46(1): 39-50. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.004
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    Inspired by the nervous system of biological movement, Central Pattern Generator (CPG) control theory is applied to achieve various gait patterns in legged robots, which is of great significance in bio-inspired motion control. For the gait movement control of hexapod robots, the classical Van der Pol (VDP) oscillator model is first improved by adding a time proportion function to adjust the rising and falling phases of the periodic rhythm signal, enabling the regulation of the swing and support phases of the robot's legs. Next, the improved VDP oscillator is used as a functional unit, and the coupling delay between units is employed to regulate gait patterns, constructing a novel time-delay coupled CPG controller with a unidirectional loop. Furthermore, a hexapod robot model is designed in SolidWorks, and co-simulation experiments using ADAMS and MATLAB are conducted to achieve three common gait patterns: tripod, tetrapod, and wave gaits. Finally, gait tests are performed on a physical prototype to verify the feasibility and effectiveness of the proposed time-delay coupled CPG control system.
  • Optic-Viscoelastic Properties of Chiral Liquid Crystal Elastomer Films Under Uniaxial and Biaxial Deformation
    GU Jieru, YU Lu, ZHAO Ying, LI Chenzhe
    2025, 46(1): 51-63. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.005
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    Chiral Liquid Crystal Elastomers (CLCE), with their ability to selectively reflect specific wavelengths of light and exhibit excellent large-deformation capabilities, have gradually become a promising flexible reflective display material. Studies show that the optical coloration properties of CLCE are closely related to local strain, displaying a significant force-optical coupling effect. As a soft material, CLCE possesses viscoelastic characteristics, resulting in a time-dependent mechanical response during deformation. However, systematic research on the optical and viscoelastic coupling properties of CLCE under uniaxial and biaxial deformation conditions remains limited. In this study, using a multi-axial opto-mechanical testing platform, we systematically investigate the time-dependent characteristics of the reflection spectrum of CLCE under uniaxial and equibiaxial deformation conditions. By analyzing the spectral properties under stress relaxation and different loading rates, we propose an improved phenomenological model for CLCE based on the stretched exponential viscoelastic constitutive relationship. This model provides theoretical support and experimental insights for further optimizing the application of CLCE in smart optical devices.
  • Warping Caused by Adsorption and Its Effect on the Static Response of Microcantilevers
    WANG Zhenxing, ZHANG Nenghui
    2025, 46(1): 64-75. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.006
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    To meet new detection requirements and achieve high sensitivity, microbeam-based biosensor technique faces challenges in the development of signal interpretation models. Through 3D finite element simulations of the detected quasi-static signals of microbeam under surface adsorption, we revealed an asymmetric distribution characteristic of the microbeam cross-section's warping. However, the existing theoretical models considering shear deformation cannot accurately describe this asymmetric warping. To address this issue, first, we simplified the complete adsorption of molecules as a uniformly distributed surface stress acting on the microbeam's surface and obtained the distribution pattern of warping zero point through 3D finite element simulation. Then, we employed the semi-inverse method of plane elasticity theory to determine the shear stress distribution and shear force that correspond to the asymmetric warping characteristics on the deformed cross-section. This led to an improvement in Timoshenko beam theory and the establishment of a new model to predict the detected quasi-static signals of microbeam. Finally, we validated the analytical model by comparing with experimental results and finite element simulations. The results indicate that the predictions of our improved model agree well with the relevant microbeam experiments. Moreover, within the geometric size ranges employed in the existing adsorption-microbeam static experiments (length-to-thickness ratio of 200-500, length-to-width ratio of 3-7), its prediction error for the microbeam's free-end deflection is less than 3 %, which is smaller than that of other theoretical predictions. Additionally, the shear effect and axial force effect negatively impact the microbeam's deflection, with the shear effect having a significantly greater influence than the axial force effect. This model and its conclusions provide a new perspective for interpreting the static detection signals of microbeam biosensors and developing the relevant design.
  • On the Tensile Response and Damage Mechanism of Metal Mesh/Fiber-Reinforced Laminates with Pores
    CHEN Taicong, SHENG Dongfa, HU Jiyuan, LI Ziheng, YU Hongquan
    2025, 46(1): 76-86. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.007
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    By conducting tensile tests and numerical simulations on 304 stainless steel wire mesh/carbon fiber hybrid composite (SSWM/CFRP) laminates, the residual strength and failure modes of single hole specimens with different aperture sizes and double hole specimens with different circular hole arrangements were investigated. Digital Image Correlation (DIC) technology and Scanning Electron Microscopy (SEM) were used to observe the deformation and damage evolution characteristics of the specimens. The results indicate that the tensile stress-strain curve of SSWM/CFRP laminates with holes generally exhibits brittle failure characteristics. The residual strength of single hole specimens decreases with the increase of hole diameter, while the effective cross-sectional area of double hole specimens is affected by the arrangement of circular holes in the specimens. The DIC technology captures the maximum tensile and shear strains of a single hole specimen locally, which appear on the left and right sides of the circular hole along the diagonal direction. The constructed finite element model can effectively predict the residual strength and fracture path of the specimen, and reveal that the main failure modes of the specimen are ductile fracture of SSWM, fiber tensile damage of 0 ° fiber layer, matrix tensile damage of 90 ° fiber layer, and interlayer delamination damage.
  • Design and Analysis of Locally Resonant Phononic Crystals Based on Low-Frequency Vibration Reduction and Noise Control in Automobiles
    WANG Xinyue, LI Cheng, GUO Limin, CHEN Zhenyu
    2025, 46(1): 87-98. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.008
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    Low-frequency vibrations and noise levels are important indicators for evaluating automobile comfort. To address the issue of low-frequency vibrations and their control in automotive panel structures, we proposed a plate-type two-dimensional phononic crystal design based on the local resonance mechanism. The bandgap range of the phononic crystal was determined through the finite element method, and the mechanism of bandgap formation was analyzed. Subsequently, the transmission characteristics curve of the phononic crystal plate was calculated, and comparisons were also carried out for the vibration displacement. The results indicate that a complete bandgap appears in the plate within the frequency range from 62.48 Hz to 74.16 Hz. Within this frequency range, coupling effects between the base plate and the cylindrical resonators occur, leading to the formation of the bandgap. Elastic waves in the phononic crystal plate are successfully confined within the bandgap range. By adjusting the material and geometric parameters of the structure, the bandgap frequency range can be tuned to meet the requirements of more practical low-frequency applications. The structural design and analysis method proposed in this paper have broad application prospects in engineering fields such as low-frequency vibration reduction and noise control in automobiles.
  • Machine Learning-Based Assessment of CO2 Rapid Leakage from Offshore Geological Storage
    ZHANG Haibin, LU Di, WANG Yongchang, GAO Fengpu, SONG Xuehang, SUN Nannan
    2025, 46(1): 99-107. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.009
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    In view of the high carbon emissions and limited land storage capacity in the eastern coastal areas of China, CO2 offshore geological storage holds significant application potential. Although the risk of CO2 leakage during offshore geological storage is extremely low, accurate assessment of CO2 diffusion in seawater under rapid leak scenarios is critical to ensure the safety of storage. Based on typical marine environment data, this study employs the Volume of Fluid (VOF) model to simulate the dynamic characteristics of CO₂ bubbles and utilizes the Euler model to simulate the diffusion characteristics of CO2 clusters in seawater, thereby completing a comprehensive simulation analysis of fluid dynamics. On this basis, a machine learning-based assessment method for subsea CO2 leakage is developed. The neural network model framework is constructed, and an inverse-problem solving model is established accordingly to analyze the morphological evolution and distribution range of CO2 leakage under different marine environmental conditions. Additionally, key parameters such as crack width and leakage velocity resulting from the leakage scenario are analyzed, enabling accurate calculation of the leakage amount. The prediction accuracy of this model can reach 95 %, demonstrating its effectiveness and applicability in addressing CO₂ leakage. This study not only offers an innovative method for rapid leakage assessment of CO2 offshore geological storage but also provides an important scientific basis and technical support for risk assessment and safety management in related fields in the future.
  • Lower Bound Limit Analysis Based on Natural Element Method
    WANG Wei, ZHAO Li, LI Ruizhi, ZHANG Yi, REN Hongping
    2025, 46(1): 108-117. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.010
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    The Natural Element Method (NEM) is a meshless method based on natural neighbor interpolation. This method offers the advantages of simple shape function construction and ease of applying essential boundary conditions. Utilizing dimensional reduction techniques, a methodology for conducting lower bound limit analysis on two-dimensional elastoplastic structures has been developed through the application of NEM. In the lower-bound limit analysis, the elastic stress field is directly obtained using the NEM. The self-equilibrated stress basis vectors are derived from the elastoplastic iteration results of the NEM, and the required self-equilibrated stress field is constructed. The whole solution process of the problem is transformed into a series of sub-problems of nonlinear programming, which are solved through the complex method. Numerical examples demonstrate that the application of the Natural Element Method to lower-bound limit analysis is both feasible and effective.
  • Structural Damage Identification Based on Improved Modal Strain Energy and DBO-BP Neural Network
    YANG Haijun, MA Lei, XU Yongzhi, YU Cong
    2025, 46(1): 118-129. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.011
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    Damage identification is one of the most important aspects of structural health monitoring. In order to further improve the efficiency and accuracy of damage identification, a two-stage structural damage identification method based on the improved modal strain energy index and DBO-BP (Dung Beetle Optimization-Back Propagation) neural network is proposed. Firstly, the improved normalized damage index of modal strain energy is used for the damage localization analysis of the structure. Then, taking the average change rate of the structure unit modal strain energy as the input parameter, the stiffness reduction coefficient of the damaged unit as the output parameter, and utilizing the DBO algorithm which is an improved version of the optimal latin hypercubic method, the weights and thresholds of the BP neural network are optimized to perform the structural damage quantitative analysis. The concrete slab structure and flat rigid frame structure are used as exemplary models for damage identification verification. The results show that the proposed method is accurate in damage location identification, with high calculation efficiency for the degree of damage and small identification error as low as 0.4 %, exhibiting excellent damage identification performance.
  • Propagation of Green-Lindsay Generalized Thermoelastic Waves Through Couple-Stress Sandwich Solids
    WANG Changda, ZHOU Yang
    2025, 46(1): 130-140. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.012
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    Under some extreme conditions such as rapid heat transfer, it is necessary to build the non-Fourier heat conduction model considering the finite heat propagation velocity, which includes the hyperbolic heat conduction equation. Based on the modified couple-stress elasticity theory and Green-Lindsay generalized thermoelasticity theory, the governing equations of the thermal mechanical coupling theory and four dispersive waves (CP wave, CT wave, SV wave and SS wave) are obtained in this paper. Using the wave function method, the linear algebraic equations are derived based on the intact interface conditions including surface force, displacement, surface couple, micro-rotation, temperature change and heat flow so as to determine the amplitude ratio of the reflected transmission wave through the finite thickness sandwich structure relative to the incident wave. The influences of two thermal relaxation durations on the CT wave reflection transmission coefficient,as well as one couple stress parameter on the SV wave and SS wave reflection transmission coefficient are studied via investigating the incident SV wave. Finally, the accuracy of the numerical results is verified through examining the conservation of normal energy flow for each wave.
  • Influence of Viscous Friction and Linear Density on the Motion of Worm-Like System
    JIANG Ziwang, ZHANG Huiwen
    2025, 46(1): 141-150. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.013
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    The influence of friction coefficient and line density on the motion of continuous worm-like system is studied in this paper. Frist, based on the dynamic model and the quasi-static model describing the motion of worm-like system, the two average velocities over one period are respectively derived by employing the square strain wave. Next, through comparing these two average velocities, it is found that the dynamic model cannot be simplified as quasi-static model for small friction or large linear density conditions. Then, the condition under which the influences of these parameters on the motion of worm-like system should be considered is given on the basis of relative error principle of the average velocity. Finally, through a numerical example, the two models are compared for the displacement-time histories over ten periods. It is found that the parameters of friction coefficient and line density have significant influences on the system motion in certain conditions.
  • Free Vibration of Non-Through Cracked Plates on Fractional-Order Viscoelastic Foundations
    WANG Gang, WEI Peijun, ZHOU Xiaoli, ZHANG Jun
    2025, 46(1): 151-161. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.014
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    The free vibration problem of non-through cracked plates on fractional-order viscoelastic foundations is studied in this paper. First, a fractional-order viscoelastic foundation model is introduced to better describe the mechanical behavior of foundation. Next, the free vibration of cracked plate with through crack under the four-edge simply-supported boundary conditions is studied. Further, the through crack situation is generalized to the non-through crack situation. Based on the relation between the energy release rate and the stress instensity factor, the additional rotation angles induced by the crack is obtained, and the compliance coefficients of the crack equivilent rotation spring are derived for both the through and non-through crack situations. Finally, the complex natural frequency are obtained according to the boundary conditions. The numerical examples are provided and the influences of the fractional order coefficient, the viscosity coefficient, crack location and crack depth on the complex natural frequency and mode shape of the cracked plate were discussed.
  • Experimental Study of Mechanical Properties and Theoretical Model of Failure Conditions for Fractured Granite
    HUANG Yongjun, LI Shiwen, LIU Xianlin, SHAO Yu, WENG Jian, REN Zhongjun, LÜ Xilin
    2025, 46(1): 162-172. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.015
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    Granite often contains initial cracks, therefore its strength characteristics are greatly affected by crack propagation. Most of the existing rock strength theories do not consider crack propagation, making them difficult to effectively reflect the strength and failure characteristics of the fractured granite. In this paper, uniaxial /triaxial compression tests and Brazilian splitting tests were conducted on the intact and fractured granite samples to study the strength and failure characteristics under tensile and compression conditions. The influences of confining pressure and crack inclination angle (the angle between the crack and the cross-section plane) on the strength stiffness and failure mode of granite were analyzed, and a method for calculating the strength of the initially cracked rocks was proposed. Based on the propensities of type II friction slip fracture in intact granite and type I-II composite fracture in fractured granite, the failure conditions of intact and fractured granite were established according to fracture mechanics theory. The experimental results show that the compressive strength and stiffness of granite specimens are significantly reduced by the introduction of initial crack. The compressive strength, elastic modulus, and secant modulus decrease with the crack inclination angle, while Poisson's ratio shows opposite trend. The initial cracks will significantly reduce the tensile strength of granite, which decreases with the decrease of crack inclination angle.
  • Approximate Noether Symmetry for Approximate Hamiltonian Systems on Time Scales
    LI Yanmin, JIN Shixin
    2025, 46(1): 173-180. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.016
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    In this paper, the approximate Noether theorems for approximate Hamiltonian systems on time scales are investigated based on the Noether symmetry theory on time scales. Firstly, the Hamilton principle for approximate Hamiltonian systems on time scales is presented, and the corresponding approximate Hamilton canonical equations are established. Secondly, the Noether identities for approximate Hamiltonian systems on time scales are derived, and the relationship between approximate Noether symmetry and approximate conserved quantities is established. As a result, the approximate Noether theorems for these systems on time scales are obtained. Finally, an example is provided to demonstrate the application of the theoretical results.
  • Study on Mechanisms of the Single Bubble Motion in Microchannels
    GUO Tianxiang, MO Chenglong, CHAN Wenqiang, CHEN Rou, YAN Weiwei
    2025, 46(1): 181-192. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.017
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    Bubbles are one of the important factors affecting the efficiency and quality of microreactors. Understanding the mechanisms of bubble transportation in the microchannel can provide guidelines for the designation. Meanwhile, bubble motion is one of the usual bubble transportation phenomena. In this paper, systematic and parametric studies of single bubble motion characteristics are conducted using computational fluid dynamics, aiming to derive fundamental principles and uncover the underlying mechanisms. The bubble motion principle during the initial detachment from the wall is proposed: while the trajectories of a single bubble may vary, the bubble will ultimately reach an equilibrium position (with a constant distance from the wall) across all parametric cases. Furthermore, the equilibrium position of the bubble is influenced by its diameter, the driving velocity, and the properties of the surrounding solution. Reynolds number (Re) and Capillary number (Ca) are selected as two characterized parameters. Based on the bubble diameter and common solution properties, the discussion cases in the range of 0.288<Re<97.2, 0.005<Ca<0.228. The relationship between Re and Ca can be distinguished by the bubble equilibrium position Ye (the dimensionless number of the distance between the final bubbles and the wall): (1) power law when 0<Ye<0.45; (2) linear when 0.45<Ye<0.95; (3) the bubble is attached to the wall (Ye=0) when the viscous effect is negligible; (4) the bubble is positioned in the center of the microchannel (Ye=1) when the viscous effect dominates. Corresponding, the mechanism can be underlaid by the manipulation forces, including wall-induced, deformable-induced, and shear stress gradient lifting forces and viscous drag force. In conclusion, the motion of the bubble is the combined influence of the wall, inertia, viscosity and surface tension effects.
  • Study on Geometric Optimization of Shear-Tensile Specimen Based on Finite Element Method
    DENG Liang, MAO Xuan, LOU Siyuan
    2025, 46(1): 193-201. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.018
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    Shear fracture models play a crucial role in characterizing metal fracture, with shear tensile tests serving as the fundamental method for calibrating their parameters. However, existing shear tensile experiments often achieve limited maximum strain, making it difficult to maintain a stable shear state under large strain conditions. In this study, finite element analysis was conducted using LS-DYNA to simulate four distinct shear-tensile specimens, verifying the feasibility of their constitutive model and boundary conditions. Based on the guidelines from GB/T 34487-2017, a novel shear-tensile specimen is proposed. This new design ensures minimal stress triaxiality fluctuations (within ± 0.05) and achieves an effective plastic strain of up to 10% prior to fracture.
  • Numerical Simulation of the Influence of Environmental Pressure and Stand-Off Distance on T2/Q235 Explosive Welding
    MIAO Guanghong, ZHU Zhiqiang, LIU Bo, DONG Jilei, CHEN Long, WEI Zhengmei, WU Weida
    2025, 46(1): 202-210. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.019
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    To investigate the effects of ambient pressure and standoff distance on the bonding quality of T2/Q235 explosive welding, a three-dimensional numerical simulation of the welding process was conducted using Ansys software. Two computational approaches-the Smooth Particle Hydrodynamics-Finite Element Method (SPH-FEM) coupled algorithm and the Arbitrary Lagrangian-Eulerian (ALE) method-were employed to analyze collision velocity and collision angle under varying ambient pressures (1 atm to 0.2 atm) and stand-off distances (3 mm, 6 mm, and 9 mm). Simulation results were systematically compared with experimental data and theoretical calculations. Key findings revealed that: (1) Under decreasing ambient pressure, maximum collision velocity occurred at 1 atm for the SPH-FEM method but shifted to 0.2 atm for the ALE method, aligning more closely with experimental observations; (2) Both algorithms consistently showed larger collision angles at the 6 mm stand-off distance compared to 3 mm and 9 mm configurations, with the ALE method yielding smaller angles closer to experimental lower bounds at 3 mm stand-off under atmospheric pressure; (3) At 0.2 atm ambient pressure and 6 mm stand-off, ALE simulations demonstrated superior agreement with theoretical predictions for both collision velocity and angle. The results conclusively demonstrate that the ALE algorithm achieves higher consistency with experimental measurements and theoretical models compared to the SPH-FEM approach, validating its effectiveness for simulating T2/Q235 explosive welding dynamics.
  • The Perspective of Energy Method on Column Buckling Teaching and Its Application in the Thermal Buckling of Carbon Nanotubes
    WU Jiye, HUANG Kun
    2025, 46(1): 211-221. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.020
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    Column buckling is a critical topic in university-level Materials Mechanics courses and is widely regarded as a challenging subject to teach. In classical Materials Mechanics theory, the critical load is determined by analyzing the non-zero solution condition of the approximate equilibrium differential equation in the critical buckling state. Although this method is straightforward, it remains highly abstract and is difficult to apply to complex engineering stability problems. To enhance students' understanding of column buckling and its analytical methods, this study revisits the classical approach through the principles of virtual work and minimum potential energy. Additionally, based on the principle of minimum potential energy, the thermal buckling behavior of carbon nanotubes under a longitudinal linear temperature gradient is examined. This work aims to provide new perspectives for the teaching and research of column buckling, helping students gain a deeper comprehension of relevant concepts and methods in handling buckling problems.
  • Load Dependence of the Friction on a Suspended Single-Layer Graphene
    ZHANG Hongwei, QU Jinfeng, ZHANG Jingnan
    2025, 46(1): 222-229. https://doi.org/10.15959/j.cnki.0254-0053.2025.01.021
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    Graphene and its related two-dimensional materials have become a hot topic in the field of nanotribology. In recent years, many significant progresses have been made in theoretical, experimental, and computational simulation studies. Due to the extremely complex nature of nanoscale friction processes, the underlying mechanisms of friction are not yet fully understood. Therefore, it is necessary to delve into the mechanisms of friction and reveal the laws of friction on the atomic-scale. In this paper, the sliding friction behavior of a diamond probe on a suspended single-layer graphene surface is studied based on molecular dynamics simulation. The dependence of the friction on the normal load and the relationship between friction and actual contact area are considered. The results show that there is a nonlinear relationship between friction force and normal load (actual contact area), which is significantly different from the friction laws of bulk materials. Specifically, the friction force gradually increases with the load in the positive load range. However, the friction force is almost unaffected by changes in the load in the negative load range. The current research findings help to understand the nanoscale friction behavior of two-dimensional materials from an atomic perspective. This research can also provide new ideas and theoretical references for the design of nanodevices and the development of nanotribology.