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The Impact of Flexural/Torsional Coupling on the Stability of Symmetrical Laminated Plates 挠扭耦合对对称层压板稳定性的影响
IF 1.2 Q3 MECHANICS Pub Date : 2023-12-30 DOI: 10.13052/ejcm2642-2085.3251
Hafid Mataich, Bouchta El Amrani
In this study, we will evaluate the effect of bending/torsion coupling on the buckling instability and free vibration behavior of symmetrical laminated plates. We will load these plates in-plane with bi-axial or uni-axial, uniform or non-uniform mechanical loads. To quantify this behavior, we’ll compare the results obtained with those of specially orthotropic symmetrical plates (where bending/torsion coupling is absent). A parametric study will be carried out by varying the plate’s aspect ratio, anisotropy ratio and/or lamination angle. The aim of these studies is to construct a planar loading margin for the plate while remaining elastically stable, and to determine a physically admissible limit where we can approximate the behavior of symmetrical laminates to that of specially orthotropic plates (easy to study). We will base ourselves on a Rayleigh-Ritz energy formulation of the problem because of the difficulty of finding closed-form solutions. Following validation of this formulation, a numerical survey of the results will be carried out to quantify the effect of bending/torsion coupling on the instability of this type of plate. Various conditions on the plate boundaries will be used.
在本研究中,我们将评估弯曲/扭转耦合对对称层压板屈曲不稳定性和自由振动行为的影响。我们将用双轴或单轴、均匀或不均匀的机械载荷对这些板材进行平面加载。为了量化这种行为,我们将把获得的结果与特别正交对称板(不存在弯曲/扭转耦合)的结果进行比较。我们将通过改变板的长宽比、各向异性比和/或层压角来进行参数研究。这些研究的目的是在保持弹性稳定的同时,为板材构建一个平面加载边缘,并确定一个物理上可接受的极限,在此极限下,我们可以将对称层压板的行为近似为特殊正交板的行为(易于研究)。由于很难找到闭式解,我们将以雷利-里兹能量公式为基础。在对这一公式进行验证后,将对结果进行数值调查,以量化弯曲/扭转耦合对这类板块不稳定性的影响。将使用板边界上的各种条件。
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引用次数: 0
Evaluation of Piezoelectric-based Composite for Actuator Application via FEM with Thermal Analogy 通过有限元与热学类比评估压电基复合材料在致动器中的应用
IF 1.2 Q3 MECHANICS Pub Date : 2023-12-30 DOI: 10.13052/ejcm2642-2085.3253
Alexander Kevin, M. Akbar, Leonardo Gunawan, Darryl Khalid Aulia, Rizqy Agung, S. S. Rawikara, R. A. Sasongko, D. Widagdo
In the present work, a new study on the piezoelectric-based structure by means of Finite Element Method (FEM) is conducted. Currently, the piezoelectric model in the FEM-based commercial software is only applicable via 2D plane stress and 3D solid elements. However, piezoelectric structures are usually manufactured as thin-walled structures, i.e., plates and disks. Therefore, it is more convenient to model a piezoelectric-based structure with 2D shell elements. In this study, FEM with a thermal analogy approach is implemented. Thermal coupling characteristics are utilised as the equivalent of electromechanical properties. Thermal analysis is much more established in FEM-based software; thus, applications with various types of elements are enabled. Therefore, the evaluation of piezoelectric structure via shell element with a thermal analogy approach could be performed. Static and dynamic analyses are conducted with experimental and numerical validations. As depicted in some details in this paper, the shell model with thermal analogy shows an excellent agreement with the 3D solid piezoelectric elements with insignificant variances, less than 0.3%.
本研究通过有限元法 (FEM) 对基于压电的结构进行了新的研究。目前,基于有限元法的商业软件中的压电模型仅适用于二维平面应力和三维实体元素。然而,压电结构通常是薄壁结构,即板和盘。因此,使用二维壳元素对基于压电的结构建模更为方便。在本研究中,有限元模型采用了热类比方法。热耦合特性等同于机电特性。热分析在基于有限元的软件中更为成熟,因此可以应用各种类型的元素。因此,可以通过壳元素和热类比方法对压电结构进行评估。通过实验和数值验证进行了静态和动态分析。正如本文详细描述的那样,采用热类比的壳体模型与三维实体压电元件显示出极好的一致性,差异小于 0.3%。
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引用次数: 0
Vortex and Core Detection using Computer Vision and Machine Learning Methods 利用计算机视觉和机器学习方法进行涡流和核心检测
IF 1.2 Q3 MECHANICS Pub Date : 2023-12-30 DOI: 10.13052/ejcm2642-2085.3252
Zhenguo Xu, Ayush Maria, Kahina Chelli, Thibaut Dumouchel De Premare, Xabadin Bilbao, Christopher Petit, Robert Zoumboulis-Airey, Irene Moulitsas, Tom-Robin Teschner, Seemal Asif, Jun Li
The identification of vortices and cores is crucial for understanding airflow motion in aerodynamics. Currently, numerous methods in Computer Vision and Machine Learning exist for detecting vortices and cores. This research develops a comprehensive framework by combining classic Computer Vision and state-of-the-art Machine Learning techniques for vortex and core detection. It enhances a CNN-based method using Computer Vision algorithms for Feature Engineering and then adopts an Ensemble Learning approach for vortex core classification, through which false positives, false negatives, and computational costs are reduced. Specifically, four features, i.e., Contour Area, Aspect Ratio, Area Difference, and Moment Centre, are employed to identify vortex regions using YOLOv5s, followed by a hard voting classifier based on Random Forest, Adaptive Boosting, and Xtreme Gradient Boosting algorithms for vortex core detection. This novel approach differs from traditional Computer Vision approaches using mathematical variables and image features such as HAAR and SIFT for vortex core detection. The findings show that vortices are detected with a high degree of statistical confidence by a fine-tuned YOLOv5s model, and the integrated technique produces an accuracy score of 97.56% in detecting vortex cores conducted on a total of 133 images generated from a rotor blade NACA0012 simulation. Future work will focus on framework generalisation with a larger and more diverse dataset and intelligent threshold development for more efficient vortex and core detection.
涡流和核心的识别对于理解空气动力学中的气流运动至关重要。目前,计算机视觉和机器学习领域有许多检测涡流和核心的方法。本研究结合经典的计算机视觉技术和最先进的机器学习技术,为涡流和核心检测开发了一个综合框架。它利用计算机视觉算法增强了基于 CNN 的特征工程方法,然后采用集合学习方法进行涡核分类,从而降低了误报、误判和计算成本。具体地说,利用 YOLOv5s 识别涡流区域时采用了四个特征,即轮廓面积、纵横比、面积差和力矩中心,然后采用基于随机森林、自适应提升和 Xtreme 梯度提升算法的硬投票分类器进行涡核检测。这种新方法不同于使用数学变量和图像特征(如 HAAR 和 SIFT)进行涡核检测的传统计算机视觉方法。研究结果表明,经过微调的 YOLOv5s 模型能以高度的统计置信度检测到涡流,而且在对转子叶片 NACA0012 仿真生成的总共 133 幅图像进行涡核检测时,该集成技术的准确率高达 97.56%。未来的工作重点是利用更大、更多样化的数据集和智能阈值开发框架的通用性,以实现更高效的涡流和核心检测。
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引用次数: 0
A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams 研究双向功能梯度多孔微梁动态稳定性的微分正交伽辽金方法
Q3 MECHANICS Pub Date : 2023-11-04 DOI: 10.13052/ejcm2642-2085.3244
Ahmed Saimi, Ismail Bensaid, Besma Khouani, Med Yassin Mazari, Ihab Eddine Houalef, Abdelmadjid Cheikh
The free vibration and buckling behaviours of 2D-FG porous microbeams are explored in this paper utilizing the Quasi-3D beam deformation theory based on the modified couple stress theory and a Differential Quadrature Galerkin Method (DQGM) systematically, as a combination of the Differential Quadrature Method (DQM) and the semi-analytical Galerkin method, which has used to reduce computational cost for problems in dynamics. The governing equations are obtained using the Lagrange’s principle. The mass and stiffness matrices are calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The matrices are expressed in a similar form to that of the Differential Quadrature Method by introducing an interpolation basis on the element boundary of the Galerkin method. The sampling points are determined by the Gauss-Lobatto node method. The influence of the thickness-to-material length scale parameter (MLSP) on the nondimensional natural frequencies and nondimensional critical buckling loads of 2D-FG porous microbeams are investigated, along with the effects of the boundary condition, aspect ratio and gradient index. The results are validated with literature to establish the accuracy of the procedure described. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These results can be applied to the engineering design of porous FG microstructures.
本文采用基于修正耦合应力理论和微分正交伽辽金法的准三维梁变形理论,系统地研究了二维fg多孔微梁的自由振动和屈曲行为,将微分正交法和半解析伽辽金法相结合,降低了动力学问题的计算成本。利用拉格朗日原理得到了控制方程。利用微分正交(DQ)和高斯-洛巴托正交规则给出的权重系数矩阵计算质量矩阵和刚度矩阵。通过在伽辽金法的单元边界上引入插值基,将矩阵表示成与微分求积法类似的形式。采样点由高斯-洛巴托节点法确定。研究了厚度-材料长度尺度参数(MLSP)对2D-FG多孔微梁无量纲固有频率和临界屈曲载荷的影响,以及边界条件、展弦比和梯度指数的影响。结果与文献验证,以建立所述程序的准确性。该工作将为微力学领域中纤维纤维微结构的设计提供数值依据。这些结果可应用于多孔FG微结构的工程设计。
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引用次数: 0
Static Mechanics and Dynamic Analysis and Control of Bridge Structures Under Multi-Load Coupling Effects 多荷载耦合作用下桥梁结构的静力力学与动力分析与控制
Q3 MECHANICS Pub Date : 2023-11-04 DOI: 10.13052/ejcm2642-2085.3243
Ma Zhifang, Sun Zhuoyu, Yuan Yuan
With the rapid development and wide application of large-span bridges, the problem of dynamics and safety control of bridge structures under multiple loads is becoming more and more prominent. To realize the dynamic analysis and mechanical control of the girder structure, this paper designs a new type of magnetorheological (MR) mechanical damper based on the mechanistic analytical method and establishes a coupled dynamics model of the vehicle-rail-MR mechanical damper. The simulation and validation results show that the error between the semi-analytical method and the finite element theory calculation results is only 1.0%, while the kinetic simulation is consistent with the measured frequency domain trend. The analytical results show that: After applying MR mechanical damper for mechanical control, the moment live load and shear values of side spans were reduced by 27.68% and 10.79%, respectively; and the maximum moment and shear values generated at the center pivot were reduced by 28.19% and 10.81%, respectively. After applying the mechanical damper, the stress distribution of the cable-stayed bridge is more balanced, and the maximum diagonal stress of the overall structure is reduced from 3.8 MPa to 2.9 MPa. After safety control, the root-mean-square (RMS) value of the mid-span displacement amplitude was reduced by 59.32% and the maximum value was reduced by 11.46%, which improved the stability of the girder dynamics. After mechanical control, the dynamic acceleration response of the beam within the span decreased between 2 and 8 seconds and increased between 8 and 10 seconds. The overall response fluctuated around −5 m/s2 with a relatively smooth trend.
随着大跨度桥梁的快速发展和广泛应用,多种荷载作用下桥梁结构的动力与安全控制问题日益突出。为实现对梁结构的动力分析和力学控制,基于力学分析方法设计了一种新型磁流变阻尼器,建立了车轨磁流变阻尼器的耦合动力学模型。仿真和验证结果表明,半解析方法与有限元理论计算结果误差仅为1.0%,而动力学模拟与实测频域趋势一致。分析结果表明:采用MR机械阻尼器进行机械控制后,侧跨弯矩活荷载和剪力值分别降低了27.68%和10.79%;中心支点处产生的最大弯矩和最大剪切值分别降低了28.19%和10.81%。施加机械阻尼器后,斜拉桥受力分布更加平衡,整体结构最大斜向应力由3.8 MPa降至2.9 MPa。安全控制后,跨中位移幅值均方根值减小59.32%,最大值减小11.46%,提高了梁的动力稳定性。机械控制后,跨内梁的动加速度响应在2 ~ 8秒之间减小,在8 ~ 10秒之间增大。总体响应在−5 m/s2附近波动,趋势相对平稳。
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引用次数: 0
Analysis of the Mechanical Characteristics of Tunnels Under the Coupling Effect of Submarine Active Faults and Ground Vibrations 海底活动断层与地面振动耦合作用下隧道力学特性分析
Q3 MECHANICS Pub Date : 2023-11-04 DOI: 10.13052/ejcm2642-2085.3242
Sun Zhuoyu, Ma Zhifang, Hou Yaolong
With the rapid development of modern transportation construction, the construction of cross-harbor tunnels has solved the problem of traffic connection between cross-straits, bays and islands. The construction of sub-sea tunnels has technical difficulties such as high difficulty of marine geological survey, close hydraulic connection between strata and seawater, and more developed adverse geology. Based on this, this paper studies the mechanical characteristics of the submarine tunnel under seismic action at the active fault. Firstly, the mechanical model of the universal fault interface is established, and the calculation model of the fault interface is theoretically derived by the method of vibration mechanics, and the influence of the change of the strength of the contact surface and the stiffness of the surrounding rock on both sides of the fault on the transfer coefficient is obtained. Secondly, based on the ground motion input method of two-dimensional homogeneous half-space field, the relevant program of viscoelastic artificial boundary ground motion input is written by MATLAB program, which lays the foundation and premise of load input for mechanical response calculation. Finally, the outcomes of the tunnel parameters and the interplay between the tunnel and the surrounding rock on the cracking of the tunnel lining shape and the mechanical response of the cross-fault sub-sea tunnel underneath seismic motion are mentioned, and it is concluded that the increase in seismic intensity for different seismic intensities under the sea floor has an essentially constant proportion to the increase in acceleration of the seismic response; the seepage effect under the sea floor for the tunnel lining structure reduces the seismic response displacement, velocity and The seabed seepage for the tunnel lining structure reduces the peak seismic response displacement, velocity and acceleration by about 20–35%.
随着现代交通建设的迅速发展,跨海隧道的建设解决了海峡两岸、海湾与岛屿之间的交通连接问题。海底隧道施工存在海洋地质调查难度大、地层与海水水力联系紧密、不利地质条件较发达等技术难点。在此基础上,研究了海底隧道在活动断层地震作用下的力学特性。首先,建立了通用断层界面的力学模型,利用振动力学的方法对断层界面的计算模型进行了理论推导,得到了断层两侧接触面强度和围岩刚度变化对传递系数的影响;其次,基于二维均匀半空间场地震动输入方法,通过MATLAB程序编写了粘弹性人工边界地震动输入的相关程序,为力学响应计算的载荷输入奠定了基础和前提。最后,讨论了隧道参数及隧道与围岩的相互作用对海底跨断层隧道衬砌形状开裂和地震作用下的力学响应的影响,得出海底不同烈度地震作用下的地震烈度增加与地震响应加速度增加的比例基本恒定的结论;海底渗流作用使隧道衬砌结构的地震响应位移、速度和加速度峰值降低约20-35%。
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引用次数: 0
Characteristic Analysis of the Response Mechanics of Asymmetric High-rise Buildings Subjected to Transverse Wind Loads Considering Second-order Vibration Patterns 考虑二阶振型的非对称高层建筑横向风荷载响应力学特征分析
Q3 MECHANICS Pub Date : 2023-11-04 DOI: 10.13052/ejcm2642-2085.3241
Xin Zuo, Die Liu, Ze Xu
The share of high-rise structures in China is growing as a response to the ordinary human wishes of today, such as high-rise accommodations and high-altitude enjoyment facilities. Because of the different traits of high-rise buildings, it is critical to find out about the load response and mechanical traits of high-rise buildings. In this paper, first of all, from the aerodynamic modeling experimental methods on the basis of three-dimensional wind-induced vibration of high-rise structures, high-rise buildings, the side-strain combination of the proposed simple and calculation formula, the basic characteristics of three-dimensional wind-induced vibration of a systematic study. The modal pushover evaluation technique is then used to analyze the elasticity and plasticity of the high-rise structure, and it is counseled that the higher-order vibration sample has a vital effect on the seismic resistance of the structure. Finally, a calculation principle of the mechanical response of high-rise construction subjected to transverse wind load thinking about the second-order vibration mode is given, and the outcomes exhibit that the Contribution of the second-order vibration mode to the dynamic displacement in the winding course of high-rise construction is inside 2%. However, the most Contribution to the acceleration response can attain 18%.
在中国,高层建筑的比例正在增长,这是对当今人类普通愿望的回应,比如高层住宿和高海拔娱乐设施。由于高层建筑的不同特性,研究高层建筑的荷载响应和力学特性是至关重要的。本文首先从高层结构三维风致振动气动建模实验方法的基础上,提出了高层建筑侧应变组合的简单方法和计算公式,对三维风致振动的基本特征进行了系统的研究。利用模态推覆评价技术对高层结构进行了弹塑性分析,认为高阶振动对结构的抗震性能有重要影响。最后,给出了考虑二阶振型的高层建筑在横向风荷载作用下的力学响应计算原则,结果表明:高层建筑在缠绕过程中二阶振型对动力位移的贡献在2%以内。然而,对加速度响应的最大贡献可以达到18%。
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引用次数: 0
Post-earthquake Dynamics of Bridge Structures using New Particle Dampers – A Case Study of the Nujiang River Bridge 基于新型质点阻尼器的桥梁结构震后动力研究——以怒江大桥为例
Q3 MECHANICS Pub Date : 2023-09-28 DOI: 10.13052/ejcm2642-2085.3233
Gong Lei, Tang Miao
In this study, a new mechanical model, named particle damping mechanics model (PU_SPD), is proposed to study the damping problem of bridge structures. The model takes the Nujiang River Bridge as a case study, and explores the mechanism of force action by analyzing the time domain vibration characteristics and frequency domain of the excitation force, vibrating body (bridge structural properties) and particle damping. the PU_SPD model and its calculation method can intuitively and scientifically describe the damping dissipation characteristics of a vibrating beam under the action of particle damping, avoiding the tedious process of parameter iterative solution and improving the computational efficiency. In addition, the damping influence law of particle damping on the beam structure is derived through the analysis of transfer function and damping level. The study also proposes an optimal design method for PU_SPD damping parameters under dynamic loading of the bridge, and its performance parameters are analyzed and verified, and compared and validated with the time-domain analysis method. The results show that the PU_SPD mechanical model based on time-frequency domain analysis can intuitively reflect the damping dissipation mechanics with high accuracy, clear solution process and reasonable and accurate parameter optimization analysis method. PU_SPD has a wide frequency range, good effect and stability, and has a good prospect of application in engineering vibration and noise reduction.
本文提出了一种新的力学模型——粒子阻尼力学模型(PU_SPD)来研究桥梁结构的阻尼问题。该模型以怒江大桥为例,通过分析激振力、振体(桥梁结构特性)和颗粒阻尼的时域振动特性和频域振动特性,探讨力的作用机理。PU_SPD模型及其计算方法可以直观、科学地描述粒子阻尼作用下振动梁的阻尼耗散特性,避免了参数迭代求解的繁琐过程,提高了计算效率。此外,通过对传递函数和阻尼水平的分析,推导了颗粒阻尼对梁结构的阻尼影响规律。研究还提出了桥梁动载下PU_SPD阻尼参数的优化设计方法,并对其性能参数进行了分析验证,并与时域分析方法进行了对比验证。结果表明,基于时频域分析的PU_SPD力学模型能直观反映阻尼耗散力学,求解过程清晰,参数优化分析方法合理准确。PU_SPD具有频率范围宽、效果好、稳定性好等特点,在工程减振降噪方面具有良好的应用前景。
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引用次数: 0
Field Test and Structural Stability Analysis of Multi-stage Slope Based on Seepage Coupling Theory 基于渗流耦合理论的多级边坡现场试验及结构稳定性分析
Q3 MECHANICS Pub Date : 2023-09-28 DOI: 10.13052/ejcm2642-2085.3232
Lu Hao, Li Qing, Li Peijun
This study takes the slope engineering of the Guangdong North Expressway as the background, and studies the impact of rainfall infiltration on the stability of high slopes through on-site monitoring, data analysis, and model construction. Firstly, based on BC theory, the mechanical calculation model of landslide rainfall is established, and the mechanical formula of slope mechanical properties and Factor of safety considering rainfall process and rainfall infiltration process is derived. Then, by constructing a Fluid–structure interaction numerical calculation model considering the seepage characteristics and mechanical state evolution of the slope, the movement of pore water in the slope under different rainfall intensities and the evolution of the mechanical state and displacement characteristics of the slope were studied. Research has found that the mechanical and numerical calculation models in this article are highly consistent with the actual site conditions, and there may be two potential sliding surfaces in the K738+995 section. The potential sliding surface of K738+910 section is located at a depth of 7 m below the first level platform and 3 m below the third level platform; There may be two potential sliding surfaces in K738+658 section, one is located at the interface between silty clay and sandy clay (9 m below the top of cutting), and the other is mainly located at the interface between sandy clay and completely weathered andesite porphyrite; The surface layer of the slope is silty clay and sandy clay, and the underlying layer is fully strongly weathered andesite porphyrite and moderately weathered dacite. Completely strongly weathered andesite porphyrite is soft, easy to soften and disintegrate when encountering water, and joint fissures are developed. The surface of some cracks is contaminated with iron and manganese, resulting in uneven weathering. The rock is relatively soft and the rock mass is broken. Due to the recent continuous heavy rainfall, the water content of the surface soil of the slope gradually increases and tends to saturation, increasing the self-weight of the slope soil.
本研究以广东北高速公路边坡工程为背景,通过现场监测、数据分析、模型构建等方法,研究降雨入渗对高边坡稳定性的影响。首先,基于BC理论,建立滑坡降雨的力学计算模型,推导考虑降雨过程和降雨入渗过程的边坡力学特性和安全系数的力学公式;然后,通过构建考虑边坡渗流特征和力学状态演化的流固耦合数值计算模型,研究了不同降雨强度下边坡孔隙水的运动规律以及边坡力学状态演化和位移特征。研究发现,本文的力学和数值计算模型与现场实际情况高度吻合,K738+995断面可能存在两个潜在滑动面。K738+910断面潜在滑动面位于一级平台下方7 m、三级平台下方3 m处;K738+658剖面可能存在两个潜在的滑动面,一个位于粉质粘土与砂质粘土的界面处(切割顶部以下9 m处),另一个主要位于砂质粘土与完全风化安山岩斑岩的界面处;坡面表层为粉质粘土和砂质粘土,下表层为完全强风化安山岩斑岩和中等风化英安岩。完全强风化安山岩斑岩质地柔软,遇水易软化崩解,节理裂隙发育。有些裂缝表面被铁和锰污染,导致风化不均匀。岩石相对较软,岩体破碎。由于近期连续强降雨,边坡表层土壤含水量逐渐增加,趋于饱和,增加了边坡土的自重。
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引用次数: 0
Research on Mechanical Characteristics and Load-bearing Behavior of Nodes of Steel Fiber Concrete Arch Bridges 钢纤维混凝土拱桥节点受力特性及承载性能研究
Q3 MECHANICS Pub Date : 2023-09-28 DOI: 10.13052/ejcm2642-2085.3231
Liu Kailiang, Wang Sen
Steel fiber reinforced concrete (SFRC) is a new type of composite material formed by dispersing discontinuous short steel fibers in a uniform and random direction throughout the concrete, which has excellent properties of tensile, shear and high toughness, can effectively improve the load-bearing capacity of arch bridges. In this paper, the mechanics of SFRP in the nodal structure of an arch bridge is initially explored by means of indoor model tests and numerical simulation studies. The results show that the maximum principal tensile stress occurs at the intersection of arch rib, arch foot and tie beam, and the maximum principal compressive stress occurs at the connection between arch rib and arch seat, which should be considered in the design. In this paper, we hope to understand the characteristics of the force and bearing capacity of this type of structure to provide a reference for similar projects.
钢纤维增强混凝土(SFRC)是将不连续的短钢纤维以均匀、随机的方向分散在混凝土各处而形成的一种新型复合材料,具有优异的抗拉、抗剪性能和高韧性,可有效提高拱桥的承载能力。本文通过室内模型试验和数值模拟研究,初步探讨了SFRP在某拱桥节点结构中的受力规律。结果表明:最大主拉应力出现在拱肋、拱脚和系梁的交会处,最大主压应力出现在拱肋与拱座的连接处,在设计中应予以考虑。在本文中,我们希望了解这类结构的受力和承载力特点,为类似工程提供参考。
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引用次数: 0
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European Journal of Computational Mechanics
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