Forces in mechanics最新文献_第4页

Free vibration analysis of a functionally graded porous nanoplate in a hygrothermal environment resting on an elastic foundation 湿热环境中位于弹性地基上的功能分级多孔纳米板的自由振动分析

IF 3.2

Forces in mechanics Pub Date : 2024-11-14 DOI: 10.1016/j.finmec.2024.100294

Ali Mottaghi , Ali Mokhtarian , Mohammad Hashemian , Mostafa Pirmoradian , Soheil Salahshour

{"title":"Free vibration analysis of a functionally graded porous nanoplate in a hygrothermal environment resting on an elastic foundation","authors":"Ali Mottaghi , Ali Mokhtarian , Mohammad Hashemian , Mostafa Pirmoradian , Soheil Salahshour","doi":"10.1016/j.finmec.2024.100294","DOIUrl":"10.1016/j.finmec.2024.100294","url":null,"abstract":"<div><div>This research investigates the free vibrational behavior of a functionally graded porous (FGP) nanoplate resting on an elastic Pasternak foundation in a hygrothermal environment. The nanoplate is modeled based on the nonlocal strain gradient theory (NSGT) and considering several plate theories including the CPT (classical plate theory), the FSDT (first-order shear deformation theory), and the TSDT (third-order shear deformation theory). Several patterns are investigated for the dispersion of pores, and the surface effects are incorporated to enhance the precision of the model. The governing equations and boundary conditions are derived via Hamilton's principle and an exact solution is provided via the Navier method. The impacts of several parameters on the natural frequencies are inspected such as length scale and nonlocal parameters, surface effects, porosity parameter, hygrothermal environment, and coefficients of the foundation. The results show that the impact of the porosity parameter on the natural frequencies of nanoplates is significantly dependent on the porosity distribution pattern. It is discovered that by increasing the porosity parameter from 0 to 0.6, the relative changes of natural frequencies vary from a decrease of 30 % to an increase of 6 %.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100294"},"PeriodicalIF":3.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Enhanced meshfree method with nodal integration for analysis of functionally graded material sandwich curved shells 用于分析功能梯度材料夹层曲面壳的节点积分增强型无网格方法

IF 3.2

Forces in mechanics Pub Date : 2024-10-23 DOI: 10.1016/j.finmec.2024.100292

Thien Tich Truong, Binh Khanh Ngo, Nha Thanh Nguyen, Vay Siu Lo

{"title":"Enhanced meshfree method with nodal integration for analysis of functionally graded material sandwich curved shells","authors":"Thien Tich Truong, Binh Khanh Ngo, Nha Thanh Nguyen, Vay Siu Lo","doi":"10.1016/j.finmec.2024.100292","DOIUrl":"10.1016/j.finmec.2024.100292","url":null,"abstract":"<div><div>This paper presents a nodal integration technique, the sub-domain stabilized conforming integration (SSCI), for the meshfree radial point interpolation method (RPIM) applied to the static and modal analysis of functionally graded material (FGM) sandwich curved shells. FGM sandwich shells with different kinds of core and face sheets are considered in this work while the interested curved shell is formulated by the first-order shear deformation theory. The numerical integration technique to compute the stiffness and mass matrices in the equilibrium equation is the SSCI, which is a stabilized nodal integration with strain smoothing to preserve the accuracy and stability of the numerical results. The RPIM shape functions are utilized in this study for interpolating both the field variables and the geometry of the curved shell due to their ability to satisfy the Kronecker delta property, a rare advantage among meshfree methods. The static and modal analysis of different geometry curved shells with various sandwich FGMs are conducted. Through several numerical examples, the accuracy and efficiency of the SSCI technique in the meshfree RPIM are demonstrated and discussed.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100292"},"PeriodicalIF":3.2,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Improved eight-node non-conforming hexahedral element for structures of various shapes 适用于各种形状结构的改进型八节点不规则六面体元素

IF 3.2

Forces in mechanics Pub Date : 2024-10-20 DOI: 10.1016/j.finmec.2024.100293

Shengrong Hu, Jingjing Xu, Xinhong Liu

引用次数: 0

A Euler-lagrange Model of dynamic internal friction 动态内摩擦力的欧拉-滞后模型

IF 3.2

Forces in mechanics Pub Date : 2024-09-23 DOI: 10.1016/j.finmec.2024.100291

H.H. Hardy

{"title":"A Euler-lagrange Model of dynamic internal friction","authors":"H.H. Hardy","doi":"10.1016/j.finmec.2024.100291","DOIUrl":"10.1016/j.finmec.2024.100291","url":null,"abstract":"<div><div>A Euler-Lagrange model of dynamic internal friction is proposed and is shown to match the frequency and decay of oscillations in both simple extension (pull) and cantilever beam experiments. The proposed dynamic internal frictional stress, <span><math><msub><mi>τ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>, is proportional to the rate of change of the engineering stress, <span><math><msub><mover><mi>σ</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>. i.e.<span><span><span><math><mrow><msub><mi>τ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>μ</mi><mi>m</mi></msub><msub><mover><mi>σ</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>,</mo></mrow></math></span></span></span>with <span><math><msub><mi>μ</mi><mi>m</mi></msub></math></span> the dynamic internal friction coefficient. A single value of the dynamic internal friction coefficient is shown to match the results of the experiments for a number of different geometries of the silicon rubber, Dragon Skin<sup>TM</sup>. Dragon Skin<sup>TM</sup> is used in skin effects for movies and in prosthetics and cushioning applications. It is chosen here because of its ease of preparation and relatively simple non-linear stress-strain response. Because of these characteristics, it provides a simple starting place for simulating more complicated synthetic rubber and biological materials, which are used in a myriad of commercial applications.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100291"},"PeriodicalIF":3.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Static bending analysis of BDFG nanobeams by nonlocal couple stress theory and nonlocal strain gradient theory 利用非局部耦合应力理论和非局部应变梯度理论对 BDFG 纳米梁进行静态弯曲分析

IF 3.2

Forces in mechanics Pub Date : 2024-09-15 DOI: 10.1016/j.finmec.2024.100289

Minhaj Uddin Mahmood Siddique , I.M. Nazmul

{"title":"Static bending analysis of BDFG nanobeams by nonlocal couple stress theory and nonlocal strain gradient theory","authors":"Minhaj Uddin Mahmood Siddique , I.M. Nazmul","doi":"10.1016/j.finmec.2024.100289","DOIUrl":"10.1016/j.finmec.2024.100289","url":null,"abstract":"<div><div>This paper presents analytical solutions for the bending behavior of bi-directional functionally graded (BDFG) micro and nanobeams, wherein the material properties vary along both the thickness and axial directions, following power-law and exponential-law profiles, respectively. This study employs two size-dependent theories, nonlocal modified couple stress theory (NCST) and nonlocal strain gradient theory (NSGT), to account for size effects inherent in nanoscale structures. The governing differential equations are derived using Hamilton's principle, and the Laplace transform technique is utilized for their solution. The study critically compares the size effects captured by NCST and NSGT and assesses the influence of material gradation parameters in both directions. Additionally, the impacts of nonlocal and length scale parameters are thoroughly investigated. The findings indicate that NSGT tends to overestimate size effects compared to NCST. This research enhances the understanding of the mechanical behavior of BDFG nanobeams, offering valuable insights for the design and analysis of nanoscale structures across diverse applications.</div></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100289"},"PeriodicalIF":3.2,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000350/pdfft?md5=2071d7bdfb7674d4acc2d527c01d7d39&pid=1-s2.0-S2666359724000350-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Response of circular type sandwich panel using JUCO-glass fiber with PU foam under three-point bending loading 使用聚氨酯泡沫的 JUCO 玻璃纤维圆形夹芯板在三点弯曲荷载下的响应

IF 3.2

Forces in mechanics Pub Date : 2024-09-13 DOI: 10.1016/j.finmec.2024.100290

Md Shahriar Haque , Md Foisal Hossain , Muhammed Sohel Rana , Md Shafiul Ferdous

{"title":"Response of circular type sandwich panel using JUCO-glass fiber with PU foam under three-point bending loading","authors":"Md Shahriar Haque , Md Foisal Hossain , Muhammed Sohel Rana , Md Shafiul Ferdous","doi":"10.1016/j.finmec.2024.100290","DOIUrl":"10.1016/j.finmec.2024.100290","url":null,"abstract":"<div><p>In this study, a circular type honeycomb sandwich panel using natural <em>JUCO</em> and synthetic woven glass fiber was fabricated, and the bending properties like bending strength, modulus of rupture (<em>MOR</em>), and modulus of elasticity (<em>MOE</em>) were evaluated. Polyurethane (<em>PU</em>) foam was injected into the core structure to improve the bending strength. The orientation of jute and cotton fiber was varied to investigate the best stiffness and strength. In addition, twill-type <em>JUCO</em> fiber mat and synthetic woven glass fiber were also used to fabricate the circular type honeycomb sandwich panel. Finite element modeling was undertaken to validate the experimental results. Prior to the finite element analysis, a tensile test was carried out to determine the boundary conditions. Injecting polyurethane foam into the honeycomb core does not show any significant impact on bending properties. However, the deformation rate increased considerably by adding <em>PU</em> foam in the core structure. According to the results, honeycomb sandwich panels made of woven glass fiber with <em>PU</em> foam exhibited more homogenous deflection and bending compliance compared with others.</p></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100290"},"PeriodicalIF":3.2,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000362/pdfft?md5=7ca57f8954aaae661ff4f20e49f8798d&pid=1-s2.0-S2666359724000362-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An improved moment distribution method for the analysis of concrete frames 用于分析混凝土框架的改进型弯矩分布法

IF 3.2

Forces in mechanics Pub Date : 2024-09-07 DOI: 10.1016/j.finmec.2024.100288

Mohammed K. Dhahir, Peter Betz, Birgit Beckmann, Steffen Marx

{"title":"An improved moment distribution method for the analysis of concrete frames","authors":"Mohammed K. Dhahir, Peter Betz, Birgit Beckmann, Steffen Marx","doi":"10.1016/j.finmec.2024.100288","DOIUrl":"10.1016/j.finmec.2024.100288","url":null,"abstract":"<div><p>The moment distribution method is considered one of the easiest and most reliable analysis methods. However, little attention has been given to modelling the stiffness of each member separately, as currently only one factor is being used to model all structural members without taking into account the loading conditions and curvature of the member. This can significantly influence the results when modelling columns, since unlike beams, which are usually bent in a single curvature configuration, columns can be bent in either a single or double curvature configuration. This paper presents a new set of stiffness factors to model each structural member separately depending on its boundary conditions and curvature. To validate this modification, an example concrete frame was modelled and analysed using the structural analysis software ETABS, and then the results were compared with that obtained from the standard moment distribution method and the modified moment distribution method. The results have revealed a significant enhancement in the accuracy of the obtained results when using the modified moment distribution method compared with the original moment distribution method, especially the values of the columns’ bending moments.</p></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"17 ","pages":"Article 100288"},"PeriodicalIF":3.2,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000349/pdfft?md5=d0b8a66813b0ef9a90fe96f818bf727d&pid=1-s2.0-S2666359724000349-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Influence of Al2O3/MoS2 hybrid nanofluid MQL on surface roughness, cutting force, tool wear and tool life in hard turning Al2O3/MoS2 混合纳米流体 MQL 对硬车削中表面粗糙度、切削力、刀具磨损和刀具寿命的影响

IF 3.2

Forces in mechanics Pub Date : 2024-08-01 DOI: 10.1016/j.finmec.2024.100285

Tran Bao Ngoc , Tran Minh Duc , Ngo Minh Tuan , Tran The Long

{"title":"Influence of Al2O3/MoS2 hybrid nanofluid MQL on surface roughness, cutting force, tool wear and tool life in hard turning","authors":"Tran Bao Ngoc , Tran Minh Duc , Ngo Minh Tuan , Tran The Long","doi":"10.1016/j.finmec.2024.100285","DOIUrl":"10.1016/j.finmec.2024.100285","url":null,"abstract":"<div><p>The improvement of hard machining efficiency has been a growing concern in the production practice while the environmental friendly characteristics have to be guaranteed. The application of nanofluid minimum quantity lubrication (NF MQL) technique was considered to be as a promising approach to obtain the cooling and lubrication effectiveness in the cutting area. In this present study, the MQL hard turning performance using CBN inserts under different cooling lubrication conditions (dry, Al<sub>2</sub>O<sub>3</sub> nano cutting oil, and Al<sub>2</sub>O<sub>3</sub>/MoS<sub>2</sub> hybrid nano cutting oil) was investigated through evaluating the cutting force, tool wear, tool life, and surface roughness. Based on the obtained results, the normal force component F<sub>y</sub> has the large values and the increasing rate is closely related to the flank wear, so it can be used as a criterion to evaluate the tool life. In addition, cutting force coefficient <span><math><msub><mi>K</mi><mi>F</mi></msub></math></span> not only presents the relative increase of the normal force F<sub>y</sub> compared to the tangential force F<sub>z</sub> but also can be used for machining performance evaluation. The wear modes are mechanical scratching and chipping, and the wear land on rake and flank faces is concentrated on the main cutting edge, which is the distinguishing feature of hard machining with conventional cutting. In addition to cutting parameters, tool wear was proven to be affected by the cooling lubrication condition. Furthermore, the machined surface roughness was improved and tool life was prolonged under Al<sub>2</sub>O<sub>3</sub>/MoS<sub>2</sub> hybrid nanofluid MQL condition when compared to those in dry and Al<sub>2</sub>O<sub>3</sub> nanofluid MQL due to the cooling and lubrication effectiveness.</p></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"16 ","pages":"Article 100285"},"PeriodicalIF":3.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000313/pdfft?md5=809326be4a7273c053e9cdb2dbc4be8a&pid=1-s2.0-S2666359724000313-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Phase-field modelings of fracture investigate the influence of interfacial effects on damage and optimal material distribution in brittle inclusion-matrix structures 断裂相场建模研究界面效应对脆性包含基体结构中损伤和最佳材料分布的影响

IF 3.2

Forces in mechanics Pub Date : 2024-08-01 DOI: 10.1016/j.finmec.2024.100282

Ba-Thanh Vu, Tien-Thanh Bui, Ngoc-Long Nguyen, The-Truyen Tran, Xuan-Lam Nguyen, Viet-Hai Hoang

{"title":"Phase-field modelings of fracture investigate the influence of interfacial effects on damage and optimal material distribution in brittle inclusion-matrix structures","authors":"Ba-Thanh Vu, Tien-Thanh Bui, Ngoc-Long Nguyen, The-Truyen Tran, Xuan-Lam Nguyen, Viet-Hai Hoang","doi":"10.1016/j.finmec.2024.100282","DOIUrl":"10.1016/j.finmec.2024.100282","url":null,"abstract":"<div><p>This present work uses the phase-field modelings to investigate the influence of interfacial effects on damage and mechanical behavior, as well as the optimal distribution of the inclusion shape within brittle inclusion-matrix structures in various typical cases. These two constituent phases in the structures are assumed to be either isotropic or anisotropic. To achieve these goals, this work will: (i) use the phase-field modelings either considering or neglecting interfacial debonding, and the anisotropic phase-field modeling; (ii) determine and incorporate the strain tensor orthogonal decompositions into each specific phase-field modeling to enhance the accuracy and effectiveness of the simulation methods; (iii) combine the phase-field modelings with the BESO topology optimization algorithm to analyze the influence of interfacial effects on relationship curves and the optimal distribution of the inclusion shape. Through proposed numerical examples, it is demonstrated that the interfacial effects strongly influence crack paths, behavior curves, and optimal material distribution in structures. When considering interfacial effects, cracks are almost unable to penetrate into the inclusion phase. However, when neglecting interfacial effects, cracks propagate into the inclusion phase. This reason makes the structure more difficult to damage than when considering the interfacial effects, as evidenced by greater peak load values in behavior curves and greater total fracture resistance of the material. Especially in the example of inclusion phase optimization, the total fracture resistance value of the case neglecting interfacial effects is more than 107.9% greater than that considering interfacial effects.</p></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"16 ","pages":"Article 100282"},"PeriodicalIF":3.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000283/pdfft?md5=1163fa0ec72a95ce19e73ea19f57b26f&pid=1-s2.0-S2666359724000283-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141963082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Crack growth in sandwich-structured foam core graphite epoxy laminate composite using a phase-field modelling approach 采用相场建模方法研究夹层结构泡沫芯材石墨环氧层压复合材料的裂纹生长情况

IF 3.2

Forces in mechanics Pub Date : 2024-08-01 DOI: 10.1016/j.finmec.2024.100284

Manish Singh Rajput, Himanshu Pathak

{"title":"Crack growth in sandwich-structured foam core graphite epoxy laminate composite using a phase-field modelling approach","authors":"Manish Singh Rajput, Himanshu Pathak","doi":"10.1016/j.finmec.2024.100284","DOIUrl":"10.1016/j.finmec.2024.100284","url":null,"abstract":"<div><p>The laminated sandwich composites have wide structure-making applications in the automotive and aviation fields due to their lightweight and superior flexural rigidity properties. Making grooves or holes to assemble more than one structure induces crack discontinuities near the stress concentration region in these sandwich structures. The present work examines the effect of crack discontinuities on the mechanical performance and failure process of the sandwich structures under different loading conditions. Phase field method (PFM) has been presented and implemented using in-house developed MATLAB code. The effect of holes, multiple cracks, number of cores, and loading conditions are analyzed for the mechanical and fracture behavior of the structure. Load-carrying capacity, threshold displacement value for crack initiation, crack propagation trajectory, and energy absorption capacity are compared for various crack discontinuities under different loading conditions. Approximately 35% increase in load carrying capacity is observed in equivalent multiple core sandwich structures.</p></div>","PeriodicalId":93433,"journal":{"name":"Forces in mechanics","volume":"16 ","pages":"Article 100284"},"PeriodicalIF":3.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666359724000301/pdfft?md5=2e0c64f9b887eece81f6844eca94fc0a&pid=1-s2.0-S2666359724000301-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141998149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0