Finite Elements in Analysis and Design最新文献_第10页

Data-driven snapshot calibration via monotonic feature matching 基于单调特征匹配的数据驱动快照校准

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-20 DOI: 10.1016/j.finel.2023.104065

Neeraj Sarna , Jan Giesselmann , Peter Benner

{"title":"Data-driven snapshot calibration via monotonic feature matching","authors":"Neeraj Sarna , Jan Giesselmann , Peter Benner","doi":"10.1016/j.finel.2023.104065","DOIUrl":"10.1016/j.finel.2023.104065","url":null,"abstract":"<div><p><span><span><span>Snapshot matrices of hyperbolic equations have a slow </span>singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular value decay by computing snapshots on a transformed spatial domain, or the so-called snapshot calibration/transformation. We are particularly interested in problems involving shock collision, shock rarefaction-fan collision, shock formation, etc. For such problems, we propose a realizable algorithm to compute the </span>spatial transform using monotonic feature matching. We consider discontinuities and kinks as features, and by carefully partitioning the parameter domain, we ensure that the spatial transform has properties that are desirable both from a theoretical and an implementation standpoint. We use these properties to prove that our method results in a fast Kolmogorov </span><span><math><mi>m</mi></math></span>-width decay of a calibrated manifold. A crucial observation we make is that due to calibration, the <span><math><mi>m</mi></math></span>-width does not only depend on <span><math><mi>m</mi></math></span><span><span> but also on the accuracy of the full-order model, which is in contrast to elliptic and parabolic problems that do not need calibration. The method we propose only requires the solution snapshots and not the underlying </span>partial differential equation (PDE) and is therefore, data-driven. We perform several numerical experiments to demonstrate the effectiveness of our method.</span></p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138085811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

A dynamic description of the smoothing gradient damage model for quasi-brittle failure 准脆性破坏光滑梯度损伤模型的动态描述

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-16 DOI: 10.1016/j.finel.2023.104084

Chanh Dinh Vuong , Xiaofei Hu , Tinh Quoc Bui

{"title":"A dynamic description of the smoothing gradient damage model for quasi-brittle failure","authors":"Chanh Dinh Vuong , Xiaofei Hu , Tinh Quoc Bui","doi":"10.1016/j.finel.2023.104084","DOIUrl":"10.1016/j.finel.2023.104084","url":null,"abstract":"<div><p><span>Quasi-static simulations are of limited interest because cracks, if they are not severely constrained, propagate dynamically. When natural disasters such as earthquakes or explosions happen, structures made of quasi-brittle or brittle materials can suffer from failures activated by, for instance, loading at a high rate. </span>Dynamic fractures<span>, especially dynamic crack branching, are often observed during those events. We present in this paper, for the first time, a dynamic description of the smoothing gradient-enhanced damage model towards the simulation of quasi-brittle failure localization<span> under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching. The study is carried out using low-order finite elements, and the merits of the developed approach are examined through our numerical experiments, including mixed-mode fracture and dynamic crack branching simulations.</span></span></p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138293100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geometrically nonlinear analysis of Reissner–Mindlin plates using multi-patch isogeometric analysis based on Nitsche’s method 基于Nitsche方法的多片等几何分析Reissner-Mindlin板的几何非线性分析

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-16 DOI: 10.1016/j.finel.2023.104086

Ziling Song , Hirshikesh , Tiantang Yu , Sundararajan Natarajan

引用次数: 0

Model development for numerical analysis of the bonding strength for friction welded lightweight structures 摩擦焊接轻型结构结合强度数值分析模型的建立

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-08 DOI: 10.1016/j.finel.2023.104063

Eric Heppner , Tomohiro Sasaki , Frank Trommer , Elmar Woschke

{"title":"Model development for numerical analysis of the bonding strength for friction welded lightweight structures","authors":"Eric Heppner , Tomohiro Sasaki , Frank Trommer , Elmar Woschke","doi":"10.1016/j.finel.2023.104063","DOIUrl":"10.1016/j.finel.2023.104063","url":null,"abstract":"<div><p>The rotary friction welding (RFW) is a robust, precise, productive and economical joining process that is used in many areas of mechanical engineering to produce lightweight structures consisting of combinations of ferrous and non-ferrous materials, for instance aluminium alloy and steel. Crucial for the design of such lightweight structures is the knowledge about the bonding strength. The bonding strength is the result of the bond formation depending on the present transient kinematic, kinetic and thermal states during the welding process being directly determined by the welding process parameters. Despite several years of empirical research, no reliable numerical modelling approach exists for the RFW process to analyse the bonding strength based on these transient state variables. For this reason, an improvement of the bond formation and therefore an increase in the bonding strength can only be tested experimentally. The main motivation of this paper is to develop an appropriate modelling approach for the estimation of the bonding strength for friction welded lightweight structures manufactured of an aluminium alloy and a structural steel. Therefore, a couple of aluminium alloy and steel welding experiments with different process parameters were performed and subsequently analysed concerning to the resulting bonding strength. Moreover, all the welding experiments were simulated in regard to the corresponding welding process in order to determine the present kinematic, kinetic and thermal state variables, like the strain rate, the stress and the temperature. Thus, a model for the characterization of the bond formation can be developed, which allows a correlation between the bond formation and the resulting bond strength based on the chosen welding process parameters. Finally, the model will be examined and discussed in terms of its plausibility and applicability.</p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71516667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nonlinear model order reduction for problems with microstructure using mesh informed neural networks 基于网格信息神经网络的微观结构非线性模型降阶

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-08 DOI: 10.1016/j.finel.2023.104068

Piermario Vitullo , Alessio Colombo , Nicola Rares Franco , Andrea Manzoni , Paolo Zunino

{"title":"Nonlinear model order reduction for problems with microstructure using mesh informed neural networks","authors":"Piermario Vitullo , Alessio Colombo , Nicola Rares Franco , Andrea Manzoni , Paolo Zunino","doi":"10.1016/j.finel.2023.104068","DOIUrl":"10.1016/j.finel.2023.104068","url":null,"abstract":"<div><p>Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. As a result, simulating such phenomena becomes unaffordable for many-query applications, such as parametrized systems with multiple scale-dependent features. Traditional projection-based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales. Specifically, we employ sparse mesh-informed neural networks (MINNs), which handle both spatial dependencies in the solutions and model parameters simultaneously. We evaluate the performance of this strategy on benchmark problems and then apply it to approximate a real-life problem involving the impact of microcirculation in transport phenomena through the tissue microenvironment.</p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168874X23001610/pdfft?md5=6a800e861cf7ff82ab9d324e6e18110a&pid=1-s2.0-S0168874X23001610-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71524160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Integrated BIM-based modeling and simulation of segmental tunnel lining by means of isogeometric analysis 基于BIM的管片衬砌等几何分析建模与仿真

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-03 DOI: 10.1016/j.finel.2023.104070

Hoang-Giang Bui , Jelena Ninić , Christian Koch , Klaus Hackl , Günther Meschke

{"title":"Integrated BIM-based modeling and simulation of segmental tunnel lining by means of isogeometric analysis","authors":"Hoang-Giang Bui , Jelena Ninić , Christian Koch , Klaus Hackl , Günther Meschke","doi":"10.1016/j.finel.2023.104070","DOIUrl":"10.1016/j.finel.2023.104070","url":null,"abstract":"<div><p>With the increasing demand for underground transport infrastructures in urban areas, and associated hazards during the construction of these complex structures characterized with a number of uncertainties, there is an acute need for the development of methods and tools that enable efficient and accurate exploration of the design options to minimize risks induced to the environment. Mechanized tunneling, although it requires high initial investments compared to other tunneling methods, offers a safe and productive way to construct urban tunnels. In the mechanized tunneling process, the lining plays a critical role to provide the support for internal structures, i.e roads, facilities. At the same time, it helps stabilize the ground condition. Together with the jacking system, the lining provides the mean to thrust the tunnel shield (TBM) during excavation. In this work, we address the problem of effective modeling and simulation of the tunnel lining segment. The objective is to demonstrate a systematic and versatile approach to analyze the tunnel lining in different practical scenarios. In terms of modeling, a BIM-based approach is used, which connects the user-friendly software interface used in daily engineering practice with effective simulation tools. The proposed approach utilizes high-order definition of geometry in the design model as well as parametric model definitions to reconstruct the corresponding high-order numerical models. This results in a high-accuracy and computationally low-cost model to analyze a complex structure including an interaction with the soil based on a nonlinear surface springs model. In addition, it allows to analyze the stress and bending moment in the lining segment with high accuracy. The numerical results show that negligible modeling efforts and a reduced computational time up to ten times for given accuracy are achieved.</p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71516710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bending and torsion induced stresses in cylindrically orthotropic and inhomogeneous timber beams 圆柱正交异性和非均匀木梁的弯曲和扭转应力

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-03 DOI: 10.1016/j.finel.2023.104072

David Hoffmeyer , A.R. Damanpack

{"title":"Bending and torsion induced stresses in cylindrically orthotropic and inhomogeneous timber beams","authors":"David Hoffmeyer , A.R. Damanpack","doi":"10.1016/j.finel.2023.104072","DOIUrl":"10.1016/j.finel.2023.104072","url":null,"abstract":"<div><p>The structural design of timber beams subject to bending often relies on the application of the simple Euler–Bernoulli beam theory. However, the simplistic formulas for stress calculations overlook the inherent characteristics of the wood material and the true distribution of the annual rings within the cross-sectional area. This paper introduces a method for determining all six stress components for a cantilever-type beam that is subjected to concentrated end loads. The method considers an inhomogeneous cross-section and employs cylindrically orthotropic material properties. Notably, this approach does not necessitate prior knowledge of elastic and shear centres. It is founded on the formulation of a displacement field incorporating unknown in-plane distortion and warping functions. These are then solved through a straightforward finite element procedure. The efficacy of the method is validated by a series of numerical examples that align with analytical results. Furthermore, a benchmark example for cylindrically orthotropic cross-sections is proposed. As a practical demonstration, an analysis is performed on a real sawn timber cross-section with material parameters representative of Norway spruce. The findings reveal significant disparities in the maximum stresses when compared to conventional engineering approaches. In this specific instance, the maximum longitudinal normal stress resulting from bending is approximately 20 % higher than the outcomes of typical engineering methods. This emphasizes the critical role played by the actual distribution of annual rings across the specific beam cross-section.</p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168874X23001658/pdfft?md5=1db3e10915aeb9f57e95e33d3d538dcc&pid=1-s2.0-S0168874X23001658-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71516712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multi-scale modelling and analysis of the behaviour of PC/ABS blends with emphasis on interfacial/bulk damage PC/ABS共混物行为的多尺度建模和分析，重点是界面/本体损伤

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-03 DOI: 10.1016/j.finel.2023.104083

Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F.M. Andrade Pires

{"title":"Multi-scale modelling and analysis of the behaviour of PC/ABS blends with emphasis on interfacial/bulk damage","authors":"Alexandre D. C. Amaro, A. Francisca Carvalho Alves, F.M. Andrade Pires","doi":"10.1016/j.finel.2023.104083","DOIUrl":"10.1016/j.finel.2023.104083","url":null,"abstract":"<div><p>The present contribution focuses on the analysis of diverse deformation mechanisms that impact the behaviour of PC/ABS blends using computational homogenisation. This includes analysing internal particle cavitation, PC/ABS interface debonding, and PC matrix shear-yielding. The goal is to investigate the optimal composition for specific applications and create tailored materials. The work involves establishing a microstructure Representative Volume Element, defining the constitutive description of both material phases, and explicitly modelling PC/ABS interfaces and matrix damage to achieve accurate predictions. A Python programme is devised to efficiently integrate zero-thickness cohesive interface elements around ABS particles, incorporating the PPR potential-based cohesive model to characterise the interface. Additionally, the finite strain visco-elastic visco-plastic constitutive model of the PC matrix is extended to incorporate a damage variable, addressing the shear-yielding failure mechanism. The PC/ABS blend’s thermomechanical response is homogenised using first-order hierarchical multi-scale analyses. The impact of considering the interface phase in the microstructure is assessed through various numerical analyses. The synergy between the constitutive models effectively captures the blend’s behaviour. These findings lay the foundation for broader applicability beyond PC/ABS blends, paving the way for future studies in the field.</p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168874X23001762/pdfft?md5=7fd69d108158f3c4a5a7de5bc5afcde9&pid=1-s2.0-S0168874X23001762-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71509669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the realization of periodic boundary conditions for hexagonal unit cells 关于六边形晶胞周期边界条件的实现

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-11-02 DOI: 10.1016/j.finel.2023.104067

Yasemin von Hoegen , Sonja Hellebrand , Lisa Scheunemann , Jörg Schröder

{"title":"On the realization of periodic boundary conditions for hexagonal unit cells","authors":"Yasemin von Hoegen , Sonja Hellebrand , Lisa Scheunemann , Jörg Schröder","doi":"10.1016/j.finel.2023.104067","DOIUrl":"10.1016/j.finel.2023.104067","url":null,"abstract":"<div><p><span>In the context of homogenization of micro-heterogeneous materials, the choice of the </span><span><math><mi>R</mi></math></span>epresentative <span><math><mi>V</mi></math></span>olume <span><math><mi>E</mi></math></span>lement (<span><math><mi>RV E</mi></math></span>) plays a crucial role. For periodic microstructures, an <span><math><mi>RV E</mi></math></span><span> is an underlying unit cell with periodic boundary conditions. Nevertheless, the question of the implementation of periodic boundary conditions may arise here; for example, some of the applications of periodic boundary conditions in the literature for hexagonal cells are incorrect or they are not given in detail. In this paper, we analyze periodic boundary conditions for two-dimensional hexagonal unit cells. Periodic boundary conditions are characterized by the periodic fluctuations in the displacement fields and anti-periodic traction vectors at associated points of the boundary of the unit cell. From comparative calculations with an ensemble of unit cells, it is evident that the natural choice for vanishing fluctuations is to be set on the midpoints of the six perimeter lines of the cell. The partially applied choice of vanishing fluctuations in the six corner points of the outer edge of the unit cell leads to wrong results. The boundary conditions proposed here are analyzed on the basis of representative examples and compared to the results with the incorrect boundary conditions.</span></p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71509667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling and simulation of microwave assisted catalytic pyrolysis system of waste plastics polymer for fuel production 用于燃料生产的废塑料-聚合物微波辅助催化热解系统的建模与仿真

IF 3.1 3区工程技术

Finite Elements in Analysis and Design Pub Date : 2023-10-31 DOI: 10.1016/j.finel.2023.104073

Fares Bandi , Saad Sulttan , Sohrab Rohani

{"title":"Modeling and simulation of microwave assisted catalytic pyrolysis system of waste plastics polymer for fuel production","authors":"Fares Bandi , Saad Sulttan , Sohrab Rohani","doi":"10.1016/j.finel.2023.104073","DOIUrl":"10.1016/j.finel.2023.104073","url":null,"abstract":"<div><p>Pyrolysis<span><span> is a promising method of chemically recycling plastic waste, as it allows for the recovery of both energy and materials. In this work, a comprehensive mathematical model<span><span><span> has been developed to predict the pyrolysis of plastic wastes over ZSM-5 catalyst in microwave-assisted pyrolysis (MAP) system for fuel production. To conduct a transient numerical analysis of the underlying processes, a lumped </span>kinetic model<span> that takes into account three lumped pyrolysis products (olefins, paraffins, and aromatics) is coupled with the equations that govern the microwave field, heat transfer, mass transfer, and fluid flow (Darcy's law). The distributions of electric field, temperature, and pyrolysis products within MAP are presented. The study investigated the effects of several factors on the rate of production and consumption in the pyrolysis reactions of a waste plastic mixture when using MAP. These factors include the microwave power input, the inlet velocity of the </span></span>fluidizing gas, as well as the mass and particle size of the catalyst used. Increasing the input power leads to a higher intensity of the electric field, which causes a greater increase in temperature within the same time frame. The mass and particle size of the catalyst used also have a significant impact on the yield of </span></span>olefins, paraffins, and aromatics. Reducing the particle size of the catalyst generally increases the reaction rate, but particle sizes smaller than 50 μm are not ideal for fluidization due to increased intermolecular forces. Increasing the inlet velocity of the fluidizing gas may result in an incomplete consumption of intermediates and a low yield of products. All in all, The MAP system is a highly efficient and effective design for using plastic waste as a source of energy, due to its superior energy efficiency and lower processing temperature compared to traditional fluidized-bed reactors.</span></p></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71509737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0