Computers & Structures最新文献_第2页

Parametric resonance of printing viscoelastic film with time-varying tension and velocity coupling based on the variable amplitude method 基于变幅法的时变张力与速度耦合的印刷粘弹性薄膜参数共振

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-16 DOI: 10.1016/j.compstruc.2025.108002

Mingyue Shao , Xiaoqing Xing , Qiumin Wu , Jimei Wu , Yijun Chen , Dingqiang Liu

{"title":"Parametric resonance of printing viscoelastic film with time-varying tension and velocity coupling based on the variable amplitude method","authors":"Mingyue Shao , Xiaoqing Xing , Qiumin Wu , Jimei Wu , Yijun Chen , Dingqiang Liu","doi":"10.1016/j.compstruc.2025.108002","DOIUrl":"10.1016/j.compstruc.2025.108002","url":null,"abstract":"<div><div>In high-precision roll-to-roll coating processes, periodic tension perturbations occur at both ends of the tensioned film due to factors such as roll eccentricity and diameter variations. Simultaneously, the film undergoes variable-velocity linear motion. According to the fundamental principles of Newtonian mechanics, tension perturbations inevitably induce acceleration responses. Based on the dynamic static equilibrium method and D’Alembert theory, the coupling equation between time-varying tension and velocity are explored, and then the nonlinear vibration control equation of printing motion viscoelastic film under time-varying tension and velocity coupling was established. The Galerkin method is applied to discretize and the variable amplitude method is employed to solve the amplitude expression of the parametric resonance response of the film system, and the Jacobi matrix is used to carry out the stability of the system’s stationary solution. The ratio of the tension variation frequency to the intrinsic frequency of the system is investigated for its influence on the vibration amplitude of the film, and MATLAB programming is used to calculate and analyze the influence of the parameters such as the aspect ratio, initial velocity, tension variation coefficient and viscoelastic coefficient on the parametric resonance of the film system.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 108002"},"PeriodicalIF":4.8,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A mechanism-informed neural network with a physical intermediate layer for predicting wall deflection induced by braced excavations in soft soil 带物理中间层的机制信息神经网络预测软土支撑开挖引起的墙体挠度

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-15 DOI: 10.1016/j.compstruc.2025.107999

Yi-Feng Yang , Shao-Ming Liao , Ying-Bin Liu , Lin-Hong Tang , Ze-Wen Li , Li-Sheng Chen

{"title":"A mechanism-informed neural network with a physical intermediate layer for predicting wall deflection induced by braced excavations in soft soil","authors":"Yi-Feng Yang , Shao-Ming Liao , Ying-Bin Liu , Lin-Hong Tang , Ze-Wen Li , Li-Sheng Chen","doi":"10.1016/j.compstruc.2025.107999","DOIUrl":"10.1016/j.compstruc.2025.107999","url":null,"abstract":"<div><div>Accurate advance prediction of wall deflection induced by braced excavations is crucial for preventing potential damage to retaining structures and the surrounding environment. Although previous studies have utilized spatiotemporal deep learning models for this purpose, they have overlooked the underlying physical mechanisms of wall deflection. To address this limitation and enhance the interpretability and transferability of deep learning models, this paper proposes a mechanism-informed neural network for predicting wall deflection, where the physical mechanism based on the beam on elastic foundation method is hardcoded in the neural network architecture. In the proposed model, a physical intermediate layer is designed to mimic the effects of the horizontal load behind the wall, and a monotonicity-preserving long short-term memory network is devised to capture the inherent monotonic characteristics of the horizontal load. Additionally, a hybrid loss function is designed to simultaneously constrain the outputs of both the final layer and the physical intermediate layer. The performance of the proposed model was validated by different excavation projects, with its significant superiority over baseline models demonstrated. The proposed model demonstrates a strong capability and generalizability for accurately forecasting wall deflections in advance by incorporating the physical mechanism.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107999"},"PeriodicalIF":4.8,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Physics-based and locally updated nonlinear damping model for cracked reinforced concrete beams 基于物理的钢筋混凝土裂缝梁非线性阻尼局部更新模型

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-15 DOI: 10.1016/j.compstruc.2025.107983

Clotilde Chambreuil , Cédric Giry , Frédéric Ragueneau , Pierre Léger

{"title":"Physics-based and locally updated nonlinear damping model for cracked reinforced concrete beams","authors":"Clotilde Chambreuil , Cédric Giry , Frédéric Ragueneau , Pierre Léger","doi":"10.1016/j.compstruc.2025.107983","DOIUrl":"10.1016/j.compstruc.2025.107983","url":null,"abstract":"<div><div>The structural design increasingly requires considering earthquake excitations even in low-seismic risk areas, particularly for critical infrastructures, such as nuclear ones. Sophisticated models are required to characterise the structural behaviour under low seismic excitations. In the case of reinforced concrete structures, nonlinear material models are considered to characterise some energy dissipative phenomena such as (i) damage due to cracking or (ii) friction of cracked surfaces. However, more than the amount of energy dissipated by these nonlinear models are required to accurately represent the physical structural dynamic responses. That is why viscous damping is generally added to dissipate the excess energy. Numerous damping models are proposed in the literature. However, their principal drawback is their need for the representativeness of physical dissipative phenomena. So, this paper proposes a viscous damping model based on such phenomena to dissipate the energy not represented through the nonlinear material model. The proposed strategy is to update the damping matrix at the element level using the intensity of nonlinearities in each element. Three local variables are compared in the paper: one variable associated to damage, another associated with friction and a damage index computed from the secant elemental rigidity. Dynamic nonlinear computations are performed with the proposed locally updated damping matrices. The results are compared with experimental data, when available, and with Rayleigh-type damping formulations classically used in engineering. As a result, it is observed that all damping formulations properly characterise the global response of the studied reinforced concrete beam. However, the use of the proposed formulations allows better representativeness of local dissipative phenomena and adds a physical meaning to the damping model.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107983"},"PeriodicalIF":4.8,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Coupled FDM-SPH modeling of CFRP-reinforced concrete damage under combined blast and fragment impact 爆破破片复合冲击下cfrp -钢筋混凝土损伤的FDM-SPH耦合建模

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-15 DOI: 10.1016/j.compstruc.2025.107980

Jian-Yu Chen , Jidong Zhao , Ruo-Feng Feng , Rui-Chen Ni , Chong Peng

{"title":"Coupled FDM-SPH modeling of CFRP-reinforced concrete damage under combined blast and fragment impact","authors":"Jian-Yu Chen , Jidong Zhao , Ruo-Feng Feng , Rui-Chen Ni , Chong Peng","doi":"10.1016/j.compstruc.2025.107980","DOIUrl":"10.1016/j.compstruc.2025.107980","url":null,"abstract":"<div><div>Reinforced concrete (RC) structures reinforced with carbon fiber-reinforced polymer (CFRP) composites are increasingly popular for blast-resistant designs, yet their failure mechanisms under combined blast and fragment loading remain poorly understood due to challenges in modeling multi-physics phenomena such as shockwave propagation, fluid-structure interaction, and fracture dynamics. This study introduces a novel GPU-accelerated finite difference method -smoothed particle hydrodynamics (FDM-SPH) framework to evaluate damage in CFRP-concrete composite structures subjected to extreme loading. The framework couples SPH for structural damage prediction with FDM for air blast simulation, linked via an immersed boundary method to enable bidirectional fluid-structure coupling. The framework is validated against multiple cases, including high-velocity impact on CFRP laminates and close-range blast loading, demonstrating strong agreement with experimental data. Detailed analysis of CFRP-concrete composites reveals that CFRP significantly mitigates blast-induced deformation, reducing displacement by 38 % compared to single CFRP plate while absorbing 73 % of impact energy through delamination and fiber fracture. The model uniquely captures synergistic damage from combined blast and fragment loads, showing localized penetration and global deformation not observed under isolated loading. These findings underscore CFRP’s efficacy in enhancing blast resilience and provide a validated computational tool for optimizing composite structures in defense and critical infrastructure applications.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107980"},"PeriodicalIF":4.8,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Body-fitted iso geometric topology optimization for maximizing phononic band gaps 体贴合iso几何拓扑优化最大化声子带隙

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-15 DOI: 10.1016/j.compstruc.2025.107981

Majd Kosta, Oded Amir

引用次数: 0

A graph convolutional network-based surrogate model with enhanced graph embedding for real-time prediction of wind turbine mainframe stress distribution 基于增强图嵌入的图卷积网络代理模型用于风力机主机应力分布的实时预测

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-14 DOI: 10.1016/j.compstruc.2025.107977

Kuangguidong Wang , Yong Liu , Xiaofang Wang , Donghao Pan

{"title":"A graph convolutional network-based surrogate model with enhanced graph embedding for real-time prediction of wind turbine mainframe stress distribution","authors":"Kuangguidong Wang , Yong Liu , Xiaofang Wang , Donghao Pan","doi":"10.1016/j.compstruc.2025.107977","DOIUrl":"10.1016/j.compstruc.2025.107977","url":null,"abstract":"<div><div>Graph Convolutional Neural Networks have been extensively applied in predicting attributes of mesh-based simulations, including Finite Element analysis. However, when the mesh of finite element models is non-uniform and the boundary conditions vary abruptly, such as in the finite element model for stress assessment of wind turbine mainframes, the accuracy of Graph Networks is compromised. In response to these limitations and to facilitate real-time stress field prediction for rapid design iteration of wind turbine mainframes, this paper proposes a surrogate model based on Graph Convolutional Networks with enhanced graph embedding. By implementing an additional master vertex and global vertex connectivity, the Graph Convolutional Network model leverages message-passing mechanisms to learn relationships between node attributes, external loading conditions, and stress distribution in an effective way. The proposed architecture includes an encoder–decoder framework with three message-passing layers. Numerical experiments demonstrate that this Graph Convolutional Network-based model achieves high precision (mean absolute percentage error < 9 % compared to finite element results) and strong generalization ability in predicting von Mises stress distributions under varying geometries and large-range boundary conditions, outperforming Graph Convolutional Network models without enhanced graph embedding. Furthermore, the model reduces computation time by orders of magnitude compared to traditional finite element solvers with less hardware usage, making it suitable for iterative design processes.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107977"},"PeriodicalIF":4.8,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Enhanced perfectly matched layer formulation for near- and far-field pressures of exterior acoustic and vibroacoustic problems 增强了完美匹配的层公式，用于近场和远场压力的外部声学和振动声学问题

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-14 DOI: 10.1016/j.compstruc.2025.107982

Xiang Xie , Guoyong Jin , Steffen Marburg

{"title":"Enhanced perfectly matched layer formulation for near- and far-field pressures of exterior acoustic and vibroacoustic problems","authors":"Xiang Xie , Guoyong Jin , Steffen Marburg","doi":"10.1016/j.compstruc.2025.107982","DOIUrl":"10.1016/j.compstruc.2025.107982","url":null,"abstract":"<div><div>This paper develops a frequency-independent surrogate of perfectly matched layer unbounded absorption function for the frequency-domain finite element analysis of exterior acoustic and fully-coupled structural-acoustic problems. It does not require a very large computational domain or a relatively thick enclosed layer, even in the low-frequency range, which saves computational resources. The introduction of fillets for the cylindrical and Cartesian geometry cases is proposed to simplify the computation of the Jacobian matrix in the absorbing layer. In addition, in order to take advantage of symmetry when solving large-scale sparse linear systems, the scalar velocity potential instead of the sound pressure is used as the fundamental unknown to describe the fluid part of vibro-acoustic interaction models. Due to the frequency-independent property of the resulting system matrices, an adaptive projection-based model order reduction technique can be directly utilized to ease the associated computational expense of frequency sweeps. After the solution inside the truncated domain is obtained, the acoustic pressure distribution in the far field, <em>i.e.</em> outside the finite element domain, is evaluated via the Kirchhoff surface integral formula. Three-dimensional acoustic problems with different boundary conditions and vibro-acoustic coupling problems with different artificial layer geometries, considering both infinite and semi-infinite fluid domains, are investigated to demonstrate the simplicity, versatility, and efficiency of the developed frequency-independent perfectly matched layer technique and model order reduction approach.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107982"},"PeriodicalIF":4.8,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A high accurate decoupling Hamiltonian absolute nodal coordinate formulation for dynamic analysis of towing cable with large deformation 大变形拖曳索动力分析的高精度解耦哈密顿绝对节点坐标公式

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-13 DOI: 10.1016/j.compstruc.2025.107994

Longjian Liu, Huaiping Ding, Xiaochun Yin, Hao Zhou, Cheng Gao, Xiaokai Deng

{"title":"A high accurate decoupling Hamiltonian absolute nodal coordinate formulation for dynamic analysis of towing cable with large deformation","authors":"Longjian Liu, Huaiping Ding, Xiaochun Yin, Hao Zhou, Cheng Gao, Xiaokai Deng","doi":"10.1016/j.compstruc.2025.107994","DOIUrl":"10.1016/j.compstruc.2025.107994","url":null,"abstract":"<div><div>For the analysis of towing cable dynamics, the absolute nodal coordinate formulation in Hamiltonian formalism is an appropriate method which can describe the large displacement and rotation of the cable while reducing the accumulative error over long-term simulation. However, large deformations of cable element in such formulation can induce spurious elastic force, which can result in the distortion of the cable element. The magnitude of spurious elastic force increases with deformation amplitude, demonstrating a coupling between geometric nonlinearity and spurious elastic force that degrade the accuracy of dynamic solutions. This paper proposes a new Hamiltonian absolute nodal coordinate formulation for high accurate dynamic modeling of towing cables with large deformation. A stiffness matrix reevaluation enables decoupling modeling of deformation and elastic forces. Hamiltonian canonical equations and symplectic difference algorithm are derived for numerical calculation. The accuracy and efficiency of the proposed method are validated by a free swing flexible cable, a three-dimensional towing system with lumped mass, a rubber cable towing experiment and a submerged pendulum experiment. The proposed method exhibits higher accuracy and efficiency compared with the existing Hamiltonian absolute nodal coordinate formulation.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107994"},"PeriodicalIF":4.8,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Mesoscopic simulation of the thermodynamic behavior of concrete-encased structural steel composites under freeze–thaw cycles 冻融循环作用下混凝土包钢复合材料热力学行为的细观模拟

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-08 DOI: 10.1016/j.compstruc.2025.107971

Yongjun Lin, Shuiyun Zhong, Sihua Jiang, Tianyi Cheng, Jie Zhou

{"title":"Mesoscopic simulation of the thermodynamic behavior of concrete-encased structural steel composites under freeze–thaw cycles","authors":"Yongjun Lin, Shuiyun Zhong, Sihua Jiang, Tianyi Cheng, Jie Zhou","doi":"10.1016/j.compstruc.2025.107971","DOIUrl":"10.1016/j.compstruc.2025.107971","url":null,"abstract":"<div><div>A thermo–hydro–mechanical coupled model is developed to simulate the heat transfer and pore water crystallization–melting processes in concrete-encased structural steel composites (commonly referred to as steel-reinforced concrete) subjected to freeze–thaw cycles. A random polygonal mesoscopic model is established, explicitly representing aggregates, mortar, reinforcement, encased steel, and three interfacial transition zones: aggregate–mortar, reinforcement–mortar, and steel–mortar. Accelerated freeze–thaw experiments are conducted on steel-reinforced concrete specimens, and corresponding numerical simulations are performed to validate the proposed thermo–hydro–mechanical framework. Based on the validated model, a mesoscopic parametric analysis is carried out to investigate the effects of mortar permeability, aggregate gradation, aggregate volume fraction, steel ratio, encased steel shape, and thermal gradients on the thermodynamic response of steel-reinforced concrete under freeze–thaw action. The results indicate that mortar permeability, aggregate volume fraction, steel ratio, and temperature gradients are the dominant factors influencing frost resistance, whereas aggregate gradation and steel section shape play secondary roles. The proposed simulation framework effectively captures multifield interactions and crystallization pressure evolution, offering valuable insights for durability assessment and design optimization of steel-reinforced concrete structures in cold regions.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107971"},"PeriodicalIF":4.8,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Multi-domain physics-based loss design for seismic response prediction 基于多域物理的地震反应预测损失设计

IF 4.8 2区工程技术

Computers & Structures Pub Date : 2025-10-07 DOI: 10.1016/j.compstruc.2025.107979

Maozu Guo , Qingyu Zhang , Miao Han , Yang Deng , Kaifeng Liu , Jicheng Yan , Lingling Zhao

{"title":"Multi-domain physics-based loss design for seismic response prediction","authors":"Maozu Guo , Qingyu Zhang , Miao Han , Yang Deng , Kaifeng Liu , Jicheng Yan , Lingling Zhao","doi":"10.1016/j.compstruc.2025.107979","DOIUrl":"10.1016/j.compstruc.2025.107979","url":null,"abstract":"<div><div>Accurate prediction of time-history responses is essential for evaluating structural performance under dynamic loading. Machine learning regression models offer the advantages of rapid, real-time, and high-accuracy predictions. However, their “black-box” nature poses challenges to interpretability and limits their broader application in structural engineering. To address this limitation, we propose a multi-domain physics-informed seismic response prediction strategy. This approach incorporates physics knowledge from the time, frequency, and energy domains into deep learning models via a customized loss function. Building upon conventional time-domain loss, we present a multi-scale frequency-domain loss to capture low-frequency components that are strongly correlated with structural characteristics, as well as momentum-based and energy-based losses that enforce consistency with fundamental dynamic principles. Experimental evaluations on two numerical simulation datasets and two shaking table test datasets indicate that the proposed strategy significantly enhances the prediction accuracy of both purely data-driven and data–knowledge-driven models. Specifically, it achieves an average improvement of 4 % in prediction confidence level within a ± 10 % confidence interval. Furthermore, ablation studies illustrate the positive contribution of the multi-scale frequency-domain and energy-domain losses to overall predictive performance.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"319 ","pages":"Article 107979"},"PeriodicalIF":4.8,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145229939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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