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Explicit phase field generalized interpolation material point method for dynamic fracture problems
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-17 DOI: 10.1016/j.compstruc.2025.107685
Chi Lv, Xiao-Ping Zhou
{"title":"Explicit phase field generalized interpolation material point method for dynamic fracture problems","authors":"Chi Lv,&nbsp;Xiao-Ping Zhou","doi":"10.1016/j.compstruc.2025.107685","DOIUrl":"10.1016/j.compstruc.2025.107685","url":null,"abstract":"<div><div>A novel explicit phase field generalized interpolation material point method (EPF-GIMPM) is proposed to solve dynamic fracture problems. An explicit rate-dependent phase field fracture model is introduced to ensure local growth of the phase field. The proposed method utilizes an explicit forward-difference time integration strategy to solve coupled-field governing equations based on the material point method. Generalized interpolation techniques are employed to improve computational accuracy by eliminating numerical noises from material points crossing cell boundaries during simulation. Additionally, the GIMP technology is combined with a particle-to-particle contact algorithm, and considers Coulomb friction to handle complex multi-body contact and collision fracture problems. Numerical examples, such as cracked square plate tests, Kalthoff-Winkler experiment, collision of rings, and dynamic crack branching, are used to verify the high accuracy and excellent capability of the proposed method while discussing the influence of explicit viscosity parameters on phase field fracture modeling.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"310 ","pages":"Article 107685"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422349","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
An optimised multi-level method for the pushover analysis of historic masonry structures accounting for the actual masonry pattern
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-17 DOI: 10.1016/j.compstruc.2025.107656
Simon Szabó , Marco Francesco Funari , Antonio Maria D’Altri , Stefano de Miranda , Paulo B. Lourenço
{"title":"An optimised multi-level method for the pushover analysis of historic masonry structures accounting for the actual masonry pattern","authors":"Simon Szabó ,&nbsp;Marco Francesco Funari ,&nbsp;Antonio Maria D’Altri ,&nbsp;Stefano de Miranda ,&nbsp;Paulo B. Lourenço","doi":"10.1016/j.compstruc.2025.107656","DOIUrl":"10.1016/j.compstruc.2025.107656","url":null,"abstract":"<div><div>In this paper, we propose an optimised multi-level method to efficiently account for the actual masonry pattern in the pushover analysis of historic masonry structures. The method begins with a rigid block-based limit analysis accounting for the actual masonry pattern to identify realistic failure mechanisms. Next, macro-blocks that outline the failure mechanism are identified using a novel optimised procedure that includes a heuristic search, which minimises the number of blocks and non-linear interfaces in the subsequent analyses. Subsequently, macro-blocks are modelled as homogeneous material interacting via cohesive-frictional interfaces in a finite element environment where pushover analysis produces force–displacement curves. Validation against various structural benchmarks with regular and irregular masonry patterns and different loading configurations demonstrates the method’s accuracy and competitiveness compared to micro-modelling approaches. Results show up to a 90% reduction in computational time and the number of blocks, with a maximum difference of about 5% in numerical prediction of force capacity.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"310 ","pages":"Article 107656"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422350","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
An explicit ABAQUS toolbox for soil-structure interaction analysis in localized regions
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-14 DOI: 10.1016/j.compstruc.2025.107675
Pengfa Zhou , Yusheng Shen , Haifeng Huang , Deng Gao , Xi Zhang , Bo Gao , Ruibin Hou
{"title":"An explicit ABAQUS toolbox for soil-structure interaction analysis in localized regions","authors":"Pengfa Zhou ,&nbsp;Yusheng Shen ,&nbsp;Haifeng Huang ,&nbsp;Deng Gao ,&nbsp;Xi Zhang ,&nbsp;Bo Gao ,&nbsp;Ruibin Hou","doi":"10.1016/j.compstruc.2025.107675","DOIUrl":"10.1016/j.compstruc.2025.107675","url":null,"abstract":"<div><div>The numerical simulation of soil-structure interaction (SSI) in unbounded media requires truncating the semi-infinite domain to create a finite computational domain. Consequently, absorbing boundary conditions (ABCs) and seismic input methods emerge as pivotal challenges. Currently, two technologies, the perfectly matched layers (PMLs) and the domain reduction method (DRM), are robust solutions to address these challenges. However, only a limited number of studies, all using implicit algorithms, have explored its application, which exhibits significant drawbacks in large-scale computations. An explicit dynamic analysis is computationally efficient for the large-scale simulations with relatively short dynamic response times and for the analysis of extremely discontinuous events. To this end, we propose an explicit formulation of the Perfectly Matched Layer (PML) based on an extended central difference method. We implement the formulation in ABAQUS/EXPLICIT through the user-defined element (VUEL) subroutine and the user predefined field (VUFIELD) subroutine. Meanwhile, we implement the DRM by developing a Python package to calculate equivalent nodal forces. Finally, several numerical experiments in the time domain demonstrate the accuracy and stability of these implementations for both 2D and 3D domains.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107675"},"PeriodicalIF":4.4,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419102","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
Prediction of hysteresis response of steel braces using long Short-Term memory artificial neural networks
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-13 DOI: 10.1016/j.compstruc.2025.107672
Sepehr Pessiyan, Fardad Mokhtari, Ali Imanpour
{"title":"Prediction of hysteresis response of steel braces using long Short-Term memory artificial neural networks","authors":"Sepehr Pessiyan,&nbsp;Fardad Mokhtari,&nbsp;Ali Imanpour","doi":"10.1016/j.compstruc.2025.107672","DOIUrl":"10.1016/j.compstruc.2025.107672","url":null,"abstract":"<div><div>This article proposes artificial neural networks that utilize the long short-term memory (LSTM) algorithm to estimate the nonlinear hysteresis response of steel buckling-restrained and conventional hollow structural section braces. The proposed models overcome the two main challenges: 1) the complexity of hysteresis response (tensile yielding and strain-hardening in tension, and compressive buckling and strength degradation in compression) and 2) limited training data, using an LSTM network and auxiliary parameters. The development of a suitable training dataset is first presented. The architectures of the proposed models are then described followed by the validation of the model against unseen brace hysteresis responses. The validation results confirm that the proposed LSTM networks are both accurate and computationally efficient in predicting the response of steel braces to random lateral loads, namely axial force – axial deformation response. The proposed models have the potential to be used for seismic response evaluation of steel braced frames, provided that their limitations are properly considered.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107672"},"PeriodicalIF":4.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403694","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
An efficient 3D corotational beam formulation using hybrid spatial discretization for nonlinear dynamics of flexible multibody system
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-11 DOI: 10.1016/j.compstruc.2025.107659
Boyang Wang , Zhuyong Liu , Tingke Wu
{"title":"An efficient 3D corotational beam formulation using hybrid spatial discretization for nonlinear dynamics of flexible multibody system","authors":"Boyang Wang ,&nbsp;Zhuyong Liu ,&nbsp;Tingke Wu","doi":"10.1016/j.compstruc.2025.107659","DOIUrl":"10.1016/j.compstruc.2025.107659","url":null,"abstract":"<div><div>In this paper, an efficient and accurate 3D corotational beam formulation in fully explicit form is proposed for the nonlinear dynamics of flexible multibody systems. A hybrid spatial discretization scheme is presented, in which the internal force terms are described in the local frame and the inertial force terms are described in the global frame. The local frame is used to decompose rigid motions and deformations, which ensures the objectivity of the rotational interpolation for the internal force evaluation. The nonlinear internal terms can be explicitly derived in the local frame based on the second-order approximation of the three-dimensional finite-elasticity theory. For inertial terms, velocity and acceleration can be obtained in simple and concise forms by utilizing the global discretization scheme. Combined with the precise orientation approximation provided by the corotational frame, the inertial terms can also be derived explicitly. Therefore, Gaussian quadrature is no longer required in the presented formulation. Finally, some classic examples are employed to verify the accuracy and efficiency compared to two widely used corotational beam formulations. The results indicate that the presented formulation not only matches the accuracy of the conventional cubic formulation but also provides a clear advantage in computational efficiency due to the fully explicit form.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107659"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378673","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
Analytical and ANN-based approaches for free vibration and nonlinear transient analysis of FG-GOEAM toroidal shell segments
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-11 DOI: 10.1016/j.compstruc.2025.107676
Vu Ngoc Viet Hoang , Pham Trung Thanh
{"title":"Analytical and ANN-based approaches for free vibration and nonlinear transient analysis of FG-GOEAM toroidal shell segments","authors":"Vu Ngoc Viet Hoang ,&nbsp;Pham Trung Thanh","doi":"10.1016/j.compstruc.2025.107676","DOIUrl":"10.1016/j.compstruc.2025.107676","url":null,"abstract":"<div><h3>Objectives</h3><div>This study investigates the free vibration and nonlinear transient response of functionally graded graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) toroidal shell segments under thermal conditions. The impact of the Winkler-Pasternak foundation, distributed in two configurations: centered and at both ends of the shell, is thoroughly examined.</div></div><div><h3>Methods</h3><div>The material properties with GOri distributions through the shell thickness are scrutinized using genetic programming-assisted micromechanical models. Nonlinear kinematic relationships are derived via Reddy's third-order shear deformation theory and von Kármán's geometric assumptions. The equations of motion are solved using Galerkin method. An Artificial Neural Network (ANN), trained with Bayesian regularization backpropagation algorithm, is developed to predict natural frequencies, using comprehensive training data validated against analytical results.</div></div><div><h3>Results</h3><div>The ANN achieves a target mean squared error (MSE) of <span><math><mn>1</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></math></span>, with error histograms showing minimal and evenly distributed errors. Regression plots confirm perfect correlations (R = 1) between predicted and actual values, indicating robust predictive accuracy. Additionally, increased GOri folding amplifies the negative Poisson's ratio, reduces Young's modulus in GOri/Cu composites, and consequently decreases shell stiffness, lowers natural frequencies, and increases vibration amplitudes. A center-concentrated foundation distribution yields higher natural frequencies and reduced vibration amplitudes compared to end-distributed configurations.</div></div><div><h3>Conclusions</h3><div>The proposed approaches demonstrate high accuracy and generalization capability in predicting the dynamic responses of FG-GOEAM shells under thermal effects. The findings emphasize the critical role of GOri folding patterns and foundation distributions in tuning vibration characteristics, offering valuable insights for the design and optimization of advanced metamaterial structures.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107676"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378687","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
Locking-free polygonal plate element based on the discrete shear projection method
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-11 DOI: 10.1016/j.compstruc.2025.107661
G. Akhila , Sundararajan Natarajan , Haojie Lian , Irwan Katili
{"title":"Locking-free polygonal plate element based on the discrete shear projection method","authors":"G. Akhila ,&nbsp;Sundararajan Natarajan ,&nbsp;Haojie Lian ,&nbsp;Irwan Katili","doi":"10.1016/j.compstruc.2025.107661","DOIUrl":"10.1016/j.compstruc.2025.107661","url":null,"abstract":"<div><div>A novel shear locking free arbitrary polygonal element is proposed for thin/thick plates modelled by Reissner-Mindlin plate theory. The shear locking problem is alleviated by adopting a shear projection method. To do this, on each edge of the element, temporary variables are introduced, which facilitates approximating the rotations with a quadratic function. These are then written in terms of the nodal unknowns by employing the orthogonality condition. With a few standard patch tests and benchmark examples, it is demonstrated that the proposed element yields accurate results for thin/thick plates and an optimal convergence rate that is in the appropriate norm.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107661"},"PeriodicalIF":4.4,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143386457","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 novel explicit-implicit time integration method for solving time-dependent finite element equation: The Versa-δ method
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-10 DOI: 10.1016/j.compstruc.2025.107664
Mohammad Mahdi Malakiyeh, Saeed Shojaee, Saleh Hamzehei-Javaran
{"title":"A novel explicit-implicit time integration method for solving time-dependent finite element equation: The Versa-δ method","authors":"Mohammad Mahdi Malakiyeh,&nbsp;Saeed Shojaee,&nbsp;Saleh Hamzehei-Javaran","doi":"10.1016/j.compstruc.2025.107664","DOIUrl":"10.1016/j.compstruc.2025.107664","url":null,"abstract":"<div><div>In this paper, we present a novel explicit–implicit time integration method for solving dynamic problems. The proposed method is designed to easily switch between explicit and implicit forms by adjusting certain control parameters. The remaining control parameters are optimized to ensure that the method would deliver a flawless performance in both forms. This method uses two sub-steps per time step and can directly be used as a first-order and a second-order method, with high capability to suppress spurious responses. The consistency, stability, numerical damping, order of accuracy, amplitude decay, and period elongation are later analyzed for both explicit and implicit forms. Additionally, the proposed method is compared specifically with other widely-used methods with two sub-steps, including both explicit and implicit approaches. Examples are also provided to demonstrate the method’s practicality.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107664"},"PeriodicalIF":4.4,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377752","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
Polygonal elements with Richardson-extrapolation based numerical integration schemes for hyperelastic large deformation analysis
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-04 DOI: 10.1016/j.compstruc.2025.107654
Du Dinh Nguyen , Minh Ngoc Nguyen , Tinh Quoc Bui
{"title":"Polygonal elements with Richardson-extrapolation based numerical integration schemes for hyperelastic large deformation analysis","authors":"Du Dinh Nguyen ,&nbsp;Minh Ngoc Nguyen ,&nbsp;Tinh Quoc Bui","doi":"10.1016/j.compstruc.2025.107654","DOIUrl":"10.1016/j.compstruc.2025.107654","url":null,"abstract":"<div><div>This paper presents a novel approach based on polygonal finite elements (PFEM) for hyperelastic large deformation analysis. Compared to the mesh of quadratic 8-node quadrangular finite elements (FEM-Q8), which is usually used in this problem type, a mesh of polygonal element usually requires less number of nodes (and thus less number of degrees of freedom), given the same number of elements. Traditionally, numerical integration in PFEM involves two steps: i) sub-division of polygonal (element) domain into triangular cells, then ii) Dunavant's integration scheme is conducted in the triangular cells. Each <em>n</em>-gonal domain could be divided into <em>n</em> triangular cells. Since the problem is non-linear, three integration points per triangular cells are typically taken. As a result, 3<em>n</em> integration points are required for each <em>n</em>-gonal element. Alternatively, the Richardson extrapolation is combined with the one-point rule, resulting in the so-called <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-point integration scheme. Due to the less number of integration points, faster computation could be achieved, yet accuracy is preserved. Here, the PFEM being incorporated with the <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-point integration scheme, namely RE-PFEM, is employed for hyperelastic large deformation analysis. Performance of the developed RE-PFEM approach in this type of nonlinear analysis, which has not been reported in the literature before, is illustrated and assessed through several numerical examples. Comparison is conducted with PFEM and FEM-Q8, as well as available reference solutions obtained by other methods.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107654"},"PeriodicalIF":4.4,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125215","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 novel Chebyshev-based both meshfree method and shear deformation theory for functionally graded triply periodic minimal surface flat plates
IF 4.4 2区 工程技术
Computers & Structures Pub Date : 2025-02-03 DOI: 10.1016/j.compstruc.2025.107660
P. Phung-Van , P.T. Hung , Sawekchai Tangaramvong , H. Nguyen-Xuan , Chien H. Thai
{"title":"A novel Chebyshev-based both meshfree method and shear deformation theory for functionally graded triply periodic minimal surface flat plates","authors":"P. Phung-Van ,&nbsp;P.T. Hung ,&nbsp;Sawekchai Tangaramvong ,&nbsp;H. Nguyen-Xuan ,&nbsp;Chien H. Thai","doi":"10.1016/j.compstruc.2025.107660","DOIUrl":"10.1016/j.compstruc.2025.107660","url":null,"abstract":"<div><div>This study introduces an innovative framework for the free vibration analysis of functionally graded (FG) triply periodic minimal surface (TPMS) plates. By utilizing Chebyshev polynomials, the study integrates a new shear deformation theory with a novel the moving Kriging meshfree method. The Chebyshev shear deformation theory is proposed, inherently satisfying the zero-shear stress condition at the plate’s top and bottom surfaces without additional constraints. Furthermore, a new shape function for the moving Kriging meshfree method is developed by integrating radial basis function with Chebyshev interpolations to significantly enhances the solution accuracy of the TPMS plate. The FG-TPMS plate, characterized by porous structures with Primitive (P), Gyroid (G), and Wrapped Package-Graph (IWP) patterns, features six distinct volume distribution cases. To determine mechanical properties such as elastic modulus, shear modulus and Poisson’s ratio, a fitting technique based on a two-phase piecewise function is employed. The governing equations for the FG-TPMS plate are derived using the virtual work principle and solved with the Chebyshev moving Kriging meshfree method. Numerical results demonstrate the high reliability to produce accurately obtained results.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"309 ","pages":"Article 107660"},"PeriodicalIF":4.4,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125243","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
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