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Axisymmetric accurate nonlinear analytical solutions for circular thin membranes under various transverse distributed loads
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-13 DOI: 10.1007/s00419-025-02827-2
Da-Guang Zhang
{"title":"Axisymmetric accurate nonlinear analytical solutions for circular thin membranes under various transverse distributed loads","authors":"Da-Guang Zhang","doi":"10.1007/s00419-025-02827-2","DOIUrl":"10.1007/s00419-025-02827-2","url":null,"abstract":"<div><p>Membrane structures, prized for their light weight and adaptability, are widely used in fields such as engineering, architecture, and aerospace. Nonlinear membrane analysis has evolved from the early works by Föppl and Hencky to modern computational methods. This paper extends the innovative orthogonal power function series, initially developed for circular thin plates, to solve general membrane problems. By expanding deflection using the innovative orthogonal power series and applying the Airy stress function, the method accounts for nonlinear interactions between deflection and in-plane forces. The energy variational method is used to derive nonlinear algebraic equations, enhancing both accuracy and computational efficiency compared to traditional methods. This approach sets new benchmarks for the verification of nonlinear solutions, making it a reliable and practical tool for membrane theory and engineering applications.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944268","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
On stability of particulate flow in a pipe of non-circular cross section
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-13 DOI: 10.1007/s00419-025-02826-3
C. Q. Ru
{"title":"On stability of particulate flow in a pipe of non-circular cross section","authors":"C. Q. Ru","doi":"10.1007/s00419-025-02826-3","DOIUrl":"10.1007/s00419-025-02826-3","url":null,"abstract":"<div><p>Linear stability of particulate flow of a viscous fluid with dispersed solid particles in a pipe of arbitrarily shaped uniform cross section is formulated using a novel two-fluid model. It is shown that the mathematical equations for linear stability of the particulate flow in a pipe of arbitrarily shaped uniform cross section are identical to that for the pipe flow of a clear fluid (without particles) with the same cross section provided that the original (real-form) mean velocity for the clear fluid is replaced by a complex-form effective mean velocity of Saffman type derived in the present work. In particular, in the two limiting cases of particles of extremely small or large Stokes number, the complex-form effective mean velocity reduces to a real-form proportional to the original mean velocity, and simple formulas are given for the critical Reynolds number ratio of the particulate fluid to the clear fluid under otherwise identical conditions. As examples, the derived formulas are applied to discuss qualitatively the critical Reynolds number for linear stability of particulate flow in a pipe of elliptical or rectangular cross section.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944269","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 thermally induced vibration of matrix-cracked variable stiffness composite laminated beams 矩阵裂纹变刚度复合材料层合梁的非线性热激振动
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-09 DOI: 10.1007/s00419-025-02831-6
Yibo Wang, Yuewu Wang
{"title":"Nonlinear thermally induced vibration of matrix-cracked variable stiffness composite laminated beams","authors":"Yibo Wang,&nbsp;Yuewu Wang","doi":"10.1007/s00419-025-02831-6","DOIUrl":"10.1007/s00419-025-02831-6","url":null,"abstract":"<div><p>The laminated composites are highly suitable for fabricating spacecraft components due to their exceptional performance-to-weight ratio. However, during orbital operations, these structures undergo severe thermal cycling, triggering thermally induced vibrations that necessitate rigorous investigation of their nonlinear dynamic responses under thermal shock. To the best of the authors’ knowledge, this study presents the first comprehensive analysis of nonlinear thermally induced vibrations in variable stiffness composite laminated (VSCL) beams. The theoretical framework employs classical lamination theory integrated with the Poisson effect and von Kármán geometric nonlinearity. An exact temporal temperature profile through the thickness is derived using the one-dimensional transient heat conduction equation with Dirichlet boundary conditions. Coupled thermomechanical governing equations are formulated through the Lagrangian method and the Ritz method, while a self-consistent model addresses matrix crack evolution. Nonlinear dynamic responses are resolved via the Newmark-β method combined with Newton–Raphson iteration. Parametric studies reveal that lay-up configuration, boundary constraints, and crack density critically influence vibration characteristics. The results indicate that reasonable laminate and angle designs can effectively reduce the response amplitude of thermally induced vibrations. Comparative case studies show that the maximum difference in thermally induced vibration responses between different laminate designs can reach 17.04%. By optimizing the angles, the thermally induced vibration response of variable stiffness composite beams is reduced by 8.74% compared to constant stiffness composite beams.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929904","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
Piezoelectric thermal elastic buckling analysis on nanostructures via nonlocal elastic theory 基于非局部弹性理论的纳米结构热弹性屈曲分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-09 DOI: 10.1007/s00419-025-02829-0
Zhengzhong Xiong, Jingyuan Zhuang, Bingdong Gu
{"title":"Piezoelectric thermal elastic buckling analysis on nanostructures via nonlocal elastic theory","authors":"Zhengzhong Xiong,&nbsp;Jingyuan Zhuang,&nbsp;Bingdong Gu","doi":"10.1007/s00419-025-02829-0","DOIUrl":"10.1007/s00419-025-02829-0","url":null,"abstract":"<div><p>Piezoelectric material nanostructures have been widely applied in micro/nano-electromechanical systems (MEMS/NEMS) due to their excellent mechanical properties. Therefore, it is essential to describe the piezoelectric thermal elastic buckling behavior of piezoelectric material nanostructures at nanoscale. The existing theories are insufficient to explain the piezoelectric thermoelastic buckling behavior and multi-physics field coupling properties on piezoelectric material nanostructures, and further development is urgently needed. To this end, the current work intends to generalize thermo-electromechanical coupling theory and conduct buckling analysis by considering the multi-physical coupling behavior on piezoelectric material nanobeam. To elucidate the multi-physics field coupling characteristics and buckling behavior on piezoelectric material nanobeam, a new model is established, and the corresponding constitutive equations are derived based on nonlocal elastic theory and thermal model. To illustrate the application of the latest model, the thermo-mechanical buckling behavior of piezoelectric material nanobeam in complex thermal environments is investigated, revealing the effects of thermal effects and electric field on piezoelectric material nanobeam. Based on the numerical results, piezo-flexoelectric and thermal effects on the buckling behavior of piezoelectric material nanobeam are examined and graphically presented. This work may provide some assistance about the design and optimization of piezoelectric material nanobeam on MEMS/NEMS.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925642","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
Tri-method analysis of contact mechanics in orthotropic-isotropic materials 正交各向异性-各向同性材料接触力学的三方法分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-09 DOI: 10.1007/s00419-025-02832-5
Erdal Öner, Mine Gül Oktay, Ecren Uzun Yaylacı, Murat Yaylacı, İrem Mirzaloğlu
{"title":"Tri-method analysis of contact mechanics in orthotropic-isotropic materials","authors":"Erdal Öner,&nbsp;Mine Gül Oktay,&nbsp;Ecren Uzun Yaylacı,&nbsp;Murat Yaylacı,&nbsp;İrem Mirzaloğlu","doi":"10.1007/s00419-025-02832-5","DOIUrl":"10.1007/s00419-025-02832-5","url":null,"abstract":"<div><p>This study examines the contact mechanics of a homogeneous orthotropic layer resting on a homogeneous isotropic half-space without being bonded, subjected to loading by a rigid cylindrical punch. The effect of the orthotropic layer’s body force has been taken into account in the study. The study is conducted in three phases. In the first phase, the contact problem is analytically tackled using advanced methods such as elasticity theory, integral transform techniques, and Gauss–Chebyshev integration. The second phase utilizes finite element analysis through ANSYS software, accurately modeling the system. In the final phase, an artificial neural network is employed, allowing the system to learn and recognize intricate patterns in the data. The standout feature of this study is its thorough comparison of these three distinct methodologies, offering a comprehensive understanding of the contact mechanics between isotropic and orthotropic materials. The results reveal key insights into contact length, maximum contact stress, critical separation load, and separation distance, all as functions of critical dimensionless parameters. This study is significant in today’s advancing field of contact mechanics as it not only explores the combined impact of body forces and the interaction between orthotropic and isotropic materials but also uniquely compares the results using three distinct methods, offering comprehensive insights that address both theoretical and practical challenges.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-025-02832-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925643","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
Development of generalized mixed-mode I/II fracture criteria for arbitrary cracked orthotropic materials considering fracture process zone 考虑断裂过程区的任意裂纹正交异性材料广义混合模式I/II断裂准则的建立
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-08 DOI: 10.1007/s00419-025-02820-9
Mohammadreza Shabrou, Zahra Daneshjoo
{"title":"Development of generalized mixed-mode I/II fracture criteria for arbitrary cracked orthotropic materials considering fracture process zone","authors":"Mohammadreza Shabrou,&nbsp;Zahra Daneshjoo","doi":"10.1007/s00419-025-02820-9","DOIUrl":"10.1007/s00419-025-02820-9","url":null,"abstract":"<div><p>Despite significant progress in developing mixed-mode I/II fracture criteria for orthotropic materials, many existing criteria still fail to fully consider the complexities of the fracture process zone (FPZ) and the arbitrary crack-fiber angles. This research addresses these limitations by developing generalized mixed-mode I/II fracture criteria for orthotropic materials. The proposed criteria are based on the concepts of minimum strain energy density and maximum strain energy release rate, which are combined with the reinforcement isotropic solid model. Including the non-singular term (T-stress) in the calculations improves the accuracy of crack growth predictions. Furthermore, based on these proposed criteria, an expression for the equivalent mode I fracture toughness is developed, which can be used to calculate the fracture toughness for any given crack orientation in orthotropic materials. The validity of the proposed criteria is evaluated through comparisons with available experimental data for wood species and composite materials. The results show that the newly proposed criteria offer more accurate predictions of material fracture behavior compared to classical criteria. The new approach, which includes the FPZ effects together with T-stress, provides a more realistic representation of crack growth in orthotropic materials under mixed-mode I/II loading conditions.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919127","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
Dynamic instability analysis of nature-inspired lattice microplates reinforced with graphene 石墨烯增强自然激发晶格微板的动态不稳定性分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-08 DOI: 10.1007/s00419-025-02817-4
Nam V. Nguyen, Son H. Nguyen
{"title":"Dynamic instability analysis of nature-inspired lattice microplates reinforced with graphene","authors":"Nam V. Nguyen,&nbsp;Son H. Nguyen","doi":"10.1007/s00419-025-02817-4","DOIUrl":"10.1007/s00419-025-02817-4","url":null,"abstract":"<div><p>With the rapid development in additive manufacturing technologies, the demand for metamaterials characterized by adjustable mechanical features for interdisciplinary engineering applications has become increasingly popular, particularly in sophisticated small-scale systems. This paper pays attention to exploring the dynamic instability responses of functionally graded microplates fabricated from nature-inspired triply periodic minimal surface (TPMS) lattice architectures. The size-dependent instability dynamic behavior of three different sheet-based TPMS lattice architectures: Primitive, Gyroid, and I-graph and Wrapped Package-graph, is analyzed using modified couple stress theory. This study examines TPMS cellular architectures within the framework of uniform and two gradient density distributions. In addition, graphene is uniformly distributed within the TPMS structures to improve the dynamic performance. The dynamic instability regions in this investigation are determined using Bolotin’s procedure. The present findings reveal that the dynamic performance of TPMS lattice architectures outperforms that of both open-cell and closed-cell cellular solids. Additionally, the distribution and density of porosity in TPMS architectures significantly influence structural stiffness. A symmetric porosity pattern is found to yield the best dynamic instability performance, while structural rigidity is significantly enhanced by the addition of graphene. Furthermore, increasing the material length scale ratio and graphene weight fraction results in improved size-dependent dynamic instability characteristics. The present findings bring valuable insights into dynamic performance as well as contribute to the development of advanced lattice structures at the small scale, inspired by nature and reinforced with graphene.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919128","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
A general contact force model for collisions with zero indentation or remaining surface deformation at the moment of separation 在分离时刻无压痕或剩余表面变形时碰撞的一般接触力模型
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-07 DOI: 10.1007/s00419-025-02828-1
Huili Huang, Guofeng Yao, Min Wang, Jianhong Hou, Yuancheng Zhu
{"title":"A general contact force model for collisions with zero indentation or remaining surface deformation at the moment of separation","authors":"Huili Huang,&nbsp;Guofeng Yao,&nbsp;Min Wang,&nbsp;Jianhong Hou,&nbsp;Yuancheng Zhu","doi":"10.1007/s00419-025-02828-1","DOIUrl":"10.1007/s00419-025-02828-1","url":null,"abstract":"<div><p>In practical engineering, collisions with zero indentation or remaining surface deformation following separation have attracted widespread attention. A general contact force model that can effectively simulate these two types of collisions is proposed in this work based on the typical formula of the continuous model. By introducing equivalent velocity, an approximate dynamic equation for the system can be established. Based on the principle of energy equivalence, the basic formula for the key parameter hysteresis damping coefficient is derived by approximating the dynamic equations and system dynamics equations. Based on the consistency of the restitution coefficient before and after collision, a general contact force model is obtained by modifying the basic formula. The effectiveness of the model is verified by comparing the simulation results with experimental results for corresponding types of collisions. Compared with other existing models, the model can not only simulate collisions with remaining surface deformation with high accuracy but also better describe collisions with zero separation indentation. The general contact force model will aid in the dynamic analysis of multibody systems.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918945","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
New weak form with reduced boundary parameters for facilitating the numerical investigation of first-order linear elastic microstructures 简化边界参数的一阶线弹性微结构弱形式
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-07 DOI: 10.1007/s00419-025-02824-5
Hossein Golbakhshi, Ahmad Soleimani, Ehsan Raeisi Estabragh
{"title":"New weak form with reduced boundary parameters for facilitating the numerical investigation of first-order linear elastic microstructures","authors":"Hossein Golbakhshi,&nbsp;Ahmad Soleimani,&nbsp;Ehsan Raeisi Estabragh","doi":"10.1007/s00419-025-02824-5","DOIUrl":"10.1007/s00419-025-02824-5","url":null,"abstract":"<div><p>In modified couple stress analysis of Timoshenko micro-beams, three geometrical parameters, including the deflection, rotation and slope are appeared as the natural boundary conditions in the variational formulation. This leads to appearance of more natural parameters at each section and increase in computational cost of numerical investigations. In this study, a new idea is proposed for revising the boundary conditions, and based on primary kinematical considerations in the classical Timoshenko beam theory, the slope is discarded from the boundary conditions. Then a modified form of governing equations is proposed for deriving the weak form. Based on this consideration, several numerical problems are investigated as the case studies and the results of proposed model are compared with exact analytical solutions and available data from the experimental investigations. According to the obtained results, the present model provides accurate results and can be reliably used for one-dimensional microstructural analysis with various loading and support conditions.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913814","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
Study of bending springback of AZ31B magnesium alloy sheet based on tension–compression asymmetry 基于拉压不对称的AZ31B镁合金板材弯曲回弹研究
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2025-05-03 DOI: 10.1007/s00419-025-02834-3
Rongjun Wang, Hao Su, Pengchong Zhang, Zhibin Yao, Hailian Gui, Zhiquan Huang, Yang Huang
{"title":"Study of bending springback of AZ31B magnesium alloy sheet based on tension–compression asymmetry","authors":"Rongjun Wang,&nbsp;Hao Su,&nbsp;Pengchong Zhang,&nbsp;Zhibin Yao,&nbsp;Hailian Gui,&nbsp;Zhiquan Huang,&nbsp;Yang Huang","doi":"10.1007/s00419-025-02834-3","DOIUrl":"10.1007/s00419-025-02834-3","url":null,"abstract":"<div><p>Accurately predicting the amount of sheet springback has practical guiding significance for perfecting the bending forming process and improving the accuracy of products, and the special tension–compression asymmetry of magnesium alloy has gradually become a hot issue in the research of magnesium alloy forming process. In this paper, based on the uniaxial tension and compression stress–strain data of AZ31B magnesium alloy in the rolled annealed state at different temperatures, taking into account the tension–compression asymmetry and neutral layer offset during the sheet bending process, a theoretical model of sheet bending springback with high prediction accuracy has been established. The validity of the results obtained from the theoretical model is jointly verified by the sheet bending springback experiments at room temperature and the sheet bending springback simulations at different temperatures using finite element simulation software. The results show that the established theoretical model of sheet bending springback can reliably predict the springback angle of AZ31B magnesium alloy sheet. The springback angle of AZ31B magnesium alloy sheet at room temperature gradually decreases with increasing sheet thickness and bending angle, and the springback angle of sheets with the same thickness gradually decreases with increasing relative bending radius. The springback angle of AZ31B magnesium alloy sheet gradually decreases with increasing temperature.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900670","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
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