Structural Mechanics of Engineering Constructions and Buildings最新文献

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Memorial stele on a compact spherical support: design-and-engineering solutions, design-basis justification 纪念碑上的一个紧凑的球形支撑:设计和工程解决方案,设计基础的理由
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2022-05-23 DOI: 10.22363/1815-5235-2022-18-1-73-88
Dmitrii V. Petrov, Aleksandr G. Yudov, V. V. Dotsenko, O. Zhabunina, Egor V. Kalaturov, Nadezhda M. Natynchik, A. Abramov, M. V. Nikulshin
{"title":"Memorial stele on a compact spherical support: design-and-engineering solutions, design-basis justification","authors":"Dmitrii V. Petrov, Aleksandr G. Yudov, V. V. Dotsenko, O. Zhabunina, Egor V. Kalaturov, Nadezhda M. Natynchik, A. Abramov, M. V. Nikulshin","doi":"10.22363/1815-5235-2022-18-1-73-88","DOIUrl":"https://doi.org/10.22363/1815-5235-2022-18-1-73-88","url":null,"abstract":"The article presents the design of the architectural and artistic composition “Memorial stele on a local spherical support” (KB-1 Stele), as well as the analysis of design solutions and the calculated justification of the strength and stability of the KB-1 Stele to external influences in conditions of the most intense climatic influences with parameters set according to building codes and regulations. The design of the KB-1 Stele is a vertically installed overall mass model of a peaceful nuclear explosive device weighing 2.8 tons and 2.8 meters high with hemispherical covers. In accordance with the terms of reference, it was required to preserve the appearance of the device as accurately as possible by placing it on a small local support. The peculiarity of the design lies in its angular mobility relative to the support. To ensure a stable equilibrium state of the stele, a hinge is organized at the place of support, the stele is installed freely by the lower sphere on an intermediate stand with a specially selected spherical surface. Additionally, the center of mass of the stele is significantly reduced by lightening (thinning the walls) of the upper part of the body and installing additional cargo in its lower part. As a result, under the action of external lateral loads, the stele acquires a stable position with possible fluctuations in the tumbler type and with a return to its original state. Analytical and numerical computational studies were performed to substantiate the strength and stability of the KB-1 Stele under external loads. It is shown that the developed design meets the regulatory requirements and is safe in operation.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":"57 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41283646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bulking of physically nonlinear plates under the action of dynamic shearing loads 物理非线性板在动剪切荷载作用下的膨胀
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2022-05-23 DOI: 10.22363/1815-5235-2022-18-1-3-10
Sergey Ivanov
{"title":"Bulking of physically nonlinear plates under the action of dynamic shearing loads","authors":"Sergey Ivanov","doi":"10.22363/1815-5235-2022-18-1-3-10","DOIUrl":"https://doi.org/10.22363/1815-5235-2022-18-1-3-10","url":null,"abstract":"The study of the stability of plates under shear under the action of dynamic loads is one of the important problems of structural mechanics. The plates are widely used in construction, mechanical engineering, shipbuilding and aircraft building. The paper presents a method for calculating plates for shear buckling, taking into account the physical nonlinearity of the material. A plate is considered under the action of a shearing dynamic load along the edges. The calculation is based on the Kirchhoff - Love hypotheses and the hypothesis of a non-linear elastic body. The plate material is assumed to be physically nonlinear. The deformation diagram is approximated as a cubic polynomial. The deflection of the plate points is determined in the form of Vlasov - Kantorovich expansions. Basic non-linear differential equations are derived using the energy method. Lagrange’s equations are used to obtain the resolving equations for plate buckling. On the basis of the developed technique, a calculation was made for the stability of a physically nonlinear square plate under the action of a shear dynamic load. The edges of the plate are hinged. The finite system of nonlinear differential equations is integrated numerically by the Runge - Kutta method. Based on the results of calculations, plots of the dependence of the relative value of the deflection of the central point of the plate on the dynamic coefficient Kd (with and without taking into account the physical nonlinearity of the material) are plotted. The influence of the degree of physical nonlinearity of the material, the parameter of the rate of change of the shear load on the criteria for the dynamic stability of a square plate is studied.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44751838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The theory of calculation of reinforced concrete structures and the principles of the Eurocode 钢筋混凝土结构的计算理论和欧洲规范的原则
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-5-455-465
Rudolf S. Sanzharovskiy, F. Sieber, T. Ter-Emmanuilyan
{"title":"The theory of calculation of reinforced concrete structures and the principles of the Eurocode","authors":"Rudolf S. Sanzharovskiy, F. Sieber, T. Ter-Emmanuilyan","doi":"10.22363/1815-5235-2021-17-5-455-465","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-5-455-465","url":null,"abstract":"The theory of calculating reinforced concrete is analyzed. As we known reinforced concrete with enormous volumes of application and huge financial costs, due to the great complexity of its nonlinear properties, has a surprisingly unscientific theory of calculation, consisting of two parts: short-term and longterm loading. The work of a number of round tables was devoted to the problem of errors in the theory of calculating reinforced concrete. The round tables held at the Peoples Friendship University of Russia (RUDN University) on the initiative and under the guidance of famous scientists: V.M. Bondarenko, S.N. Krivoshapko, V.V. Galishnikova (the last one took place in 2020) with a large number of participants of authoritative scientists from Russia and other countries. It is shown that the theory of calculation of reinforced concrete structures, which are widely used (with long-term loading all over the world), includes five inconsistent (among them erroneous) theories, the essence of which and one postulate are set further. Using the rules of mathematics, the principles of mechanics and the results of solid experiments, it was revealed that the analyzed theory contains a set of theories rejecting each other for various purposes, including erroneous ones.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41409325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Diagnostics of thin-walled structures of complex geometry and structure 复杂几何和结构薄壁结构的诊断
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-576-587
N. M. Yakupov, S. Yakupov
{"title":"Diagnostics of thin-walled structures of complex geometry and structure","authors":"N. M. Yakupov, S. Yakupov","doi":"10.22363/1815-5235-2021-17-6-576-587","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-576-587","url":null,"abstract":"The main stages of the birth of thin-walled structures, changes in their relative thickness and mass of a unit area are given; ways of creating perfect thin-walled structures are indicated. The problems arising during the operation of thin-walled structures of complex geometry, as well as approaches and methods of their calculation are noted. To ensure trouble-free operation of a thin-walled structure with a thin-layer coating, under load and exposed to physical fields and environments, it is necessary to correctly diagnose the condition of structural elements. The spline variant of the finite element method in two-dimensional (SV FEM-2) and three-dimensional (SV FEM-3) productions is noted, as well as the synthesis of these variants - SV FEM-2 + SV FEM-3. The combination of the idea of parametrization of the entire domain and approximation of the desired variables within the element by Hermitian cubic splines makes it possible to obtain high-precision consistent finite elements. The developed variants of the finite element method make it possible to evaluate the stress-strain state of structures of complex geometry, including the calculation of multilayer, thin-walled structures with coating and local defects, as well as to take into account specific surface properties other than those of the main array. Studies of stress concentration near local depressions are considered. Two-dimensional experimental and theoretical methods are noted for evaluating the stiffness properties and adhesion of thin-walled, thin-layer and composite structural elements of complex structure, which, along with a distributed complex structure, may have distributed defects. The developments were used in solving specific tasks of a number of enterprises.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42580652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The economic feasibility of taking into account the joint work of load-bearing and enclosing elements in large-span wooden spatial structures 考虑大跨度木质空间结构承重与围护构件联合工作的经济可行性
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-664-678
Konstantin P. Pyatikrestovsky, B. Sokolov
{"title":"The economic feasibility of taking into account the joint work of load-bearing and enclosing elements in large-span wooden spatial structures","authors":"Konstantin P. Pyatikrestovsky, B. Sokolov","doi":"10.22363/1815-5235-2021-17-6-664-678","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-664-678","url":null,"abstract":"Large-span wooden spatial structures in the form of domes, developed in JSC Research Center of Construction under the leadership of A.A. Pogoreltsev, are built in large numbers for roofing various buildings. Such designs have high performance indicators and continue to improve. In 2020 the Manual on accounting for the joint work of the frame and fencing in wooden spatial structures of buildings and structures was developed as an addition to SP 64.13330.2017, containing examples of strength calculation and optimization of rib cross-section dimensions, as well as an example of determining the long-term strength of the shell cladding. These structures, in fact unique, are designed so far in the margin of safety without taking into account the participation of the enclosing part (panels, decking, etc.) in the bearing loads. Taking into account the work of the decking, especially when exposed to asymmetric loads, can lead to material savings. In addition to the above theory of nonlinear shell calculation, the authors have also developed a calculation of composite anisotropic panels operating under complex stress conditions, i.e. under biaxial compression (tension) and shear. The calculation of such structures under both short-term and long-term loads presents certain difficulties and requires the introduction of strength theories and criteria for their description that are unusual for specialists of design organizations.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43389568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometry of the normal ruled surfaces 法向直纹曲面的几何学
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-562-575
V. N. Ivanov
{"title":"Geometry of the normal ruled surfaces","authors":"V. N. Ivanov","doi":"10.22363/1815-5235-2021-17-6-562-575","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-562-575","url":null,"abstract":"The wide circle of the surfaces formed by the motion of the right line in the normal plain of some base directrix curve is regarded. The generate right line may rotate at some low at the normal plane of the base curve. The vector equation of the surface with any plane or space base curve is received. There are given the formulas of the geometry characteristics of the surfaces, on the base of them there is shown that the coordinate system of the normal ruled surfaces is orthogonal but there is not conjugated in common, that is that the normal ruled surfaces there are not developable surfaces in common way. The condition of the rotation of directrix plane line when the coordinate system of the normal ruled surfaces will be conjugated and the normal ruled surface will be developable is received. The condition that the normal ruled surface with space base curve will be the developable surface there is connected with its curvature of base curve. The developable normal ruled surface with plane base curve is formed by motion of right line at the normal plane of the base curve with the constant angle to the plane of the base curve; the received surface is a surface of constant slope. On the base of the vector equation of the surfaces there are made the figures of the normal ruled surfaces with the help of program complex MathCAD.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48150320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical analysis of cylindrical shell stability interacting with inhomogeneous soil 非均匀土作用下圆柱壳稳定性的数值分析
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-608-616
S. Kosytsyn, V. Akulich
{"title":"Numerical analysis of cylindrical shell stability interacting with inhomogeneous soil","authors":"S. Kosytsyn, V. Akulich","doi":"10.22363/1815-5235-2021-17-6-608-616","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-608-616","url":null,"abstract":"The research is aimed at determining the critical buckling load of the spatial model shell - soil system in the case of inhomogeneous physical and mechanical soil properties along the longitudinal axis of the cylindrical shell in a nonlinear formulations of the task. Methods. The task is solved by a numerical method using a finite element complex ANSYS. Two calculated cases of the spatial model shell - soil system are compiled. The soil is divided into two equal parts with different physical and mechanical properties. The problem was solved in geometrically, physically and constructively nonlinear statement. Nonlinearity is due to the need to find the contact zone through an iterative process and determine the time-varying position of the shell. The soil is modeled by volumetric elements, each consisting of twenty nodes. The shell is modeled by flat elements, each consisting of four nodes. Contact elements of one-side action are used. Critical buckling load are determined relative to the actual load of its own weight. Results. Critical loads are obtained from two calculated cases of the spatial model shell - soil system. There is a comparative analysis of the results. An assessment of the stability margin of the shell relative to the actual load is given.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42341305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Influence of constructive solutions on the stiffness characteristics of the rammed monolithic reinforced concrete cone-shaped piles with side and bottom forms from crushed stones 施工方案对侧底式碎石夯实钢筋混凝土整体锥桩刚度特性的影响
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-5-500-518
E. Kuzhakhmetova
{"title":"Influence of constructive solutions on the stiffness characteristics of the rammed monolithic reinforced concrete cone-shaped piles with side and bottom forms from crushed stones","authors":"E. Kuzhakhmetova","doi":"10.22363/1815-5235-2021-17-5-500-518","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-5-500-518","url":null,"abstract":"Relevance. The article discusses the design solutions of a new pile structure, which is a monolithic reinforced concrete cone-shaped pile, enclosed in a crushed stone shell and resting on a spherical crushed stone broadening. In the course of a numerical study, carried out using the finite element method, the influence of the geometric parameters of the crushed stone formations of the pile foundation, such as the wall thickness of the crushed stone shell and the radius of the crushed stone broadening, on its bearing capacity was revealed. The aim of the study is to perform a comparative numerical analysis of the stressstrain state of a pile structure with different design solutions, operating as part of a soil massif. Materials and methods. Numerical static analysis of the structure of a monolithic reinforced concrete pile foundation operating in a soil massif was carried out using a spatial finite element model in the CAE-class software package. The article presents the results of a numerical analysis of the stress-strain state of a rammed monolithic reinforced concrete cone-shaped pile with different wall thicknesses of the crushed stone shell and different diameters of the lower spherical crushed stone broadening. The analysis showed that changes in the specified geometric parameters of the pile foundation have a significant impact on its bearing capacity under external forces. The rational choice of these parameters allows you to economically use the concrete mixture and reinforcing rods intended for the manufacture of monolithic reinforced concrete rammed piles, which, in turn, leads to a decrease in financial costs for the manufacture of the pile foundation and the entire building as a whole. The next research is supposed to carry out a comparative analysis of the numerical results with experimental data obtained in laboratory and field conditions.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49433237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Investigation of the accuracy and convergence of the results of thin shells analysis using the PRINS program 用PRINS程序研究薄壳分析结果的准确性和收敛性
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-617-627
V. Agapov, A. S. Markovich
{"title":"Investigation of the accuracy and convergence of the results of thin shells analysis using the PRINS program","authors":"V. Agapov, A. S. Markovich","doi":"10.22363/1815-5235-2021-17-6-617-627","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-617-627","url":null,"abstract":"The theoretical foundations of compatible finite elements construction for static and dynamic analysis of single-layer and multilayer shells are discussed. These finite elements are implemented in the PRINS computer program. The paper presents verification tests to investigate the accuracy and convergence of the results of calculating various shells using these finite elements. Shell structures are widely used in various fields of technology - construction, mechanical engineering, aircraft construction, shipbuilding, etc. Specialists on the design and calculation of such structures need a reliable and accessible tool for the practical problems solving. Computer program PRINS can be one of such tools. It can be effectively used by engineers of design and scientific organizations to solve a wide class of engineering problems related to the calculations of shell structures. The paper describes the finite elements of the shells, implemented in the PRINS program. The results of verification calculations are presented, which confirm the high accuracy of this program.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47308856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Shell structures and shells at the beginning of the 21st century 21世纪初的壳体结构和壳体
Structural Mechanics of Engineering Constructions and Buildings Pub Date : 2021-12-30 DOI: 10.22363/1815-5235-2021-17-6-553-561
S. Krivoshapko
{"title":"Shell structures and shells at the beginning of the 21st century","authors":"S. Krivoshapko","doi":"10.22363/1815-5235-2021-17-6-553-561","DOIUrl":"https://doi.org/10.22363/1815-5235-2021-17-6-553-561","url":null,"abstract":"Researchers know that golden century of shells falls on 1920-1960 when the finishing of building of a thin-walled shell became an important event in life of country where this shell was erected. Every built shell was analyzed in tens of scientific works with a point of view of used method of analysis, applied constructive materials, cost of erection. Later on, an interest to thin-walled shells fell down. On the base of the fulfilled research in a paper, it is shown that application of shell structures is increasing in the 21st century because it was closely connected with needs of different branches of human activity. It is proved, that practically in all countries of the world, design and building of shell structures and shells was carried out. Only priority in application constructive materials changed. In the main, reinforced concrete was used earlier but now bar curvilinear structures, composite shells, and bar structures with the glass filling are in priority. It is shown that young and prominent architects and engineers tale part in construction of considered structures and thin-walled shells. All conclusions are confirmed by references containing 38 used original sources.","PeriodicalId":32610,"journal":{"name":"Structural Mechanics of Engineering Constructions and Buildings","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41996356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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