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Main beam positioning and posture analysis under the hinge influence for suspension bridges with short extended spans in the splicing construction state: An analytical algorithm

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ENGINEERING STRUCTURES 2025年 326卷

作者： Zhang, Wen-ming Wang, Zhen-ping Zhang, Xiao-yi Tian, Gen-min Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China

In suspension bridges with short extended spans, the main beam in the side spans is usually installed before that in the main span. Splicing of the main beam in the main and side spans is commonly performed at the site of towers after the main beam erection is completed in the main span, in order to reduce the main beam construction period. The position and posture of the main beam in the side spans are determined by the line shape of the main span. In the splicing construction state, some beam segments in the main beam are still connected by hinges. The number and position of hinges will affect the line shape of the main beam in the main span. As the line shape varies, the position and inclination angle of the end face of the main beam change accordingly at the site of the splice, further affecting the construction schedule and precision. Addressing the above issue, this study proposes an analytical algorithm for solving the main beam's line shape and internal force, considering the number and position of hinges. Using the known parameters of the completed bridge state, the main cable deformation, main beam deformation, hanger inclination, and tower saddle pre-offset are successively derived. Governing equations are constructed based on different conditions: conservation of unstrained length of main cable in different spans, compatibility between hanger forces and hanger deformation, closure of span lengths, closure of elevation differences, and force equilibrium in the main beam. These governing equations are combined into one objective function, and the basic unknown parameters are solved as a programming problem. Once the above parameters are derived, the line shape of the main beam and inclination angle and position of the beam-end face at the splice site are calculated. The proposed method is then applied to a suspension bridge with short extended spans with a span length layout of 100 m+ 1080 m+ 100 m as a verification.

关键词： Suspension bridge Short extended spans Splicing construction state Line shape analytical algorithm

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analytical algorithm for Strand End Leakage Reactance of Transposition Bar in AC Machine

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2015年第2期30卷 533-540页

作者： Liang, Yanping Bian, Xu Yu, Honghao Wu, Lei Wang, Bing Harbin Univ Sci & Technol Coll Elect & Elect Engn Harbin 150080 Peoples R China

Calculation of circulating current in transposition bars is the key problem in the design of stator windings, which will determine the transposition type of stator windings. The circuit equation method, in which the calculation of strand end leakage reactance in transposition bars is the premise, is widely used in engineering to calculate circulating current. This paper describes an analytical algorithm for the calculation of strand end leakage reactance in transposition bars, which is based on mirror image principle. The end leakage reactance of strands in transposition bar is calculated by the integral of transposition path discretized into many key points. Contrary to the existing calculation method, the analytical algorithm proposed in this paper is a general method for calculating the end leakage reactance, which can simulate the transposition path of strands in the end region for different transposition types. In order to validate the proposed method, the end coil self and mutual leakage reactance are calculated by proposed analytical algorithm and finite element method.

关键词： AC machine analytical algorithm circulating current discrete integral end leakage reactance transposition bars

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analytical algorithm for Capacities of Classical and Classical-Quantum Channels

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第3期69卷 1381-1393页

作者： Hayashi, Masahito Southern Univ Sci & Technol Shenzhen Inst Quantum Sci & Engn Shenzhen Nanshan Peoples R China

We derive an analytical algorithm for the channel capacity of a classical channel without any iteration, while its existing algorithms require iterations and the number of iterations depends on the required precision level. Hence, our algorithm is its first analytical algorithm for this task without any iteration, while this algorithm needs several conditions for the channel. We apply the obtained algorithm to examples, and see how the obtained algorithm works in these examples. Then, we extend it to the channel capacity of a classical-quantum (cq-) channel. Many existing studies proposed algorithms for a cq-channel and all of them require iterations. Our extended analytical algorithm has also no iteration, and outputs the exactly optimum value.

关键词： Channel capacity Approximation algorithms STEM Mathematical models Complexity theory Iterative algorithms Upper bound Mutual information maximization channel capacity classical-quantum channel analytical algorithm

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analytical algorithm of weighted 3D datum transformation using the constraint of orthonormal matrix

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EARTH PLANETS AND SPACE 2015年第1期67卷 1-10页

作者： Zeng, Huaien China Three Gorges Univ Minist Educ Key Lab Geol Hazards Three Gorges Reservoir Area Yichang 443002 Peoples R China China Three Gorges Univ Hubei Key Lab Construct & Management Hydropower E Yichang 443002 Peoples R China

Based on the Lagrangian extremum law with the constraint that rotation matrix is an orthonormal matrix, the paper presents a new analytical algorithm of weighted 3D datum transformation. It is a stepwise algorithm. Firstly, the rotation matrix is computed using eigenvalue-eigenvector decomposition. Then, the scale parameter is computed with computed rotation matrix. Lastly, the translation parameters are computed with computed rotation matrix and scale parameter. The paper investigates the stability of the presented algorithm in the cases that the common points are distributed in 3D, 2D, and 1D spaces including the approximate 2D and 1D spaces, and gives the corresponding modified formula of rotation matrix. The comparison of the presented algorithm and classic Procrustes algorithm is investigated, and an improved Procrustes algorithm is presented since that the classic Procrustes algorithm may yield a reflection rather than a rotation in the cases that the common points are distributed in 2D space. A simulative numerical case and a practical case are illustrated.

关键词： Weighted 3D datum transformation analytical algorithm Lagrangian extremum Constraint of orthonormal matrix Procrustes algorithm

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AN analytical algorithm TO DETERMINE ALLOWABLE AMPACITIES OF HORIZONTALLY INSTALLED RECTANGULAR BUS BARS

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THERMAL SCIENCE 2016年第2期20卷 717-730页

作者： Klimenta, Dardan O. Perovic, Bojan D. Jevtic, Miroljub D. Radosavljevic, Jordan N. Univ Pristina Kosovska Mitrovica Fac Tech Sci Kosovska Mitrovica Serbia

The main objective of this paper is to propose an algorithm for the determination of the allowable ampacities of single rectangular-section bus bars without the occurrence of correction factors. Without correction factors, the ampacity computation of the copper and aluminum bus bars is fully automatized. The analytical algorithm has been implemented in a computer program code that along with the allowable ampacity can compute the bus bar temperature and the individual heat transfer coefficient for each side of the bus bar, as well as their corresponding power losses. Natural and forced convection correlations for rectangular bus bars are applied Effects of the solar radiation and radiation heat losses from the bus bar surface are taken into consideration as well. The finite element method has been used for the linear/non-linear steady-state thermal analysis, i. e. for validation of the analytical algorithm. All finite element method based numerical computations were carried out using the COMSOL heat transfer module.

关键词： allowable ampacity analytical algorithm bus bar empirical correlations heat transfer

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A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1999年第3期114卷 610-625页

作者： Ghomi, SMTF Hashemin, SS Amirkabir Univ Technol Dept Ind Engn Tehran Iran Islamic Azad Univ Dept Ind Engn Ardabil Iran

An analytical algorithm is presented to compute the network completion time distribution function, where each are has a continuous, defined, and independent completion time distribution function. Through a transformation method, the algorithm is simplified into simple multiple integrals. Then Gaussian quadrature formula is generalized for numerical solution of these integrals. Also the generalized Gaussian quadrature formula is applied for conditional Monte Carlo simulation to increase its speed and develop its domain of application. A suitable criterion is presented for the efficiency of conditional Monte Carlo simulation. For variance reduction in estimation, the antithetic random variates are used for simulation methods, conditional Monte Carlo simulation and crude Monte Carlo simulation. Several examples are presented and solved through generalized Gaussian quadrature formula, conditional Monte Carlo simulation, and crude Monte Carlo simulation. For the aspects of speed and accuracy, different methods are compared, where analytical solutions are provided and used for comparison purposes. Finally, conclusions and recommendations are made. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

关键词： network completion time distribution function Gaussian quadrature formula multiple integrals analytical algorithm

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Determination of main cable shape and hanger tensions of a suspension bridge based on the measured live-load deflection of the main beam: An analytical algorithm

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ENGINEERING STRUCTURES 2022年 272卷 1页

作者： Zhang, Wen-ming Chang, Jia-qi Feng, Dan-dian Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China

Hanger tensions and the main cable shape are key parameters of suspension bridges that must be assessed during their construction and operation phases. An analytical algorithm is proposed for assessing these parameters via the measured deflection of the main beam and tower-top displacements. First, the hanger tension increments caused by the live load are derived based on the known live load and measured deflection of the main beam. Next, the hanger tensions in the initial state are determined according to the conditions for conserving the unstrained length of each main cable segment and the force-deformation coordination of each hanger with and without the live load. Finally, the main cable shape is derived from the hanger tensions in the initial state. In contrast to the conventional method, the proposed analytical approach requires no complex dynamic equations. At the same time, the expression based on static analysis has a simpler form and higher universality and practicality. The proposed approach allows for a faster and more accurate evaluation of the suspension bridge's main cable shape and hanger tensions. The feasibility and effectiveness of the proposed method are verified for an exemplary suspension bridge with a main span of 1080 m.

关键词： Suspension bridge Hanger tension Main cable shape Live load Main beam deflection analytical algorithm

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Tension design of heated-mandrel winding process based on analytical algorithm

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JOURNAL OF REINFORCED PLASTICS AND COMPOSITES 2014年第16期33卷 1529-1541页

作者： Xu, Jiazhong Miao, Yanan Qiao, Ming Li, Shuang Harbin Univ Sci & Technol Dept Automat Harbin 150080 Peoples R China

Resin matrix filament wound composite shells are widely applied in the fields of military, aerospace, energy transportation, pressure vessel, and civil engineering. The curing and winding are regarded as the necessary procedures during molding, and they are the key factors affecting the final performance of the composite shells. This paper discusses the application of a new molding process called the heated-mandrel winding process, to take the place of the traditional molding process, which has a two-step procedure. It is proved that the heated-mandrel winding process can not only improve the product quality and production efficiency, but can also reduce the labor cost, without moving the wound shell from the winding machine to the oven. In contrast to the traditional molding process, some properties of the composite formed with the heated-mandrel winding process, including the curing degree and elastic modulus, will be changed because of the heat conduction from the heated mandrel during winding. Therefore, the traditional winding tension system design method is no longer suitable for this new process. Taking the temperature changes into account, this paper uses a theoretical investigation and calculations to suggest a tension system model that describes the relationship between the changeable parameters and the winding tension and to calculate the appropriate tension values for winding, based on the heated-mandrel winding process. The accuracy of the model is verified using an experiment. This paper applies an analytical algorithm based on simple iterative steps to design the tension system. The calculation procedures are simplified, and fewer calculation cycles are required in the analytical algorithm proposed in this paper because it is easier to calculate a few simple linear equations rather than complex nonlinear differential equations under the condition that some initial parameters can be known. As seen during practical application, the model is suitable for

关键词： Heated-mandrel winding residual stress winding with tensioning tension system analytical algorithm

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Suspension bridge deformation and internal forces under the concentrated live load: analytical algorithm

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ENGINEERING STRUCTURES 2021年 248卷 113271-113271页

作者： Zhang, Wen-ming Chang, Jia-qi Lu, Xiao-fan Tian, Gen-min Li, Jin-guo Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China Tongji Architectural Design Grp Co Ltd Shanghai 200092 Peoples R China

Suspension bridge is a flexible structure, which responses to live loads are quite complicated due to the coupling of several factors. In this paper, an analytical algorithm is proposed for estimating the deformation and internal forces of earth-anchored suspension bridges under the concentrated live load. Based on the known parameters of the completed bridge and the live load, the deformation of the main cable, the deformation of the girder, the relationship between the main cable and the girder, and the deformation of towers are successively analyzed. Next, four categories of governing equations are set up, namely, the conservation of the unstrained length of each main cable segment, the force and deformation coordination of each hanger, the closure of length and elevation difference in each span, and the mechanical balance of the girder. The total number of governing equations is equal to that of basic unknown parameters. Finally, all the governing equations are incorporated into an objective function, and the programming solution is carried out. The values of the basic unknown parameters are determined so that all the governing equations hold true simultaneously. Based on this, all other parameters are derived and the deformed state of the structure is expressed. The proposed method's feasibility and effectiveness are verified by its application to an earth-anchored suspension bridge with a main span of 1080 m. Both the deformation and internal forces under the live load are accurately estimated using the proposed analytical algorithm, which agree well with the finite element analysis.

关键词： Suspension bridge Concentrated live load Structural deformation Internal force Governing equation analytical algorithm

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Improved analytical algorithm for Magnetic Field of End Windings in 300Mvar Synchronous Condenser

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IEEE ACCESS 2021年 9卷 85885-85893页

作者： Zhu, Erhang Liang, Yanping Han, Xiao Bian, Xu Wang, Chenguang Harbin Univ Sci & Technol Coll Elect & Elect Engn Harbin 150080 Peoples R China

The magnetic field of end windings affects the leakage reactance of end windings and the eddy current losses of end structures in the large electrical machine. With the rising of single-machine capacity, such effect becomes more obvious. However, due to the complexity of end structures of large electrical machine, it will cause difficulty in meshing and long calculation time to calculate the magnetic field of end windings by using 3-D finite element method (FEM). In order to calculate the magnetic field of end windings quickly and accurately, an improved analytical algorithm (IAA) is proposed based on the mirror image principle, which takes into account the influence of stator back core and air-gap on the magnetic field of end windings by adding the fictitious boundary current and air-gap current, respectively. Taking a 300Mvar synchronous condenser (SC) as an example, the boundary current, air-gap current and magnetic field of end windings are calculated. Then, the influence of stator back core and stator involute segment current on the magnetic field of end windings are analyzed, which provides a theoretical support for the design and optimization of SC. To validate the accuracy of IAA, the calculation result is compared with 3-D FEM.

关键词： Windings Magnetic fields Stator cores Stator windings Magnetic cores Mirrors Air gaps Synchronous condenser magnetic field analytical algorithm mirror image stator back core

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