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An analytical model for coplanar waveguide on silicon-on-insulator substrate with Conformal mapping technique

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Chinese Physics B 2011年第1期20卷 98-104页

作者：何大伟程新红王中健徐大伟宋朝瑞俞跃辉 State Key Laboratory of Functional Materials for Informatics Shanghai Institute of Microsystem and Information TechnologyChinese Academy of Sciences Graduate University of the Chinese Academy of Sciences

In this paper, the authors present an analytical model for coplanar waveguide on silicon-on-insulator substrate. The four-element topological network and the Conformal mapping technique are used to analyse the capacitance and the conductance of the sandwich substrate. The validity of the model is verified by the full-wave method and the experimental data. It is found that the inductance, the resistance, the capacitance and the conductance from the analytical model show they are in good agreement with the corresponding values extracted from experimental Sparameter until 10 GHz.

关键词： coplanar waveguide silicon-on-insulator Conformal mapping

Analysis of geometric parameters of straight wall three-centered arch and stress of surrounding rock based on Conformal mapping

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Yantu Lixue/Rock and Soil Mechanics 2020年 41卷 74-84页

作者： Wu, Su Li, Ke-Gang Wu, Shun-Chuan Wang, Hang-Long Qin, Qing-Ci Li, Ming-Liang He, Fa-Yun Faculty of Land Resources Engineering Kunming University of Science and Technology Kunming 650093 China Yunnan Key Laboratory of Sino-German Blue Mining and Utilization of Special Underground Space Kunming 650093 China Kunming Prospecting Design Institute of China Nonferrous Metals Industry Co. Ltd. Kunming 650051 China

In order to obtain the mapping function with a much higher accuracy, the barrier function algorithm based on the fmincon optimization function is used to solve the mapping function. It is considered that the Conformal mapping from the outer boundary of the straight wall three-centered arch to the outer domain of the unit circle can be realized by m = 18 and n = 6, which is superior to the traditional algorithm. Based on the calculation results of analytical solution, the shape effect and size effect caused by the change of geometric parameters of the straight wall three-centered arch tunnel on the surrounding rock stress are analyzed. The results show that the increase rate of stress concentration coefficient in the arc area of the tunnel with small arch width ratio is much larger. The large stress concentration coefficient in the arc area of the tunnel with width-height ratio close to 1 is at the arch shoulder, while the maximum value, which is small, occurs at the corner of the wall. On the contrary, the large stress concentration coefficient in the arc area of the tunnel with width-height ratio far less than 1 is far away from the arch shoulder, while the maximum value is far away from the corner of the wall. When the width-height ratio is equal to 1, the maximum value of stress concentration coefficient appears at the corner, which is approximately the same as that of the stress concentration coefficient at the arch shoulder. © 2020, Science Press. All right reserved.

关键词： Conformal mapping

Precise method to control elastic waves by Conformal mapping

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Theoretical & Applied Mechanics Letters 2013年第2期3卷 62-67页

作者： Yongquan Liu Wei Liu Xianyue Su LTCS and Department of Mechanics and Aerospace Engineering College of Engineering Peking University

The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the Conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.

关键词： transformation method elastic waves Conformal mapping Helmholtz decompositionmethod metamaterials

Dynamic characteristics of large permanent magnet direct‐drive generators considering electromagnetic–structural coupling effects

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International Journal of Mechanical System Dynamics 2023年第1期3卷 25-38页

作者： Qinkai Han Xueping Xu Zhihong Zhang Yifeng Yan Chao Peng Fulei Chu Department of Mechanical Engineering The State Key Laboratory of TribologyTsinghua UniversityBeijingChina School of Instrumentation and Optoelectronic Engineering Research Institute for Frontier ScienceBeihang UniversityBeijingChina Institute of Research Center Xinjiang Goldwind Science and Technology Co.Ltd.XinjiangChina

Dynamic characteristics of large permanent magnet direct‐drive generators(PMDGs)considering electromagnetic–structural coupling effects are analyzed in this study.Using the Conformal mapping method,the scalar magnetic potential of the air gap magnetic field considering the slot effect is calculated.On the basis of the discrete current element and magnetic equivalent circuit model,the local magnetic saturation effect of the stator and rotor is quantitatively simulated and the air gap magnetic field intensity distribution is obtained via numerical simulation.A series of uniformly distributed equivalent electromagnetic springs are introduced to develop an electromagnetic–structural coupling finite element PMDG model.The proposed air gap field analysis method is verified by the finite element analysis results.On the basis of the test platform for the Goldwind 1.5MW PMDG,both modal and dynamic response tests for the stator/rotor coupling system are conducted,and the results are compared with the natural frequencies,mode shapes,and vibration responses obtained using the numerical model.The effects of the air gap length and rotor speed on the natural frequencies of the coupling system are analyzed.The proposed model has the potential to accurately evaluate the PMDG vibration energy,avoiding resonance points,and maintaining stable operations of the unit.

关键词： permanent magnet direct‐drive generators dynamic characteristics electromagnetic–structural coupling effects Conformal mapping magnetic equivalent circuit model electromagnetic springs

Optimal thermal design of anisotropic plates with arbitrary cutouts using genetic algorithm

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Theoretical & Applied Mechanics Letters 2022年第3期12卷 165-177页

作者： Mohammad Jafari Soheila Yari Mohammad Jafari Mechanical Engineering Department Shahrood University of TechnologyShahroodIran Faculty of Mechanical and Mechatronics Engineering Shahrood University of TechnologyShahroodIran

Anisotropic plates in different applications may have geometric defects such as openings and cracks.The presence of the opening disturbs the heat flow,which creates significant thermal stress around the opening.When the heat flux is high enough,these extreme stresses can lead to structural failure.This article aims to obtain the optimal parameters for achieving the minimum value of the normalized stress near the cutout’s boundary in perforated anisotropic plates utilizing the genetic algorithm.Optimization parameters include the curvature of opening’s corners,orientation angle of opening,fibers angle,heat flux angle,and opening’s elongation.The plate is under heat flux,and the opening’s border is thermally insulated.The stress distribution around the opening is calculated using Lekhnitskii’s complex variable method and complex potential functions.The genetic algorithm is then implemented to find the optimal values for design parameters.The results show that by selecting the optimal parameters related to the anisotropic material and the opening’s geometry,the stress intensity factor of the perforated anisotropic plates is remarkably reduced.Furthermore,this optimization algorithm can be extended to find the optimized parameters and achieve the optimal designs in anisotropic and isotropic perforated plates under thermal loadings.

关键词： Anisotropic materials Perforated plate Optimization Genetic algorithm Thermal stress Complex variable method Conformal mapping

A screw dislocation near one open inhomogeneity and another closed inhomogeneity both permitting constant interior stresses

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Applied Mathematics and Mechanics(English Edition) 2021年第2期42卷 173-182页

作者： Xu WANG Ping YANG P.SCHIAVONE School of Mechanical and Power Engineering East China University of Science and Technology Department of Mechanical Engineering University of Alberta Innovation Centre for Engineering

We prove that the interior stresses within both a non-parabolic open inhomogeneity and another interacting non-elliptical closed inhomogeneity can still remain constant when the matrix is simultaneously under the action of a screw dislocation and uniform remote anti-plane stresses.The constancy of interior stresses is realized through the construction of a Conformal mapping function for the doubly connected domain occupied by the surrounding matrix.The mapping function is endowed with the information describing the screw dislocation via the incorporation of two specifically defined logarithmic terms.The constant interior stress fields are observed to be independent of the specific open and closed shapes of the two inhomogeneities and the existence of the screw dislocation.In contrast,the existence of the neighboring screw dislocation significantly affects the open and closed shapes of the two inhomogeneities.

关键词： constant stress field open inhomogeneity closed inhomogeneity screw dislocation Conformal mapping

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

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Applied Mathematics and Mechanics(English Edition) 2020年第6期41卷 899-908页

作者： Lianhe LI Xiaowei CUI Junhong GUO College of Mathematics Science Inner Mongolia Normal UniversityHohhot 010022China Department of Mechanics Inner Mongolia University of TechnologyHohhot 010051China

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional(1 D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.

关键词： screw dislocation elliptical hole Conformal mapping stress field onedimensional(1D)hexagonal quasicrystal with piezoelectric effect

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

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Applied Mathematics and Mechanics(English Edition) 2018年第8期39卷 1103-1118页

作者： M.HAJIMOHAMADI R.GHAJAR Mechanical Properties Research Lab (MPRL) Faculty of Mechanical Engineering K.N. Toosi University of Technology

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A Conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.

关键词： complex variable Conformal mapping unequal crack elliptical hole stress intensity factor(SIF)

Anti-plane problem of four edge cracks emanating from a square hole in piezoelectric solids

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Chinese Journal of Aeronautics 2017年第1期30卷 461-468页

作者： Fan Shiwang Guo Junhong Yu Jing School of Science Inner Mongolia University of Technology College of General Education Inner Mongolia Normal University

By constructing a new numerical Conformal mapping and using the Stroh-type formulism, an anti-plane problem of four edge cracks emanating from a square hole in piezoelectric solids is investigated. The explicit expressions of the complex potential function, field intensity factors, energy release rates and mechanical strain energy release rate near the crack tip are obtained under the assumptions that the surfaces of the cracks and hole are electrically permeable and electrically impermeable. Numerical examples are presented to show the influences of the geometrical parameters of defects and applied mechanical/electrical loads on the energy release rate and mechanical strain energy release rate under two electrical boundary conditions.

关键词： Cracks Conformal mapping Hole Piezoelectric material Stroh-type formulism