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FIELD INTENSITY FACTORS OF THREE CRACKS ORIGINATING FROM A CIRCULAR HOLE IN A THERMOELECTRIC MATERIAL

JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES 2020年第5期15卷 605-617页

作者： Liu, Qing-Nan Ding, Sheng-Hu Ningxia Univ Sch Math & Stat Yinchuan 750021 Ningxia Peoples R China

The fracture behavior of three cracks originating from a circular hole in a thermoelectric material is studied. The basic theory of thermoelectric materials is given under the condition of the impermeable boundary of the heat flux and electric current. By introducing the conformal mapping function, the infinite plane on the physical plane is mapped into the inner unit circle on the mathematical plane. The formulas of the relevant temperature and stress fields are derived, and the analytical solutions of the complex stress functions are obtained by the complex variable function method. According to Cauchy integral formula, the analytical expressions of the electric current intensity factor and the stress intensity factor for three cracks originating from a circular hole are obtained. The effects of the hole radius and the crack lengths on the electric current intensity factor and stress intensity factors were investigated.

关键词： thermoelectric material circular hole three cracks complex variable function intensity factors

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Stress Intensity Factors for Crack Problems in Bonded Dissimilar Materials

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JOURNAL OF ENGINEERING AND TECHNOLOGICAL SCIENCES 2020年第5期52卷 665-676页

作者： Hamzah, Khairum Long, Nik Mohd Asri Nik Senu, Norazak Eshkuvatov, Zainidin Univ Putra Malaysia Inst Math Res Lab Computat Sci & Math Phys Serdang 43400 Selangor Malaysia Univ Putra Malaysia Fac Sci Math Dept Serdang 43400 Selangor Malaysia Univ Malaysia Terengganu Fac Ocean Engn Technol & Informat Kuala Terengganu 21030 Malaysia Univ Teknikal Malaysia Melaka Fak Teknol Kejuruteraan Mekanikal & Pembuatan Durian Tunggal 76100 Malaysia

The inclined crack problem in bonded dissimilar materials was considered in this study. The system of hypersingular integral equations (HSIEs) was formulated using the modified complex potentials (MCP) function method, where the continuity conditions of the resultant force and the displacement are applied. In the equations, the crack opening displacement (COD) serves as the unknown function and the traction along the cracks as the right-hand terms. By applying the curved length coordinate method and the appropriate quadrature formulas, the HSIEs are reduced to the system of linear equations. It was found that the nondimensional stress intensity factors (SIF) at the crack tips depend on the ratio of elastic constants, the crack geometries and the distance between the crack and the boundary.

关键词： complex variable function bonded dissimilar materials hypersingular integral equation stress intensity factor

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Ground Effect on Lift of Thick Wing Airfoil

Ground Effect on Lift of Thick Wing Airfoil

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International Conference on Mechanical, System and Control Engineering (ICMSC)

作者： Frolov, Vladimir Samara Natl Res Univ Dept Aircraft Construct & Design Samara Russia

ISBN: (纸本)9781509065301

The paper investigates the influence of the ground on the airfoil lift. The Numerical Analytic Method (NAM) and the Discrete Vortices Method (DVM) are developed for simulating the flow around an airfoil when it is in the close proximity to the ground. The author proposes the NAM for modeling the flow around the airfoil near the ground and analyzes two approaches to solving the problem of Wing-in-Ground (WIG). The first method is based on the simulation of the ground surface, while the second one uses the reflection method. It has been shown that the increasing in the relative airfoil thickness reduces the positive WIG lift effect. It is also established that there is an optimal airfoil angle of attack at which the maximum lift occurs near the ground.

关键词： ground effect flat ground complex variable function conformal mapping discrete vortices

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Analytical Solution for a Lined Tunnel with Arbitrary Cross Sections Excavated in Orthogonal Anisotropic Rock Mass

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2017年第9期17卷 1-20页

作者： Lu, Aizhong Zhang, Ning Wang, Shaojie Zhang, Xiaoli North China Elect Power Univ Inst Hydroelect & Geotech Engn Beijing 102206 Peoples R China

A complete and accurate method for determining the stresses and displacements of a lined arbitrary shaped tunnel excavated in orthogonal anisotropic rock mass is proposed. The method is based on an analytical method, the complex variable method, and the power series method. The basic equations can be obtained according to the stress boundary conditions along the inner boundary of the lining and the stress and displacement continuity conditions along the lining-rock interface. Based on the method, the tangential stresses along the excavation boundary, the inner and outer boundaries of the lining, and the normal and shear stresses along the lining-rock interface are given. Results show that, when the number of terms of the series is large enough, solutions with high accuracy can be obtained. The positions of the tangential stress concentration, the effect of the displacement release coefficient, and the angle of the rock layers on the tangential stresses along the excavation boundary and both boundaries of the lining are discussed. (C) 2017 American Society of Civil Engineers.

关键词： Lined tunnel Orthogonal anisotropic rock mass complex variable function Power series method Stress and displacement Analytical solution

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A new calculation model for the stress field of hydraulic fracture propagation at the formation interface

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ENVIRONMENTAL EARTH SCIENCES 2016年第16期75卷 1178页

作者： Lu, Cong Guo, Jian-chun Liu, Li-ming Southwest Petr Univ State Key Lab Oil & Gas Reservoir Geol & Exploita Chengdu 610500 Peoples R China PetroChina Southwest Oil & Gas Field Co Cent Sichuan Oil & Gas Field Suining 629000 Peoples R China

Reservoirs with different formation interfaces are becoming increasingly common in the exploitation of unconventional oil and gas reservoirs, such as shale oil and gas. Therefore, it is essential to calculate the stress field of fracture propagation to understand the mechanism of propagating hydraulic fractures near formation interfaces. This study adopts the superposition principle of same-type fractures and considers the model propagating hydraulic fractures at interfaces as the superposition of three issues: actuating the fluid pressure inside the fracture without far-field stress, analysis with far-field stress and without fractures, and calculating the self-balancing surface force effect on the surface of fractures without far-field stress. Then, the study establishes the stress field calculation model for propagating hydraulic fractures at the formation interfaces, which considers different rock properties on both sides of the formation interfaces, as well as the influence of the dip angle based on the complex variable function method and fracture mechanics theory. Finally, this paper proposes corresponding numerical methods. It is determined by analyzing different stress concentration which occurs around the fractures and stress singularity which occurs at the hydraulic fracture tips, analyzing the plastic zone at hydraulic fracture tips which propagates contacts with formation interfaces;the maximum compressive stress and normal stress change gradually from tensile stress to compressive stress as the distance between the interface and the hydraulic fracture tip increases, and the exhibiting stress reverses on the formation interfaces.

关键词： Formation interface Fracture propagation Stress field complex variable function Superposition principle

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Teaching Thoughts of Mathematics,Information and Control Courses

Teaching Thoughts of Mathematics,Information and Control Cou...

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1st International Conference on Management, Education and Social Science (ICMESS 2017)

作者： Xueyan Lin Qiqi Song Automation School Beijing University of Posts and Telecommunications

ISBN: (纸本)9781510842274

The purpose of this paper is to coordinate the relationship between the set up time,content and teaching methods of mathematics,and information and control courses in automatic control *** achieve goals by research visits,questionnaires,students' feedback and other *** should teach complex variable function first,then Signal and System,and finally Automatic Control *** three courses are offered in the third,the fourth and the fifth semester respectively,which are 2 credits,2 credits and 4 credits required *** construct a reasonable knowledge on the content of teaching,the mathematics course focuses on the mathematical foundation and method,the information course focuses on the nature and application of the three transformations,strengthen their application in the field of automatic *** control course focuses on the feedback,analysis and correction of the three performance indexes of the three major mathematical models in three analysis *** the teaching methods MATLAB will be applied to these three courses teaching,to stimulate students' learning interest and improve teaching effectiveness.

关键词： Automatic Control Principle Signals and Systems complex variable function Curriculum integration and optimization Teaching thoughts

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Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

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Journal of Central South University 2014年第5期21卷 2074-2082页

作者：吴庆良吕爱钟高永涛吴顺川张宁 Key Laboratory for Efficient Mining and Safety of Metal Mine of Ministry of Education(University of Science and Technology Beijing) Institute of Hydroelectric and Geotechnical Engineering North China Electric Power University

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be *** for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common *** analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is *** power series method of complex function is *** stress analytical solution is obtained with the assumption that two layers of a cylinder are fully *** distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are *** example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous *** that way,stress concentration at the inner surface can be alleviated and the stress distribution is more *** is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

关键词： thick-walled cylinder stress analytical solution complex variable function non-uniform distributed pressure stressconcentration combination of different elastic moduli

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A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks

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INTERNATIONAL JOURNAL OF FATIGUE 2012年第1期35卷 2-9页

作者： Zhao, Jinfang Xie, Liyang Liu, Jianzhong Zhao, Qun Northeastern Univ Sch Mech Engn & Automat Shenyang Peoples R China Beijing Inst Aeronaut Mat Beijing Peoples R China Shenyang Inst Engn Dept Mech Engn Shenyang Peoples R China

Multiple site damage is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor of an infinite plate containing multiple hole-edge cracks was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve stress intensity factor problems on multiple holes. The equivalent crack is introduced to modify the method. Some numerical examples of an infinite plate containing two hole-edge cracks are examined by the method. By comparing the analytical and finite element analysis results it was realized that the analytical results are accurate and reliable. This modified analytical method is easier to apply than some traditional analytical methods and can provide stress intensity factor solutions for an infinite plate containing a random distribution of multiple hole-edge cracks. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Multiple site damage complex variable function Equivalent crack Analytical method Stress intensity factor

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A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks

A method for stress intensity factor calculation of infinite...

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2nd International Conference on Advances in Product Development and Reliability (PDR)

关键词： Multiple site damage complex variable function Equivalent crack Analytical method Stress intensity factor

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Green's function for T-stress of semi-infinite plane crack

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Applied Mathematics and Mechanics(English Edition) 2011年第8期32卷 973-980页

作者：崔元庆杨卫仲政 School of Aerospace Engineering and Applied Mechanics Tongji University Office of the Presidents Zhejiang University

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

关键词： Green’s function T-stress complex variable function semi-infinite crack fracture mechanics

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