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4th International Conference on Mechanical, Manufacturing and Plant Engineering (ICMMPE)

作者： Patel, Nirav P. Sharma, Dharmendra S. Dhari, Rahul Singh Pandit Deendayal Petr Univ Sch Technol Dept Mech Engn Gandhinagar 382007 Gujarat India Maharaja Sayajirao Univ Baroda Fac Technol & Engn Mech Engn Dept Vadodara 390002 Gujarat India

ISBN: (纸本)9789811382970;9789811382963

This article presents the analytical investigation of stress concentration factor around the circular and square hole in an infinite carbon/epoxy plate at four different temperatures of 23, 60, 90, and 120 degrees C. The micromechanics model is executed in conjunction with a complex variable approach to calculate the stress distribution around these cut-outs considering biaxial and uniaxial loading. The carbon fibers are assumed to be thermal insensitive materials and elastic properties of epoxy are defined at various temperatures. The influences of temperatures, fiber angles and stacking sequence on maximum stress concentration factor are stated. The results show that the values of the stress concentration factor are highly affected by these parameters. The present article will serve as a tool for designers who wish to study the behavior of composites at various temperatures.

关键词： complex variable method Circular hole Square Hole Stress concentration Temperature

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General solution of stress field in exponential functionally graded material plates containing a quasi-rectangular cutout

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JOURNAL OF COMPOSITE MATERIALS 2019年第3期53卷 405-421页

作者： Jafari, Mohammad Chaleshtari, Mohammad Hossein Bayati Abdolalian, Hamid Shahrood Univ Technol Fac Mech & Mechatron Engn Shahrood Semnan Iran Iran Univ Sci & Technol Sch Mech Engn Tehran Iran Shahrood Univ Technol Mech Engn Dept Shahrood Semnan Iran

In this paper, using an analytic technique based on complex variable method, the stress resultants and moments in infinite functionally graded plates with rectangular cutout under uniaxial tensile load are investigated. The mechanical properties of the functionally graded plate are assumed to change exponentially. The effect of different parameters such as cutout orientation, aspect ratio of the cutout, and cutout corner curvature on the distribution of stress resultants and moments is investigated. To verify the accuracy of the presented analytical method, its results are compared with the numerical results obtained from finite element modeling in ABAQUS. The comparisons demonstrate a good level of agreement between the obtained numerical and analytical results. According to the results, the above parameters have a significant impact on the distribution of stress resultants and moments around the cutout, and the load-bearing capacity of the functionally graded plates with cutouts can be improved by careful selection of these parameters.

关键词： Stress resultants and moments rectangular cutout exponential functionally graded material plate complex variable method conformal mapping

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Effective in-plane stiffness of unidirectional periodic nanoporous materials with surface elasticity

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2019年第4期70卷 1-11页

作者： Yang, Hai-Bing Wang, Shuang Yu, Chuanbin South China Univ Technol Sch Civil Engn & Transportat Dept Mech Engn Guangzhou 510641 Guangdong Peoples R China Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China

In this paper, the in-plane effective elastic properties of a porous material with periodic nanoscale holes of arbitrary shapes are investigated. A square representative unit cell (RUC) with a central hole is analysed for the original structure. On the edges of the RUC, proper periodic displacement boundary conditions are imposed. On the surfaces of the holes, the stress boundary condition is formulated through the Gurtin-Murdoch surface elasticity model. The problem is finally solved via the complex variable techniques, like superposition principle, conformal mapping, series expansion and collocation methods. Numerical examples for two common shapes, circle and square, of holes are presented. The results show that the in-plane effective properties of the structure are significantly influenced by the volume fraction (VF), size, shape of the holes, along with the surface elasticity. Specifically, a decrease in the VF or an increase in the size of the holes can lead to an increase in most of the effective moduli of the structure;a structure with circular holes has overall larger effective moduli than a structure with square holes;the surface elasticity can play a dominant role for certain effective moduli.

关键词： Effective stiffness Periodic nanoscale holes Arbitrary shape complex variable method Surface elasticity

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Elastic analytical solution of shallow tunnel owing to twin tunnelling based on a unified displacement function

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APPLIED MATHEMATICAL MODELLING 2019年 68卷 422-442页

作者： Kong, Fanchao Lu, Dechun Du, Xiuli Shen, Chenpeng Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing 100124 Peoples R China

A unified displacement function is used as the displacement boundary condition of the cross-section of each tunnel, which can be used to capture the asymmetrical deformation behaviors about the horizontal and vertical center line. complex variable method is adopted to obtain the analytical solution of a single tunnel. Based on the Schwartz alternating method, the analytical solution of twin tunnels is obtained and the correctness of the analytical solution of twin tunnels is verified. A series of analyses are carried out to investigate the effects of the displacement boundary condition of the tunnel cross-section and the distance of twin tunnels on the ground surface settlement trough curve and the ground displacement field. Based on the proposed method, the parameters of displacement mode of the cross-section of twin tunnels are calibrated through field monitoring data of the Bangkok Subway Tunnel project, and the displacement field of the whole ground are analyzed. The proposed method can provides guidance in the conceptual stage of the design process of twin tunnels. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Analytical Solution of twin tunnels Unified displacement function complex variable method Schwartz alternating method Analyses of ground displacement field

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Interaction between two nanoscale elliptical holes with surface tension

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MATHEMATICS AND MECHANICS OF SOLIDS 2019年第5期24卷 1556-1566页

作者： Wang, Shuang Gao, Cun-Fa Chen, Zeng-Tao Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Jiangsu Peoples R China Univ Alberta Dept Mech Engn Edmonton AB T6G 1H9 Canada

In this paper, the plane problem of two elliptical nanoscale holes with surface tension is investigated. Firstly, the basic equations are given via the complex variable methods. Then, the stress boundary condition caused by surface tension is derived through the integral-form Gurtin-Murdoch model. The problem is finally solved by the conformal mapping along with the series expansion methods. The results show that the stress field decreases as the two holes become further away from each other. When the distance between the two holes is more than three times the sum of their sizes, the interaction between the two holes can be neglected. In addition, the stress field is greatly influenced by the orientation, aspect ratio and size of the holes. The positions of the maximum hoop stress are also discussed. When the two elliptical holes are put close horizontally, the hoop stress around one hole usually obtain its maximum at the endpoint close to the other hole. However, if one elliptical hole is not horizontal, the hoop stress around it will no longer attain its maximum at the endpoints. Another exception is that when one elliptical hole becomes larger, the hoop stress around the smaller hole would tend to achieve a local minimum at the endpoint close to the larger hole.

关键词： Plane problem two elliptical holes nanoscale surface tension complex variable method

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Analytic stress solution for a circular tunnel in half plane with a concentrated force

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MATHEMATICS AND MECHANICS OF SOLIDS 2019年第12期24卷 3862-3879页

作者： Cai, Hui Lu, Ai-zhong Ma, Yao-cai North China Elect Power Univ Renewable Energy Sch Inst Hydroelect & Geotech Engn 2 Beinong Rd Beijing 102206 Peoples R China

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

关键词： Analytic solution half plane concentrated force complex variable method stress tunnel

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An Analytical Solution for an Arbitrary Cavity in an Elastic Half-Plane

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ROCK MECHANICS AND ROCK ENGINEERING 2019年第11期52卷 4509-4526页

作者： Zeng, Gui-sen Cai, Hui Lu, Ai-zhong North China Elect Power Univ Inst Hydroelect & Geotech Engn 2 Beinong Rd Beijing 102206 Peoples R China Guizhou Power Grid Co Ltd Elect Power Res Inst Guiyang 550002 Guizhou Peoples R China

The complex variable method is used for an analytical solution for an arbitrary cavity in a homogeneous elastic half-plane. Proposing a method for solving the coefficients of the function by conformally mapping the region that contains an arbitrary cavity onto a circular ring utilizing a mapping function, which can be used for arbitrary shape cavity. Considering the stress-free condition of the upper surface, the relationship between two analytic functions is derived;consequently, the problem of solving two analytic functions is attributed to solving one analytic function, and the solve process for the analytic function in general case is given in detail, finally, achieving the solution of an arbitrary shape cavity in an elastic half-plane. The effects of cavity shape and depth were analyzed to the required terms of analytic function under a given accuracy. Examples for a vertical-wall semicircle cavity and a horseshoe cavity are given through the present method, and verification example is given by ANSYS software.

关键词： Elastic half-plane Analytical solution complex variable method Mapping function Arbitrary cavity

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Analytic stress solutions for a lined circular tunnel under frictional slip contact conditions

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2019年 75卷 10-20页

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

The contact condition on the interface between the lining and the surrounding rock is assumed to be frictional slip contact. The state of the minimum relative sliding on the interface is considered as the true working state of the lining. The mechanical process of the support delay is taken into consideration, and the stress analytic solutions for a lined circular tunnel subjected to in situ stress and internal water pressure are derived based on the complex variable method and optimization theory. The analytic solutions are verified by finite element method. Under different friction coefficients and lateral pressure coefficients, the distributions of the tangential stresses along the inner and outer boundaries of the lining, the contact stresses and the tangential displacement discontinuity value along the interface are given. There exists a threshold of the friction coefficient that distinguishes the cases of the perfect bonding contact and the frictional slip contact, which is related to the lateral pressure coefficient and the material parameters.

关键词： Tunnel Support delay Frictional slip boundary complex variable method Optimization method Stress analytic solutions

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A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses

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COMPTES RENDUS MECANIQUE 2019年第2期347卷 181-190页

作者： Wang, Xu Chen, Liang Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghai 200237 Peoples R China Univ Alberta Dept Mech Engn 10-203 Donadeo Innovat Ctr Engn Edmonton AB T6G 1H9 Canada

We consider the anti-plane shear deformation of a three-phase inhomogeneity-coatingmatrix composite containing a coated non-elliptical inhomogeneity whose surrounding matrix is subjected to the action of a screw dislocation and uniform remote anti-plane shear stresses. Our objective is to establish conditions under which the inhomogeneity maintains an internal uniform stress field. Our analysis, which is based on a carefully chosen conformal mapping function, clearly indicates that such an internal uniform stress distribution can be achieved independently of the action of the screw dislocation, which influences the shape of the inhomogeneity depending on its proximity to the dislocation. In fact, we find that when the screw dislocation is located far from the coated inhomogeneity, the corresponding material interfaces become two confocal ellipses as reported previously in the literature. A simple criterion for the convergence of the series in the conformal mapping function is established. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

关键词： Conformal mapping complex variable method Anti-plane elasticity Coating Non-elliptical inhomogeneity Internal uniform stress field

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Closed-Form Solution to the Poromechanics of Deep Arbitrary-Shaped Openings Subjected to Rock Mass Alteration

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2020年第12期20卷

作者： Dong, Xiangjian Karrech, Ali Basarir, Hakan Elchalakani, Mohamed Qi, Chongchong Univ Western Australia Dept Civil Environm & Min Engn 35 Stirling Hwy Crawley WA 6009 Australia Norwegian Univ Sci & Technol Dept Petr Geosci Trondheim Norway

The aim of this paper is to propose a closed-form solution to the poromechanics problem of stress and pore pressure distribution around noncircular openings at great depth subjected to hydrostatic water pressure and far-field geostresses. The problem is solved by superposing the effects of fluid and solid skeleton obtained over simple circular geometries and generalizing the obtained expression to various geometries of mined ore bodies using complex variable functions and conformal mapping techniques. The principal stresses obtained analytically over the opening boundary and within the domain are compared with the results of finite-element analysis to verify the proposed approach. The comparison conducted for a representative noncircular opening indicates good agreement between the analytical and numerical methods. Hence, a parametric study is used to investigate in detail the stress variation under different opening dimensions, heterogeneous initial total stress conditions, and far-field pore pressure values. The proposed solution could be instrumental in the design of underground openings and deep mass alterations (that include local anthropogenic damage zones). It could also be used to provide reinforcement solutions where stresses can reach the mechanical stability thresholds.

关键词： Closed-form solution Arbitrary-shaped opening complex variable method Deep excavation

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