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ELASTIC FIELDS FOR A PARABOLIC HOLE ENDOWED WITH SURFACE EFFECTS

JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES 2020年第2期15卷 241-248页

作者： Wang, Xu Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn Shanghai Peoples R China Univ Alberta Dept Mech Engn 10-203 Donadeo Innovat Ctr Engn Edmonton AB Canada

We study the contribution of surface energy to the plane strain deformations of an isotropic elastic material with a parabolic hole. A closed-form full-field solution is derived using Muskhelishvili's complex variable formulation and the technique of conformal mapping. We also obtain the corresponding expressions for the stresses and displacements in the full-field arising solely from the influence of the surface effects. When the radius of curvature at the vertex of the parabola is reduced to the order of the square of the ratio of surface energy to the generalized stress intensity factor, the surface contribution is significant and cannot be disregarded.

关键词： surface effect blunt crack plane elasticity closed-form solution complex variable method

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Torsion of Circular Shaft with Elliptical Inclusions or Cracks

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Transactions of Nanjing University of Aeronautics and Astronautics 2021年第1期38卷 96-105页

作者： HUANG Cheng YIN Maoshu QI Xiao GUO Hun School of Aviation and Mechanical Engineering Changzhou Institute of TechnologyChangzhou 213032P.R.China Physical Power Division Shanghai Institute of Space Power-SourcesShanghai 200240P.R.China

This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable *** complex potentials are first derived for the shaft with N elliptical inclusions by introducing Faber series expansion,and then the shear stresses and torsional rigidity are *** the inclusions degenerate into cracks,the solutions for the intensity factors of stress are ***,several numerical examples are carried out to discuss the effects of geometry parameters,different shear modulus ratios and array-types of the elliptical inclusions/cracks on the fields of *** obtained results show that the proposed approach has advantages such as high accuracy and good convergence.

关键词： Saint-Venant’s torsion complex variable method Faber series

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Wave function expansion method for the scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2019年 106卷 389-396页

作者： Liu, Qijian Zhao, Mingjuan Liu, Zhongxian Hunan Univ Coll Civil Engn Changsha 410082 Hunan Peoples R China Hunan Univ Key Lab Bldg Safety & Energy Efficiency Minist Educ Changsha 410082 Hunan Peoples R China Delft Univ Technol Fac Civil Engn & Geosci NL-2600 GA Delft Netherlands Tianjin Key Lab Civil Struct Protect & Reinforcem Tianjin 300384 Peoples R China

A wave function expansion method for out-of-plane scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces is presented by using the plane elastic complex variable theory. The medium is composed of a semi-infinite homogeneous space with a circular cavity and a bonded exponentially graded half-space with a symmetrical circular cavity along the boundary interface. In terms of Helmholtz decomposition to the wave propagation equation, the stresses and displacements of the medium are expressed by the displacement potentials. The scattered waves by the boundary interface are assumed to transmit from the images of the origins of the respective two cavities. A conformal mapping function is introduced to convert the physical plane of two bonded semi-infinite spaces into two jointed concentric annular regions. The boundary value problem is formulated as a series of infinite algebraic equations. The convergence of the present solution is examined by investigating the variations of the solution results with the truncation of the series number. Parametric study shows that the interface displacements are almost independent to the inhomogeneous coefficient beta R of the right medium. The amplification of the interface displacement becomes great for high incident frequency and with the decreasing of the distance-to-radius ratio h/R. The distribution of stress concentration of the right cavity depends significantly on the inhomogeneous coefficient beta R, the distance-radius ratio h/R, the incident angle and frequency of the excitations.

关键词： Scattering of SH waves Wave function expansion method Two symmetrical circular cavities Exponentially graded material complex variable method

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On debonding at interface in the Eshelby's elliptical inclusion under remote loading

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ENGINEERING FRACTURE MECHANICS 2021年 255卷 107910-107910页

作者： Chen, Y. Z. Jiangsu Univ Div Engn Mech Zhenjiang 212013 Jiangsu Peoples R China

This technical note studies the debonding problem in the Eshelby's elliptical inclusion with remote stresses. Usually, if one inserts eigenstrains in the inclusion, the normal stress along the interface of matrix and inclusion is negative. In addition, if one increases the remote loading gradually, the normal negative stress along interface will be becoming vanishing. This limit loading for the remote stresses becomes the debonding loading. Two particular cases for debonding problem are solved in the present note.

关键词： Eshelny's inclusion complex variable method Debonding Closed form solution Numerical analysis

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Layout optimization of porous sound-absorbing material in mid-frequency vibro-acoustic systems

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JOURNAL OF FLUIDS AND STRUCTURES 2021年 100卷 103197-103197页

作者： Yu, Yang Zhao, Guozhong Ren, Shanhong Wang, Boping Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Hefei Univ Technol Sch Civil & Hydraul Engn Hefei Peoples R China Univ Texas Arlington Dept Mech & Aerosp Engn Arlington TX 76019 USA

In this paper, a new layout optimization technique is integrated with a statistical modal energy distribution analysis (SmEdA) model to obtain the optimal layout of a porous sound-absorbing material for noise control in mid-frequency vibro-acoustic systems. The considered optimization problem is minimizing the total energy of the internal acoustic cavity within the prescribed frequency range by reasonably positioning porous sound-absorbing material patches under a given volume constraint. The principle of SmEdA is based on the power balance between different modes of coupled structural and acoustic subsystems. A modal strain and kinetic energy (MSKE) method is employed to estimate the acoustic modal damping loss factors that are associated with the energy attenuation between different modes of the coupled subsystems. The developed real-valued optimization formulation provides the feasibility of adopting an accurate sensitivity analysis technique, the complex variable method (CVM). The effectiveness of the optimization procedure is demonstrated through a significant reduction in the total acoustic energy. Additionally, some conclusions with realistic significance are obtained: (a) The optimal material layout creates a more uniform distribution of modal energies in the SmEdA model;(b) The acoustic modes tend to move out of the prescribed frequency band through optimization. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Porous sound-absorbing material Layout optimization Mid-frequency Vibro-acoustic system Statistical modal energy distribution analysis complex variable method

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Circular inclusion problem of two-dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

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ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 2021年第12期101卷

作者： Zhai, Ting Ma, Yuan-Yuan Ding, Sheng-Hu Zhao, Xue-Fen Ningxia Univ Sch Math & Stat Yinchuan 750021 Ningxia Peoples R China Ningxia Univ Xinhua Coll Yinchuan 750021 Ningxia Peoples R China

The plane problem of two-dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two-dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two-dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

关键词： circular inclusion complex variable method interfacial rigid line Riemann boundary problem two-dimensional decagonal quasicrystals

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A Closed-Form Elastic Solution of Ground Response Curve for Noncircular Openings

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2021年第12期21卷 04021235-04021235页

作者： Yan, Q. Xu, B. S. Yuan, Y. Taiyuan Univ Technol Coll Civil Engn Taiyuan 030024 Shanxi Peoples R China Shanxi Transportat Technol Res & Dev Co Ltd Taiyuan 030024 Shanxi Peoples R China Shandong Univ Sch Qilu Transportat Jinan 250061 Shandong Peoples R China China Railway 14th Bur Grp 2nd Engn Co Ltd Tai An 271000 Shandong Peoples R China

Ground response curves (GRCs) can be used to characterize the evolution law of stress and displacement during tunnel excavation. In this study, an attempt is made to obtain the GRC and find the stress field for a noncircular tunnel using a complex variable method. The analytical solution of an elastic GRC for a noncircular tunnel with a complex geometry configuration is proposed, and the stress and displacement of the rock mass caused by tunnel excavation are provided. The proposed analytical solution for a noncircular tunnel is compared with the known solutions of circular openings by degenerating the proposed model. The proposed solution is compared with a quasi-two-dimensional calculation model using FLAC finite-difference code, as well as with the known solutions of circular openings by degenerating the proposed model. The results indicated good agreement with the analytical and numerical solutions, verifying the correctness of the derivation. Finally, the GRCs are investigated based on three key points. It illustrates that the stresses and displacements of the three key points are linear and that the predicted GRCs of three key points by both models are in general agreement, if the difference in gravity field between the two methods is not considered.

关键词： Noncircular opening Ground response curve complex variable method Conformal mapping

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Analytical solution of stress and displacement for a circular underwater shallow tunnel based on a unified stress function

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OCEAN ENGINEERING 2021年 219卷 108352-108352页

作者： Kong, Fanchao Lu, Dechun Du, Xiuli Li, Xiaoqiang Su, Cancan Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing Peoples R China

A unified stress function is represented in a Fourier series to capture the complex stress state of an underwater shallow tunnel perimeter. The first-order unified stress function is employed as stress boundary condition of the tunnel perimeter (SBCTP) to describe the non-symmetrical stress with respect to the horizontal and vertical centerlines of the tunnel. The mechanical analysis model of an underwater shallow tunnel is established. Combining the complex variable theory, the elastic analytical solution of the stress and displacement are obtained. The rationality of the elastic solution is verified by comparing the stress fields between the proposed method and the finite element method (FEM). Based on the obtained elastic solution, the fractional viscoelastic solution is determined by the correspondence principle. The time-dependent ground displacement are investigated considering the effect of stress release. A series of parameter analyses are carried out to discuss the ground vertical and horizontal stress distributions under the influences of SBCTPs.

关键词： Underwater shallow tunnel Unified stress function complex variable method Fractional viscoelastic analytical solution Stress and displacement field

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Interaction of collinear interface cracks between dissimilar one-dimensional hexagonal piezoelectric quasicrystals

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ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 2021年第11期101卷

作者： Hu, Keqiang Gao, Cunfa Zhong, Zheng Chen, Zengtao Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China Harbin Inst Technol Sch Sci Shenzhen 518055 Peoples R China Univ Alberta Dept Mech Engn Edmonton AB T6G 1H9 Canada

In this paper, the interaction of collinear interface cracks between dissimilar one-dimensional (1D) hexagonal quasicrystals with piezoelectric effect under anti-plane shear and in-plane electric loading has been studied. By using complex variable method the mixed boundary value problem for the interface cracks was reduced to the solution of Riemann-Hilbert problem. Analytic full-field solution for phonon and phason stresses, electric fields, electric displacement in the cracked bi-materials has been obtained based on the electrically permeable crack model. The electric field and electric displacement inside the interface cracks are found to be nonlinearly distributed under line loadings. The field intensity factors of the interface cracks depend on both the mechanical and electric load for the line loading case, but the field intensity factors depend only on mechanical loading when the uniform loadings are applied at infinity. The investigation of the SIFs of neighboring interface cracks has been used to predict possible crack propagation. It is found that when the neighboring cracks are close enough, the inner crack tips are more likely to propagate and when the neighboring cracks are far away from each other, the outer crack tip of the bigger crack has more possibility to propagate.

关键词： complex variable method crack propagation interface crack one-dimensional quasicrystal materials Riemann-Hilbert problem

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The Analytical Study of Stress Concentration Factor in an Infinite Plate at Various Temperatures 4th

The Analytical Study of Stress Concentration Factor in an In...

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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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