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Applied Mathematics and Mechanics(English Edition) 2023年第3期44卷 411-430页

作者： Sha XIAO Zhongqi YUE Key Laboratory of Urban Security and Disaster Engineering of China Ministry of Education Beijing University of TechnologyBeijing 100124China Department of Civil Engineering The University of Hong KongHong KongChina

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse *** FGMs are approximated with n-layered *** of the n-layered materials is homogeneous and transversely *** complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel *** ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical *** singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic *** results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

关键词： functionally graded material(FGM) transverse isotropy elasticity closedform singular solution Green's function point load vector

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

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Acta Mechanica Sinica 2015年第5期31卷 601-626页

作者： Wei-Qiu Chen Department of Engineering Mechanics Zhejiang University

Significant progress has been made in mixed boundary-value problems associated with three-dimensional（3D） crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic *** include material anisotropy and multifield coupling,two typical characteristics of most current multifunctional *** this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of *** ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential *** are particularly interested in crack and contact problems with certain nonlinear *** is also placed on the coupling between the temperature field（or the like） and other physical fields（e.g.,elastic,electric,and magnetic fields）.We further highlight the practical significance of 3D contact solutions,in particular in applications related to modern scanning probe microscopes.

关键词： Crack Contact Mixed boundary-value problem transverse isotropy Multifield coupling Potential theory Exact solution Scanning probe microscope

Interaction between transverse isotropy rock slope and supporting structure

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Interaction between transverse isotropy rock slope and suppo...

Pure Bending of Simply Supported Circular Plate of Functionally Graded Magneto-Electro-Elastic Material with transverse isotropy

The 9th National Conference on Rheology

作者：段靓靓方理刚 College of Civil Engineering Architecture and MechanicsCentral South University of Forestry and Technology School of Architectural and Civil Engineering Central South University

＜正＞In order to study the interaction between transverse isotropy rock mass and supporting structure,the laboratory tests for rock sampled from the slope at expressway project were carded out,and the parameters of elasticity for transverse isotropic rock were determined by the uniaxial compression tests for rock sample with different strike of stratification ***,based on the relationship of stress—stain for transverse isotropic rock mass,the analytical model was established for the interaction between transverse isotropic rock mass and frame beam with pre-stressed anchor ***,the conception of the best anchorage-angle in pre-stressed anchor cable was *** last,the parameters of the interaction between transverse isotropy rock mass and frame beam with pre-stressed anchor cable were investigated by finite element method,and the best anchorage-angle in pre-stressed anchor cable was *** rules of the influence of the directivity of stratification plane on supporting structure were *** results show that the analytical model and numerical method on the design of pre-stressed anchor cable with frame beam supporting for transverse isotropy rock slope are reasonable and reliable in practical engineering design.

关键词： rock mechanics transverse isotropy pre-stressed anchor cable frame beam finite element analysis anchorage angle

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Pure Bending of Simply Supported Circular Plate of Functiona...

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

第二届全国压电和声波理论及器件技术研讨会

作者： Xiangyu Li,Haojiang Ding,Weiqiu Chen (Department of Civil Engineering,Zhejiang University,Hangzhou 310027,P.R.China)

This paper considers the pure bending problem of simply supported transversely isotropic magneto-electro-elastic circular plates with material coefficients being arbitrary functions of z,the thickness *** expanding the displacement,electric potential and magnetic potential into suitable polynomials in r,the radial coordinate,with the coefficients being the undetermined functions of z,the partial differential equations governing the axisymmetric problems are converted into a set of ordinary differentials,which can be solved by integrating step by step and incorporating with the boundary conditions.A 3D analytical solution for the pure bending problem,which can be degenerated into the homogeneous cases,is thus obtained.A numerical example is present to show the influence of the material inhomogeneity on the elastic,elastic and magnetic fields in the simply supported circular plate of functionally graded magneto-electro-elastic material wtih transverse isotropy.

关键词： transverse isotropy Functionally graded magneto-electro-elastic materials Pure bending problem Simply supported plate Axisymmetric deformation

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Petroleum Science 2024年第1期21卷 221-243页

作者： Zheng-Qian Ma Xing-Yao Yin Zhao-Yun Zong Yuan-Yuan Tan Ya-Ming Yang National Key Laboratory of Deep Oil and Gas China University of Petroleum(East China)Qingdao266580ShandongChina School of Geosciences China University of Petroleum(East China)Qingdao 266580ShandongChina Pilot National Laboratory for Marine Science and Technology(Qingdao) Qingdao266200ShandongChina

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is ***,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the ***,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical *** on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic ***,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked *** analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity ***,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip *** increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip *** comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness ***,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the or

关键词： Effective elastic property Tilted crack transverse isotropy Analytical solution Crack opening displacement

A local homogenization approach for simulating the reinforcement effect of the fully grouted bolt in deep underground openings

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International Journal of Mining Science and Technology 2022年第2期32卷 247-259页

作者： Dingping Xu Xiuyang Liu Quan Jiang Shaojun Li Yangyi Zhou Shili Qiu Fei Yan Hong Zheng Xiang Huang State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhan 430071China University of Chinese Academy of Sciences Beijing 100049China Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines Northeastern UniversityShenyang 110819China

Fully grouted bolts are a key component of the support system for underground *** considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is *** study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock *** the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element *** RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt *** RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic *** L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and *** the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is *** results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock *** L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.

关键词： Fully grouted bolt Reinforcement effect Representative volume transverse isotropy Homogenization

Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2012年第1期13卷 9-17页

作者： Zhi-yong AI Nai-rui CANG Jie HAN Key Laboratory of Geotechnical and Underground Engineering of MOE Department of Geotechnical Engineering Tongji University Shanghai 200092 China Department of Ciwl Environmental and Architectural Engineering The University of Kansas Lawrence KS 66045 USA

This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric *** on the basic constitutive equations and the HU Hai-chang's solutions for transversely isotropic elastic media,the state vectors of a multi-layered transversely isotropic medium were *** the state vectors,an analytical layer element for a single layer(i.e.,a symmetric and exact stiffness matrix) was acquired in the Hankel transformed domain,which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential *** global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer *** solving the algebraic equations of the global stiffness matrix which satisfy the boundary conditions,the solutions for multi-layered transversely isotropic media in the Hankel transformed domain were *** actual solutions of this problem in the physical domain were acquired by inverting the Hankel *** paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.

关键词： transverse isotropy Analytical layer element Multi-layered elastic medium Axisymmetric loading Hankel transform

Exact simulation for direction-dependent large elastic strain responses of soft fibre-reinforced composites

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Applied Mathematics and Mechanics(English Edition) 2023年第9期44卷 1497-1510页

作者： Huifeng XI Guicheng ZHAO OBRUHNS Siyu WANG Heng XIAO School of Mechanics and Construction Engineering MOE Key Lab of Disaster Forecast and Control in EngineeringJinan UniversityGuangzhou 510632China Institute of Mechanics Ruhr-University BochumBochum D-44780Germany

An explicit form of the elastic strain-energy function for direction-dependent large elastic strain behaviors of soft fiber-reinforced composites is first presented based upon a decoupled approach for simulating complex nonlinear coupling *** this form,the exact closed-form solutions are then obtained for the uniaxial tension responses in the fiber and cross-fiber *** such exact solutions,the issue of simultaneously simulating strongly coupling nonlinear responses in the fiber and cross-fiber directions may be reduced to the issue of separately treating each decoupled uniaxial stress-strain response,thus bypassing usual complexities and uncertainties involved in identifying a large number of strongly coupled adjustable *** numerical examples given are in good agreement with the experimental data for large strain responses.

关键词： soft solid fiber-reinforced composite large elastic strain transverse isotropy strain-energy function logarithmic strain decoupling approach

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

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Science China(Physics,Mechanics & Astronomy) 2015年第8期58卷 49-57页

作者： LIU Le LIN WeiJun ZHANG HaiLan WANG XiuMing State Key Laboratory of Acoustics Institute of Acoustics Chinese Academy of Sciences

A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.

关键词： deviated borehole transverse isotropy acoustic mode waves dispersion curve sensitivity analysis

Analysis of stresses at the center of transversely isotropic Brazilian disk

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Journal of Rock Mechanics and Geotechnical Engineering 2023年第3期15卷 618-629页

作者： Ali Aminzadeh Florian Amann Institute of Geology of the Czech Academy of Sciences PragueCzech Republic Chair of Engineering Geology RWTH Aachen UniversityAachenGermany

This article presents the stresses at the center of a Brazilian disk(BD)for transversely isotropic *** is shown that the solution of stresses at the center of an anisotropic disk is a function of the disk radius and the magnitude of applied load,as well as the material orientation with respect to the load axis and two dimensionless ratios with specific physical meanings and *** two dimensionless parameters are the ratios of Young’s modulus and apparent shear modulus,although the ratio of apparent shear modulus will be eliminated if the Saint-Venant assumption is *** finite element simulations are carried out to find the stresses at the disk center concerning the material orientation and the two dimensionless ***,an approximate formula obtained from analytical results,previously proposed in the literature for solving the tensile and compressive stresses at the disk center,is re-written and simplified based on these new *** results of the approximate formula fitted to the analytical results are compared to those obtained from numerical solutions,suggesting a good agreement between the numerical and analytical *** approximate equation for the shear stress at the disk center is also formulated based on the numerical ***,the influence of the assumptions for simplification of the proposed formula for the tensile,compressive,and shear stresses at the disk center is discussed,and simple and practical equations are proposed as estimations for the stresses at the center of the BD specimen for low to moderate anisotropic *** highly anisotropic rocks,the reference plots can be used for more accuracy.

关键词： Brazilian test transverse isotropy Rock anisotropy Anisotropic disk Tensile stress Shear stress