Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008.     

各向同性和横观各向同性材料的统一点力解

本文根据横观各向同性弹性力学的通解获得了无限体的点力解，由它可以直接退化到各向同性情形的Ｋｅｌｖｉｎ解，利用这个点力解编制的边界元法程序，适用于横观各向同性材料也适用于各向同性材料，因此是真正的统一点力解。还用边界元法计算了两个数值例题。     

Slip-line field theory of transversely isotropic body

ＳＬＩＰ－ＬＩＮＥＦＩＥＬＤＴＨＥＯＲＹＯＦＴＲＡＮＳＶＥＲＳＥＬＹＩＳＯＴＲＯＰＩＣＢＯＤＹＲｕａｎＨｕａｉ－ｎｉｎｇ（阮怀宁）（ＨｅｈａｉＵｎｉｖｅｒｓｉｔｙ）ＮａｎｊｉｎｇＷａｎｇＷｅｉ－ｘｉａｎｇ（王维襄）（ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆ...     

Stress state of a transversely isotropic medium with an anisotropic inclusion. Arbitrary linear force field at infinity

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 7, pp. 25–35, July, 1991.     

General solutions of axisymmetric problems in transversely isotropic body

In this paper we solve axisymmetric problems by stress and deduce a series of valuable general solutions by unified method. Some of them are well-known solutions, and others have not appeared in the literature. We also prove the completeness of these general solutions.     

POINT FORCE SOLUTION FOR A TRANSVERSELY ISOTROPIC ELASTIC LAYER

ＰＯＩＮＴＦＯＲＣＥＳＯＬＵＴＩＯＮＦＯＲＡＴＲＡＮＳＶＥＲＳＥＬＹＩＳＯＴＲＯＰＩＣＥＬＡＳＴＩＣＬＡＹＥＲＰＯＩＮＴＦＯＲＣＥＳＯＬＵＴＩＯＮＦＯＲＡＴＲＡＮＳＶＥＲＳＥＬＹＩＳＯＴＲＯＰＩＣＥＬＡＳＴＩＣＬＡＹＥＲ￥ＤｉｎｇＨａｏｊｉａｎｇ（丁...     

Circular crack in a transversely isotropic piezoelectric space under point forces and point charges

In this paper, two kinds of circular crack including external circular crack and penny-shaped crack in a transversely isotropic piezoelectric space are considered. Firstly, we obtain the solution to the problem of an external circular crack in a transversely isotropic piezoelectric space subjected to antisymmetric normal point forces and point charges. Based on this, the solution of one-sided loading of an external circular crack is constructed. Secondly, the real shape of an external circular crack and the opening displacement of a penny-shaped crack under an arbitrary point force and point charge are further obtained. At last, the results are presented in a graphical form. The project supported by the National Natural Science Foundation of China (19872060 and 69982009) and the Postdoctoral Foundation of China     

Effective thermal conductivity of transversely isotropic media with arbitrary oriented ellipsoïdal inhomogeneities

The objective of this work is to investigate the thermal conduction phenomena in transversely isotropic geomaterials or rock-like composites with arbitrary oriented ellipsoïdal inhomogeneities of low aspect ratio. Based on the evaluation of the Green function, we provide here new expressions for the interaction tensor whose knowledge permits to obtain the concentration tensor of the polarization field used itself to evaluate the effective thermal conductivity tensor by homogenization. Some particular cases of the obtained general solution are equally presented, in order to validate the developed formalism. The obtained results are next used to study the effect of matrix anisotropy, pores systems and microstructure-related parameters on the overall effective thermal conductivity in transversely isotropic rocks. A two-step homogenization scheme is developed for the prediction of the initial anisotropy effects and to test the ability of the proposed model in the evaluation of effective thermal conductivity. With the help of an Orientation Distribution Function (ODF) the anisotropy due to the pore systems is also accounted. Numerical applications and comparisons with available experimental data are finally carried out for a partially saturated Opalinus clay and an argillite which are both composed of an argillaceous matrix and multiple solid minerals constituents.     

Stress state of a transversely isotropic piezoceramic body with a spheroidal cavity

The exact solution is found to the three-dimensional electroelastic problem for a transversely isotropic piezoceramic body with a spheroidal cavity. The solutions of static electroelastic problems are represented in terms of harmonic functions. The case of stretching the piezoceramic medium at a right angle to the spheroid axis of symmetry is analyzed numerically. The dependence of the stress concentration factor on the geometry of the spheroid and the electromechanical characteristics of the material is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 92–105, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Wave propagation in transversely isotropic cylinders

Various approaches have been used for model1ing problems dealing with interaction of acoustic/elastic waves with transversely isotropic cylinders. The authors developed the first mathematical model for the scattering of acoustic waves from transversely isotropic cylinders [Honarvar, F., Sinclair, A.N., 1996. Acoustic wave scattering from transversely isotropic cylinders. Journal of the Acoustical Society of America 100, 57–63.]. In the current paper, this model is used for derivation of the frequency equations of longitudinal and flexural wave propagation in free transversely isotropic cylinders. Consistency of this model with the physics of the problem is demonstrated and a systematic solution to the corresponding equations is developed. Numerical results obtained for a number of transversely isotopic cylinders are used for verification of the mathematical model.     

Elastic contact between a sphere and a semi infinite transversely isotropic body

The problem is solved by using a Hankel transformation. The stress and displacement expressions are explicitly given for any point of the medium. Curves of numerical results are presented.     

《Elaticity of Transversely Isotropic Materials》一书评介

浙江大学土木系丁皓江教授和陈伟球教授及澳大利亚悉尼大学航空、机械与机电工程学院章亮炽教授的专著“Elasticity of Transversely Isotropic Ma- terials”(ISBN：1-4020-4033-4),2006年由Springer公司出版,该书是加拿大著名力学家G．M．L．Gladwell     

A point heat source on the apex of a transversely isotropic piezothermoelastic cone

We use the compact harmonic general solutions of transversely isotropic piezothermoelastic materials to construct the three-dimensional solutions of a steady point heat source on the apex of a transversely isotropic piezothermoelastic cone by four newly introduced harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. When the apex angle 2α equals to π, the solutions reduce to those of the semi-infinite body problem, which is called Green's function. Numerical results are given graphically by contours.     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.Work supported in part by National Science Foundation Grant INT-9106519.     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.     

Elastic fields in rotating transversely isotropic media

Representation of elastic fields in terms of scalar functions, which permit reducing the problems of determining these fields to determining scalar potentials, are generalized to the case of transversely isotropic media rotating at a constant angular velocity. Relations for calculating the parameters of surface acoustic waves (SAW) propagating in a rotating transversely isotropic halfspace with various directions of the medium material symmetry axis with respect to the half-space surface are given.     

Penny-shaped crack in transversely isotropic piezoelectric materials

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r ^−1/2) singularity. The project supported by the Natural Science Foundation of Shaanxi Province, China     

Shear modulus of transversely isotropic materials

A new and simple method is presented to determine the inde-pendent shear modulus of transversely isotropic material.Mathematical formulation,derivation and solution are given,and test apparatus and results are presented.The method wastested on one of such materials-Green River Formation oilshale.Comparisons wich other approximate results and acou-stical methods are made.Confirmation of the test methodwith materials having known shear moduli is also presented.     

Point forces and point charge applied to a circular crack in a transversely isotropic piezoelectric space

Interaction between an arbitrarily located and oriented point force and point charge with a circular crack is considered. Obtained are the exact expressions for the stress intensity factors (SIFs) k_j (j=1,2,3) and electric displacement intensity factor (EDIF) k_D; they are given in terms of elementary functions. The results are also presented in graphical form.     

An electric point charge moving along the poling direction of a transversely isotropic piezoelectric solid

The problem of an electric point charge moving constantly along the poling direction of a transversely isotropic piezoelectric solid is considered in a moving coordinate system, which moves together with the electric point charge. A general solution in the moving coordinate system is given, and all the field components, such as displacements, electric potential, stresses and electric displacements, can be concisely expressed in terms of four quasi-harmonic functions. We also present two examples to demonstrate the effect of the moving velocity on the values of _i. Once the general solution is given, the axisymmetric problem of a moving electric point charge can be easily solved. The explicit expressions of all the field components caused by the moving electric charge are presented, and the effect of the moving velocity on these field components is numerically investigated.