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Applied Mathematics and Mechanics(English Edition) 2016年第6期37卷 683-694页

作者： Bo YANG Weiqiu CHEN haojiang ding Department of Civil Engineering Zhejiang Sci-Tech University State Key Laboratory of CAD & CG Zhejiang University Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Soft Matter Research CenterDepartment of Engineering MechanicsZhejiang UniversityYuquan Campus Department of Civil Engineering Zhejiang University

The problem of a transversely isotropic functionally graded material （FGM） plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional （3D） general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.

关键词： plate functionally graded material (FGM) welded circular inclusion,analytical solution

INDENTATION OF A TRANSVERSELY ISOTROPIC PIEZOELECTRIC HALF-SPACE BY A RIGID SPHERE

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Acta Mechanica Solida Sinica 1999年第2期12卷 114-120页

作者： Chen Weiqiu ding haojiang Zhejiang Univ Dept Civil Engn Hangzhou 310027 Peoples R China

This paper exactly analyzes the problem of a rigid sphereindenting a transversely isotropic piezoelectric half-space. Thepotential theory method is employed and generalized to included thepiezoelec- tric effect. By using the previous results of elasticity,an exact solution is derived. It is found that all the elastoelectricvariables can be expressed in terms of elementary functions.

关键词： general solution potential theory rigid sphere

AN ORTHOTROPIC PIEZOELECTRIC ELLIPSOID IN A CENTRIFUGAL FIELD

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Acta Mechanica Solida Sinica 2000年第4期13卷 346-352页

作者： Hou Penfei ding haojiang Zhejiang Univ Dept Civil Engn Hangzhou 310027 Peoples R China

A rotating ellipsoid composed of an orthotropic piezoelectricmaterial (2mm) are considered, and the stress and electricdisplacement fields in this rotating ellipsoid are obtained exactlyand completely. The solutions of the same problem for transverselyisotropic piezoelectric material (6 mm) are also given byDegenerating above results. At last, numerical examples for fourkinds of media are illustrated in figures for Comparison.

关键词： orthotropy transverse isotropy piezoelectric ellipsoid centrifugalfield

THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

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Acta Mechanica Solida Sinica 2005年第3期18卷 265-271页

作者： Hou Pengfei Pan Xiaoping ding haojiang Department of Engineering Mechanics Hunan University Changsha 410082 China Bureau of Traffic Linan 311300 Zhejiang Province China Department of Civil Engineering Zhejiang University Hangzhou 310027 China

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.

关键词： half-plane crack piezoelectric space intensity factor resultant source

BENding OF FUNCTIONALLY GRADED PIEZOELECTRIC RECTANGULAR PLATES

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Acta Mechanica Solida Sinica 2000年第4期13卷 312-319页

作者： Chen Weiqiu ding haojiang Key Laboratory of Solid Mechanics of MOE Tongji UniversityShanghai 200092China Department of Civil Engineering Zhejiang UniversityHangzhou 310027China

By introducing two displacement functions as well as two stressfunctions, two independent state equations with variable coefficientsare derived from the three-dimensional theory equations of piezo-elasticity for transverse isotropy. A laminated approximation is usedto transform the state equations to those with constant coefficientsin each sub-layer. The bending problem of a functionally gradedrectangular plate is then analyzed based on the state *** results are presented and the effect of material gradi- entindex is discussed.

关键词： functionally graded piezoelectric material transverse isotropy statespace method

The Boundary Contour Method for Half-Plane Piezoelectric Media

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上海交通大学学报 2004年第Z2期38卷 176-181页

作者： WANG Guoqing WANG Qing LIU Zhengxing ding haojiang Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Civil Engineering Zhejiang Univ. Hangzhou310027 China

This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.

关键词： boundary contour method piezoelectricity half-plane shape function

Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference

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Science China(Physics,Mechanics & Astronomy) 2008年第8期51卷 1116-1125页

作者： LI XiangYu ding haojiang CHEN WeiQiu Department of Civil Engineering Zhejiang UniversityHangzhou 310027China

This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms,five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form,which still involve four undetermined integral constants,through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence,three-dimen sional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness,and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis,and the effect of material inhomogeneity on the elastic and electric fields is discussed.

关键词： functionally graded material piezoelectric material circular plates uniform electric potential direct displacement method

A THEORETICAL SOLUTION OF CYLINDRICALLY ISOTROPIC CYLINDRICAL TUBE FOR AXISYMMETRIC PLANE STRAIN DYNAMIC THERMOELASTIC PROBLEM

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Acta Mechanica Solida Sinica 2001年第4期14卷 357-363页

作者： ding haojiang Wang Huiming Chen Weiqiu Department of Civil Engineering Zhejiang UniversityHangzhou 310027China Department of Mechanics Zhejiang UniversityHangzhou 310027China

A dynamic thermoelastic solution of a cylindrically isotropiccylindrical tube or solid cylinder with axisymmetric planedeformations is developed. Since there exist thermal boundaryconditions and trac- tions on the two surfaces of a cylindrical tube,the problem under consideration is with inhomogeneous bound- aryconditions. Therefore we introduce a special function to transformthe inhomogeneous boundary conditions to homogeneous ones for anunknown function. They by using the method of separation ofvariables, the un- known function can be expressed as themultiplication series of Bessel functions and unknown time functions.

关键词： ding haojiang Wang Huiming Chen Weiqiu

FREE AXISYMMETRIC VIBRATION OF TRANSVERSELY ISOTROPIC LAMINATED CIRCULAR PLATES

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Acta Mechanica Solida Sinica 1998年第3期11卷 209-215页

作者： ding haojiang Xu Rongqiao Chen Weiqiu Zhejiang Univ Dept Civil Engn Hangzhou 310027 Peoples R China Tongji Univ Dept Geotech Engn Shanghai 200092 Peoples R China

Based on the three dimensional elastic theory, the state equationfo the axisymmetric free vibration of transversely isotropic circularplates is established. Taking the advantage of finite Hankeltransform, tow exact solutions are derived for two boundaryconditions, i.e. the rigid-slipping boundary and elastic simplysupported boundary. Finally, numerical results are presented and com-pared with those of FEM.

关键词： axisymmetric vibration transversely isotropic circular plate

A GENERAL SOLUTION FOR STATIC PIEZOTHERMOELASTIC PROBLEMS OF CRYSTAL CLASS 6mm SOLIDS

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Acta Mechanica Solida Sinica 1999年第3期12卷 189-197页

作者： ding haojiang Guo Fenglin Hou Pengfei Zhejiang Univ Dept Civil Engn Hangzhou 310027 Peoples R China Tongji Univ Dept Geotech Engn Shanghai 200092 Peoples R China

In this paper, a general solution for three-dimensional staticpiezothermoleastic prob- lems of crystal class 6mm solids ispresented. The general solution involves four piezoelastic potentialfunctions and a piezothermoelastic potential function, of which fourpiezoelastic potential functions are governed by weighted harmonicdifferential equations. Compared with the general solution given byAshida et al., in which seven potential functions are introduced, thegeneral solution proposed in the Present paper is more rigorouslyderived.

关键词： general solution piezothermoelasticity thermoelasticity