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GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY "HARMONIC FUNCTIONS 认领 引用 被引量：3
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作者 丁皓江 王国庆 陈伟球 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第8期757-764,共8页
First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the gener... First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three 'harmonic functions'. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane. 展开更多
关键词 piezoelectric media plane problem general solution wedge
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A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid 认领 引用 被引量：2
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作者 Xiang-Yu Li Si-Cong Ren Qi-Chang He 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2015年第1期32-44,共13页
A general solution for 3D Stokes flow is given which is different from, and more compact than the exist ing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution ... A general solution for 3D Stokes flow is given which is different from, and more compact than the exist ing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape trans lating along the direction normal to it in an unbounded fluid. The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the ve locity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and ellip tic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences. 展开更多
关键词 Stokes flow 3D general solutions Potentialtheory method Circular plate Elliptic plate
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General Solutions of Thermoelastic Plane Problems of Two-Dimensional Quasicrystals 认领 引用 被引量：2
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作者 张亮亮 杨连枝 +1 位作者 余莲英 高阳 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第2期132-136,共5页
The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to a... The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions. 展开更多
关键词 two-dimensional quasicrystals thermoelasticity general solutions point heat source
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General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction 认领 引用 被引量：1
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作者 Constatin Fetecau Nehad Ali Shah Dumitru Vieru 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第12期768-782,共15页
The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and... The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter. 展开更多
关键词 hydromagnetic free convection Newtonian heating heat source mass diffusion chemical reaction general solutions
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A GENERAL SOLUTION AND THE APPLICATION OF SPACE AXISYMMETRIC PROBLEM IN PIEZOELECTRIC MATERIAL 认领 引用 被引量：1
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作者 王子昆 陈庚超 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第7期615-626,共12页
According to the structure feature of the governing equations of spaceaxisymmetric problem in transversely, isotropic piezoelectric material. using the methodof introducing potential .function one by. one, in this pap... According to the structure feature of the governing equations of spaceaxisymmetric problem in transversely, isotropic piezoelectric material. using the methodof introducing potential .function one by. one, in this paper we obtain the so-calledgeneral solution of displacement and eleclric potential function denoied by uniquepoiential.function which satisfies specific partiality equations. As an applying exampleof the general solution, we solve problem of semi-infinile boodt. made of piezoelectricmaterial, on the surface of the semi-infinite body a concentrative .force is applied, andget the analytic .formulations of stress and electric displacement comiponenis. Thegeneral solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity inclusion. penny-shape crack. and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between twopiezoelectric bodies or piezoelectric body. and elastic body . 展开更多
关键词 piezoelectric material. mechanical-electrical coupling. spaceaxisymmetric problem. general solution
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GENERAL SOLUTION FOR THE COUPLED EQUATIONS OF TRANSVERSELY ISOTROPIC MAGNETOELECTRO-ELASTIC SOLIDS 认领 引用
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作者 刘金喜 王祥琴 王彪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第7期774-781,共8页
The coupling feature of transversely isotropic magnetoelectroelastic solids are governed by a system of five partial differential equations with respect to the elastic displacements, the electric potential and the mag... The coupling feature of transversely isotropic magnetoelectroelastic solids are governed by a system of five partial differential equations with respect to the elastic displacements, the electric potential and the magnetic potential. Based on the potential theory, the coupled equations are reduced to the five uncoupled generalized Laplace equations with respect to five potential functions. Further, the elastic fields and electromagnetic fields are expressed in terms of the potential functions. These expressions construct the general solution of transversely isotropic magnetoelectroelastic media. 展开更多
关键词 magnetoelectroelastic solids general solution potential function
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GENERAL SOLUTION FOR DYNAMICAL PROBLEM OF INFINITE BEAM ON AN ELASTIC FOUNDATION 认领 引用
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作者 郑小平 王尚文 陈百屏 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第7期633-637,共5页
Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variabl... Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed. 展开更多
关键词 elastic foundation infinite beam dynamical problem,general solution integral transformation method
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THERMOELASTIC PROBLEMS IN THE HALF SPACE—AN APPLICATION OF THE GENERAL SOLUTION IN ELASTICITY 认领 引用
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作者 王敏中 黄克服 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第9期849-862,共14页
In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the h... In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems. 展开更多
关键词 half space thermoelastic potential elastic general solution,thermoelastic problems
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CONSTRUCTIONS OF THE GENERAL SOLUTION FOR A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 认领 引用
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作者 张鸿庆 杨光 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第2期149-153,共5页
Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a sy... Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations. 展开更多
关键词 general solution noncommutative ring construction of solution,conjugate operator
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A Remark on General Solution for Motion of Relativistic Strings in Minkowski Space ■1+n 认领 引用
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作者 WANG Zeng-Gui 《Communications in Theoretical Physics》 SCIE CAS 2009年第11期914-918,共5页
This note concerns the motion of relativistic strings in the Minkowski space R1+n.We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is differen... This note concerns the motion of relativistic strings in the Minkowski space R1+n.We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others. 展开更多
关键词 space-time the equations for the motion of relativistic string general solution formula
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A General Solution for Trinomial Linear Recurrence with Two Indices 认领 引用
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作者 YU Chang'an 《Wuhan University Journal of Natural Sciences》 CAS 2011年第3期190-192,共3页
In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete ... In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete and applicable model to solve the relevant problem with computer. 展开更多
关键词 a formula of general solution homogeneous trinomial recurrence variable coefficients two indices
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THE GENERAL SOLUTION ON NONLINEAR AXIAL SYMMETRICAL DEFORMATION OF NONHOMOGENEOUS CYLINDRICAL SHELLS 认领 引用
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作者 叶开沅 纪振义 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1989年第3期197-204,共8页
In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method[1]. The general formula of displacements and stress resultants, ... In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method[1]. The general formula of displacements and stress resultants, which is used to solve the bending problems of nonhomogeneous cylindrical shells under arbitrary axial symmetric loads, is derived. Its uniform convergence is proved. Finally, it is only necessary to solve one set of binary linear algebraic equations. A numerical example is given at the end of the paper which indicates satisfactory results of displacement and stress resultants can be obtained and converge to the exact solution. 展开更多
关键词 THE GENERAL SOLUTION ON NONLINEAR AXIAL SYMMETRICAL DEFORMATION OF NONHOMOGENEOUS CYLINDRICAL SHELLS
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A General Solution for a Class of Non-Homogeneous Recurrence Relations with Two Indices 认领 引用
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作者 YU Chang’an 《Wuhan University Journal of Natural Sciences》 CAS 2010年第4期287-291,共5页
In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions.It provides a conc... In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions.It provides a concrete model to solve the concerned prob-lems with modern computing tools. 展开更多
关键词 two indices non-homogeneous recurrence relation formula of general solution
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THE GENERAL SOLUTION FOR AXIAL SYMMETRICAL BENDING OF NONHOMOGENEOUS CIRCULAR PLATES RESTING ON AN ELASTIC FOUNDATION 认领 引用
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作者 纪振义 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第9期871-879,共9页
In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates wit... In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting, on an elastfc foundation is obtained under arbitrary axial symmetrical loads' and boundary conditions. The uniform convergence of the solution is proved. This general solution can also he applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method. 展开更多
关键词 exact analytic method nonhomogeneous circular thin plate general solution
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Comments on “General solutions of plane problem for power function curved cracks” 认领 引用
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作者 陈宜周 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第8期1093-1094,共2页
An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：
关键词 General solutions of plane problem for power function curved cracks Comments on
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GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION 认领 引用
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作者 ZHU Wei-ping +1 位作者 HUANG Qian 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第8期889-897,共9页
The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and th... The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega_shaped bellows; (Ⅲ) Calculation for C_shaped bellows; (Ⅳ) Calculation for U_shaped bellows. This paper is the first part. 展开更多
关键词 theory of flexible shell circular ring shell bellows lateral bending load moderately slender ratio general solution
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GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS 认领 引用
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作者 ZHU Wei-ping +1 位作者 HUANG Qian 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第10期1153-1163,共11页
This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protrudi... This is one of the applications of Part (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of C_shaped bellows were calculated. The bellows was divided into protruding sections and concave sections for the use of the general solution (Ⅰ), but the continuity of the stress resultants and the deformations at each joint of the sections were entirely satisfied. The present results were compared with those of the other theories and experiments, and are also tested by the numerically integral method. It is shown that the governing equation and the general solution (Ⅰ) are very effective. 展开更多
关键词 theory of flexible shell circular ring shell C_shaped bellows overall bending general solution
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GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS 认领 引用
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作者 ZHU Wei-ping +1 位作者 HUANG Qian 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第10期1164-1169,共6页
This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sec... This is one of the applications of Part (Ⅰ),in which the angular stiffness, and the corresponding stress distributions of U_shaped bellows were discussed. The bellows was divided into protruding sections, concave sections and ring plates for the calculation that the general solution (Ⅰ) with its reduced form to ring plates were used respectively, but the continuity of the surface stresses and the meridian rotations at each joint of the sections were entirely satisfied. The present results were compared with those of the slender ring shell solution proposed earlier by the authors, the standards of the Expansion Joint Manufacturers Association (EJMA), the experiment and the finite element method. It is shown that the governing equation and the general solution (Ⅰ) are very effective. 展开更多
关键词 theory of flexible shell circular ring shell U_shaped bellows pure bending general solution
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GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅱ)- CALCULATION FOR OMEGA-SHAPED BELLOWS 认领 引用
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作者 ZHU Wei-ping +1 位作者 HUANG Qian 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第8期898-905,共8页
is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with ... is one of the applications of (Ⅰ), in which the angular stiffness, the lateral stiffness and the corresponding stress distributions of Omega_shaped bellows were calculated, and the present results were compared with those of the other theories and experiments. It is shown that the non_homogeneous solution of (Ⅰ) can solve the pure bending problem of the bellows by itself, and be more effective than by the theory of slender ring shells; but if a lateral slide of the bellows support exists the non_homogeneous solution will no longer entirely satisfy the boundary conditions of the problem, in this case the homogeneous solution of (Ⅰ) should be included, that is to say, the full solution of (Ⅰ) can meet all the requirements. 展开更多
关键词 theory of flexible shell circular ring shell Omega_shaped bellows general solution
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GENERAL SOLUTIONS OF COUPLED THERMOELASTIC PROBLEM 认领 引用
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作者 丁皓江 国凤林 侯鹏飞 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第6期631-636,共6页
A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since i... A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since it involves one less potential function than Blot's solution. 展开更多
关键词 coupled thermoelasticity general solution
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