THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

THE CALCULATION OF THE MULTIPLY－CONNECTED ELASTIC PLANE PROBLEMS BY MEANS OF STRESS FUNCTIONS OF MULTIPLE COMPLEX VARIABLES

ＴＨＥＣＡＬＣＵＬＡＴＩＯＮＯＦＴＨＥＭＵＬＴＩＰＬＹ－ＣＯＮＮＥＣＴＥＤＥＬＡＳＴＩＣＰＬＡＮＥＰＲＯＢＬＥＭＳＢＹＭＥＡＮＳＯＦＳＴＲＥＳＳＦＵＮＣＴＩＯＮＳＯＦＭＵＬＴＩＰＬＥＣＯＭＰＬＥＸＶＡＲＩＡＢＬＥＳｗａｎｇＬｉｎｄｉａｎｇ（王林江）Ｌ...     

STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

ＳＴＵＤＩＥＳ　ＯＦ　ＭＥＬＮＩＫＯＶ　ＭＥＴＨＯＤ　ＡＮＤ　ＴＲＡＮＳＶＥＲＳＡＬ　ＨＯＭＯＣＬＩＮＩＣ　ＯＲＢＩＴＳ　ＩＮ　ＴＨＥ　ＣＩＲＣＵＬＡＲ　ＰＬＡＮＡＲ　ＲＥＳＴＲＩＣＴＥＤ　ＴＨＲＥＥ－ＢＯＤＹ　ＰＲＯＢＬＥＭＺｈｕＲｕｚｅｎｇ（朱如...     

NUMERICAL SIMULATION OF FLOW OF HIGHLY VISCOELASTIC FLOW IN THREE－DIMENSIONAL VARYING THICK SLIT CHANNEL

（杨伯源）（李勇）ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＦＬＯＷＯＦＨＩＧＨＬＹＶＩＳＣＯＥＬＡＳＴＩＣＦＬＯＷＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＡＲＹＩＮＧＴＨＩＣＫＳＬＩＴＣＨＡＮＮＥＬ￥ＹａｎｇＢｏｙｕａｎ；ＬｉＹｏｎｇ（Ｄｅｐａｒｔ...     

FINITE ELEMENT ANALYSIS FOR THE UNSTEADY NEARSHORE CIRCULATION DUE TO WAVE－CURRENT INTERACTION（II）──TWO－STEP EXPLICIT FINITE ELEMENT METHOD

ＦＩＮＩＴＥＥＬＥＭＥＮＴＡＮＡＬＹＳＩＳＦＯＲＴＨＥＵＮＳＴＥＡＤＹＮＥＡＲＳＨＯＲＥＣＩＲＣＵＬＡＴＩＯＮＤＵＥＴＯＷＡＶＥ－ＣＵＲＲＥＮＴＩＮＴＥＲＡＣＴＩＯＮ（ＩＩ）──ＴＷＯ－ＳＴＥＰＥＸＰＬＩＣＩＴＦＩＮＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＷ...     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

A STUDY OF THE ELASTO－PLASTIC AXIALLY TENSILE PROPERTIES OF METAL MATRIX COMPOSITES WITH FIBER－END DEBONDING

ＡＳＴＵＤＹＯＦＴＨＥＥＬＡＳＴＯ－ＰＬＡＳＴＩＣＡＸＩＡＬＬＹＴＥＮＳＩＬＥＰＲＯＰＥＲＴＩＥＳＯＦＭＥＴＡＬＭＡＴＲＩＸＣＯＭＰＯＳＩＴＥＳＷＩＴＨＦＩＢＥＲ－ＥＮＤＤＥＢＯＮＤＩＮＧＳｕＸｉａｏｆｅｎｇ（苏晓风）ＣｈｅｎＨａｏｒａｎ（陈浩然）（...     

THE SOLUTIONS OF STEADY－STATE CONVECTION EQUATIONS IN THE SPACES THAT POSSESS RESTORI NGNUCLEUS

ＴＨＥＳＯＬＵＴＩＯＮＳＯＦＳＴＥＡＤＹ－ＳＴＡＴＥＣＯＮＶＥＣＴＩＯＮＥＱＵＡＴＩＯＮＳＩＮＴＨＥＳＰＡＣＥＳＴＨＡＴＰＯＳＳＥＳＳＲＥＳＴＯＲＩＮＧＮＵＣＬＥＵＳＺｈａｎｇＣｈｉ－ｐｉｎｇ（张池平）;ＣｕｉＭｉｎｇ－ｇｅｎ（崔明根）（Ｈａｒｂｉｎ...     

THE METHOD OF DERIVATION OF MAC－MILLAN＇S EQUATION FOR THE NON－LINEAR NON－HOLONOMIC SYSTEM

ＴＨＥＭＥＴＨＯＤＯＦＤＥＲＩＶＡＴＩＯＮＯＦＭＡＣ－ＭＩＬＬＡＮ＇ＳＥＱＵＡＴＩＯＮＦＯＲＴＨＥＮＯＮ－ＬＩＮＥＡＲＮＯＮ－ＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭ￥ＱｉｕＲｏｎｇ（邱荣）（ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ，ＦｕｚｈｏｕＵｎｉｖｅｒｓｉ...     

EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＥＸＴＲＥＭＡＬＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｏｎｇＧｕａｎｇｘｉｎｇ（宋光兴）（ＲｅｃｅｉｖｅｄＭａｙ４，１９９５；Ｃｏｍ...     

用三维弹性力学方法研究圆板的稳定问题

用三维弹性力学方法研究任意边界条件圆板的轴对称稳定问题，利用Ｈ变换和Ｓｔｏｃｋｅｓ变换，导出位移函数及其偏导数的一种新型双重极数式，并由数学弹性定理论的基本方程和边界条件建立的特征方程，求得最小临界载荷的精确解，文末以简支圆板为例进行数字计算，结果表明：在弹性失稳范围内，三维弹性力学方法求得的临界载荷略低于经典理论的结果，对于薄板的弹性稳定问题，经典板理论有足够的精度。     

The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plates on the elastic foundation

The validity and the range of applicability of the classical plate theory (CPT) and the first-order shear deformation plate theory, also called Mindlin plate theory (MPT), in comparison with three-dimensional (3-D) p-Ritz solution are presented for freely vibrating circular plates on the elastic foundation with different boundary conditions. In order to achieve this purpose, a study of the 3-D elasticity solution is carried out to determine the free vibration frequencies of clamped, simply supported and free circular plates resting on an elastic foundation. The Pasternak model with adding a shear layer to the Winkler model is used for describing the elastic foundation. In addition to being employed the p-Ritz algorithm, the analysis is based on the linear, small strain and 3-D elasticity theory. In this analysis method, a set of orthogonal polynomial series in a cylindrical polar coordinate system is used to arrive eigenvalue equation yielding the natural frequencies for the circular plates. The accuracy of these results is verified by appropriate convergence studies and checked with the available literature and the MPT. Furthermore, the effect of the foundation stiffness parameters, thickness-radius ratio, and different boundary conditions on the ill-conditioning of the mass matrix as well as on the vibration behavior of the circular plates is investigated. Afterwards, the validity and the range of applicability of the results obtained on the basis of the CPT and MPT for a thin and moderately thick circular plate with different values of the foundation stiffness parameters are graphically presented through comparing them with those obtained by the present 3-D p-Ritz solution. Finally, the phenomenon of mode shape switching is investigated in graphical forms for a wide range of the Winkler foundation stiffness parameters.     

The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

In this paper,a new method,the exact analytic method,is presented on the basis of stepreduction method.By this method,the general solution for the bending of nonhomogenouscircular plates and circular plates with a circular hole at the center resting,on an elastfcfoundation is obtained under arbitrary axial symmetrical loads and boundary conditions.The uniform convergence of the solution is proved.This general solution can also be applieddirectly to the bending of circular plates without elastic foundation.Finally,it is onlynecessary to solve a set of binary linear algebraic equation.Numerical examples are givenat the end of this paper which indicate satisfactory results of stress resultants anddisplacements can be obtained by the present method.     

Torsion of a square isotropic plate by forces applied at the corners and by distributed torques

We consider the classical problem of the theory of elastic plates, namely, the problem on the torsion of a square isotropic plane by forces applied at the corners. The traditional solution of this problem based on the classical theory of plates and Kirchhoff and Thomson–Tait transformations is compared with the solution obtained in the improved theory of plates and with experimental results. The solution, which does not exist in the classical theory of plates, of the problem on the torsion of a plate by torques uniformly distributed over the plate contour is presented as well.     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-kirchhoff-Love assumption for three dimensional elastic plates with arbitrary shapes^[1],[2], the author derives a functional of generalized variation for three dimensional elastic circular plates, thereby obtains a set of differential equations and the relate boundary conditions to establish a first order approximation theory for elastic circular plate with fixed boundary and under uniform loading on one of its surface. The analytical solution of this problem will present in another paper.     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

I.1ntroductionTheaxisymmetricproblemofthreedimensionalelasticcircularplatecanbetreatedasthreedimensionalaxisymmetricproblemofelasticity.Weconsideracircularplatewithauniformthicknessh,andsetupacircumferentialcoordinates(r,o)onitsmidd1esurfacewithabscissazp…     

On the boundary conditions for transversely isotropic piezoelectric plates

By invoking the theorem of work reciprocity for piezoelectric media, necessary conditions, which the prescribed edge data of the plate must fulfill in order that it should generate a decaying state within the plate, are established through generalizing the method proposed by Gregory and Wan. These decaying state conditions for the case of axisymmetric deformation of a transversely isotropic piezoelectric circular plate when stress and electric displacement conditions are imposed on the plate edge are derived explicitly, which are then used for the formulation of boundary conditions for the plate theory solution (or the interior solution). Also an analytical solution of the axisymmetric decaying state of transversely isotropic piezoelectric circular plates is derived. Furthermore, the corresponding necessary conditions for the axisymmetric deformation of elastic circular plates are indeed reproduced directly.     

Hamiltonian systems of propagation of elastic waves and localized vibrations in the strip plate

In this paper, based on Lagrange–Germanian theory of elastic thin plates, applying the method in Hamiltonian state space, the elastic waves and vibrations when the boundary of the two lateral sides of the strip plate are free of traction are investigated, and the process of analysis and solution are proposed. The existence of all kinds of vibration modes and wave propagation modes is also analyzed. By using eigenfunction expansion method, the dispersion relations of waveguide modes in the strip plate are derived, and the comparisons with the dispersion relations directly obtained by the classical theory of thin plates are also presented. At last, the results are analyzed and discussed.     

General solution for large deflection problems of nonhomogeneous circular plates on elastic foundation

In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resullants and displacements can be obtained by the present method. The correctness of the theory in this paper is, confirmed.     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.