应用数学和力学

2002 Vol. 23, No. 2

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Restudy of Coupled Field Theories for Micropolar Continua(I)─Micropolar Thermoelasticity

DAI Tian-min

2002, 23(2): 111-118.

Abstract(2817) PDF(782)

Abstract:
Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the thoery of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed.The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.

The Displacement Function of Quasi-Conforming Element and Its Node Error

HE Dong-sheng, TANG Li-min

2002, 23(2): 119-127.

Abstract(2956) PDF(594)

Abstract:
Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacementitems, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems

DING Hao-jiang, WANG Hui-ming, CHEN Wei-qiu

2002, 23(2): 128-134.

Abstract(2695) PDF(645)

Abstract:
A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.

Carastrophe Fracture of Thin-Wall Pressure Tubes

WEI De-min, YANG Gui-tong

2002, 23(2): 135-138.

Abstract(2802) PDF(620)

Abstract:
Catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for the fracture was established, and a critical condition associated with the model is given.

Global Solution of the Inverse Problem for a Class of Nonlinear Evolution Equations of Dispersive Type

CHEN Fang-qi, CHEN Yu-shu, WU Zhi-qiang

2002, 23(2): 139-143.

Abstract(2886) PDF(749)

Abstract:
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhongxin.

Boundary Element Method for Buckling Eigenvalue Problem and Its Convergence Analysis

DING Rui, DING Fang-yun, ZHANG Ying

2002, 23(2): 144-156.

Abstract(2830) PDF(730)

Abstract:
The conditions for determining solution of buckling eigenvalue problem are discussed. The corresponding system of integral equations with constraint conditions and boundary variational equations with Lagrange multiplier are established. The theorems on the existence and uniqueness of the solution for these problems are given. The corresponding boundary element method is constructed and the error estimation for the approximation solution is obtained. Finally the numerical example is give.

On Cauchy Problems for the RLW Equation in Two Space Dimensions

HUANG Zheng-hong

2002, 23(2): 157-164.

Abstract(2816) PDF(886)

Abstract:
A cnoidal wave solution of the two dimensional RLW equation of are obtained by elliptic integral method, and the some estimations the uniqueness and the stability of the periodic solution with both x, y to the Cauchy problem are proved by the priori estimations.

The Study on a Kind of Control System With Nonlinear Parabolic Distributed Parameters

ZHOU Jian-jun, XU Yan-hou

2002, 23(2): 165-172.

Abstract(2924) PDF(680)

Abstract:
The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented. Two methods were used to investigate the basic characteristics of the system: 1) transforming the system in the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable: the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary would stop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the sys-temis well posed, stable, measurable and controllable.

On the Stability Boundary of Hamiltonian Systems

QI Zhao-hui, Alexander P. Seyranian

2002, 23(2): 173-178.

Abstract(2698) PDF(883)

Abstract:
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.

Electroelastic Field for an Impermeable Anti-Plane Shear Crack in a Piezoelectric Ceramics Plate

LI Xian-fang, FAN Tian-you

2002, 23(2): 179-187.

Abstract(2816) PDF(666)

Abstract:
Electroelastic behavior of a cracked piezo electric ceramics plate subjected to four cases of combined mechanical-electrical loads was analyzed. The integral transform method was applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electr oelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the me chanical strain energy releaser ate were obtained. The known results for an infinite piezoelectr icceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate hy.

Generalized Reciprocal Theorems and Their Applications

FU Bao-lian

2002, 23(2): 188-194.

Abstract(2293) PDF(782)

Abstract:
Generalized reciprocal theorems of non-coupled and coupled systems, which are valid for two deformed bodies with different constitutive relations are established by generalizing the idea of Betti's reciprocal theorem. When the constitutive relations of the two deformed bodies are all alike and linear elastic, the generalized reciprocal theorem of non-coupled systems just becomes Betti's. Meanwhile, the generalized reciprocal theorems are applied to simulate calculations in elasticity.

Stability and Strict Positive Realness of Convex Polytopes of Interval Polynomials

WANG Zhi-zhen, WANG Long, YU Wen-sheng

2002, 23(2): 195-200.

Abstract(2757) PDF(674)

Abstract:
For an uncertain system described by convex combination of interval polynomials, its Hurwitz-stability can be guaranteed by certain subset composed of vertices and edges. Fur thermore, the testing set does not increase when the order of given system increases.

The Axisymmetric Mixed Boundary-Value Problem of the Vertical Vibration of a Rigid Foundation on Saturated Layered Soil Subgrade

CHEN Sheng-li, CHEN Long-zhu

2002, 23(2): 201-206.

Abstract(2329) PDF(634)

Abstract:
Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elasti clayer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient C_v versus the dimensionless frequency a₀ are presented.

On Numerical Solutios of Periodically Perturbed Conservative Systems

LIU Guo-qing, FU Dong-sheng, SHEN Zu-he

2002, 23(2): 207-216.

Abstract(2906) PDF(733)

Abstract:
A nonlinear perturbed conservative system is discussed. By means of Hadamard. stheorem, the existence and uniqueness of the solution of the continuous problem are proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution. Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation.

Block H-Matrices and Spectrum of Block Matrices

HUANG Ting-zhu, LI Wen

2002, 23(2): 217-220.

Abstract(2866) PDF(777)

Abstract:
The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.