应用数学和力学

2001 Vol. 22, No. 9

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A Universal Variational Formulation for Two Dimensional Fluid Mechanics

HE Ji-huan

2001, 22(9): 891-897.

Abstract(2693) PDF(1647)

Abstract:
A universal variational formulation for two dimensional fluid mechanics is obtained,which is subject to the so-called parameter-constrained equations(the relationship between paramters in two governing equations).By eliminating the constraints,the generalied variational principle(GVPs)can be readily derived from the formulation.The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms.Some illustrative examples are given to testify the effectiveness and simplicity of the method.

Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces

ZHANG Shi-sheng

2001, 22(9): 898-904.

Abstract(1871) PDF(734)

Abstract:
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces.The results extend and improve some recent results.

Analysis of Financial Derivatives by Mechanical Method(Ⅱ)——Basic Equation of Market Price of Option

YUN Tian-quan

2001, 22(9): 905-910.

Abstract(1953) PDF(792)

Abstract:
The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: h_v>0(t)=m₁v₀^-1(t)-n₁ v₀(t)+F,where h,m₁,n₁,F are constants.The main assumptions are:the ups and downs of market price v₀(t)are determined by supply and demand of the market;the factors,such as the strike price,tenor,volatility,etc.that affect on v₀(t)are demonstrated by using proportion or inverse proportion relation;opposite rules are used for purchasing and selling respectively.The solutions of the basic equation under various conditions are found and are compared with the solution v_f(t)of the basic equation of market price of futures.Furthermore the one-one corre-spondence between v_f and v₀(t)is proved by implicit function theorem,which forms the theoretic base for study of v_f affecting the market price of option v₀(t).

Finite Element Galerkin Approach for a Computational Study of Arterial Flow

G. C. Sharma, Madhu Jain, Anil Kumar

2001, 22(9): 911-917.

Abstract(2075) PDF(578)

Abstract:
A finite element solution for the Navier-Stokes equations for steady flow through a double branched two dimensional section of three dimensional model of canine aorta is obtained. The numerical technique involves transformation of the physical coordinates to a curvilinear boundary fitted coordinate system. The shear stress at the wall is calculated for Reynolds number of 1000 with branch to main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and it is observed that the results are very close to their solutions. This work in fact is an improvement of the work of Sharma and Kapoor (1995) in the sense that computations scheme is economic and Renolds number islarge.

Natural Frequency for Rectangular Orthotropic Corrugated-Core Sandwich Plates with All Edges Simply-Supported

WU Hui, YU Huan-ran

2001, 22(9): 919-926.

Abstract(2616) PDF(696)

Abstract:
A simple approach to reduce the governing equations for orthotropic corrugated-core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.

Constitutive Theory of Plasticity Coupled With Orthotropic Damage for Geomaterials

SHEN Xin-pu, Zenon Mroz, XU Bing-ye

2001, 22(9): 927-933.

Abstract(2087) PDF(583)

Abstract:
Constitutive theory of plasticity coupled with orthotropic damage for geomaterials was established in the framework of irreversible thermodynamics. Prime results include: 1) evolution laws are presented for coupled evolution of plasticity and orthotropic damage; 2) the orthotropic damage tensor isintroduced into the Mohr-Coulomb criterion through homogenization. Both the degradation of shear strength and degradation of friction angle caused by damage are included in this model. The dilatancy is calculated with the so-called damage strain.

An Exact Analysis for Free Vibration of a Composite Shell Structure-Hermetic Capsule

SHANG Xin-chun

2001, 22(9): 934-942.

Abstract(2645) PDF(762)

Abstract:
Anexact analytical solution was presented for free vibration of composite shell structure-hermetic capsule. The basice quations on axisymmetric vibration were based onthe Love classical thin shell theory and derived for shells of revolution with arbitrary meridian shape. The conditions of the junction between the spherical and the cylindrical shell segments are givenby the continuity of deformation and the equilibrium relations near the junction point. The mathematical model of problem is reduced to as an eigenvalue problem for a system of ordinary differential equations in two separate domains corresponding to the spherical and the cylindrical shell segments. By using Legendre and trigonometric functions, exact and explicitly analytical solutions of the mode functions were constructed andthe exact frequency equation were obtained. The implementation of Maple programme indicates that all calculations are simple and efficient in both the exact symbolic calculation and the numerical results of natural frequencies compare with the results using finite element methods and other numerical methdos. As a benchmark, the exactly analytical solutions presented in this paper is valuable to examine the accuracy of various approximate methods.

Splitting Modulus Finite Element Method for Orthogonal Anisotropic Plate Bending

DANG Fa-ning, RONG Ting-yu, SUN Xun-fang

2001, 22(9): 943-951.

Abstract(1993) PDF(656)

Abstract:
Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

Computation Formulas of Generalised Inverse Padé Approximant Using for Solution of Integral Equations

GU Chuan-qing, LI Chun-jing

2001, 22(9): 952-958.

Abstract(2172) PDF(843)

Abstract:
For the generalizedinverse function-valued Pad approximants, its intact computation formulas are given, The explicit determinantal formulas for the denominator scalar polynomials and the numrator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.

The Formation of Shock Waves of the Equations of Magnetohydrodynamics

DONG Li-ming, SHI Yi-peng

2001, 22(9): 959-968.

Abstract(2005) PDF(566)

Abstract:
The property of fluid field of one-dimensional magnetohy drodynamics(MHD) transverse flow after the appearance of singularity is discussed. By the method of iteration, the strong discontinuity (shock wave) and entropy solution are constructed and the estimations on the singularity of the solution near the point of blow-up are obtained.

Analysis of Beams with Piezoelectric Actuators

LIN Qi-rong, LIU Zheng-xing, WANG Zong-li

2001, 22(9): 969-975.

Abstract(2172) PDF(594)

Abstract:
Based on the two-dimensional constitutive relationships of the piezoelectric material, an analytical solution for an intelligent beam excited by a pair of piezoelectric actuators is derived. With the solution the force and moment generated by two piezoelectric actuators anda pair of piezoelectric actuator/sensor are obtained. Examples of a cantilever piezoelectric laminatedbeam or a simply supported piezoelectric laminated beam, applied with voltages, are given.

Scattering of Plane SH-Wave by a Cylindrical Hill of Arbitrary Shape

CAO Xin-rong, SONG Tian-shu, LIU Dian-kui

2001, 22(9): 976-982.

Abstract(2559) PDF(577)

Abstract:
The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Further more appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method(FEM).

A Damage Accumulating Modeling of Failure Waves in Glass under High Velocity Impact

LIU Zhan-fang, YAO Guo-wen, ZHAN Xian-yi

2001, 22(9): 983-987.

Abstract(2258) PDF(632)

Abstract:
The failure wave phenomenon was interpreted in glassmedia under the high velocity impact with the stress levels below the Hugoniot elastic limit. Inview of the plate impact experimental observations a damage-accumulating model predominated by the deviatoric stress impulse was proposed while Heaviside function was adopted in the damage-accumulating model to describe the failure delay inthe interior of materials. Features of the failure layer and propagation mechanism as well as their dynamic characteristics were further presented. The reduction in failure wave propagation speed is pointed out as the reflected rarefaction waves reflect again from the failure layer boundary.

Bifurcations of Invariant Curves of a Difference Equation

HE Tian-lan

2001, 22(9): 988-996.

Abstract(2424) PDF(497)

Abstract:
Bifurcation of the invariant curves of a difference equationis studied. The system defined by the difference equation is integrable, sothe study of the invariant curves of the difference system canbecome the study of topological classification of the planar phase portraits defined by a planar Hamiltonia system. By strict qualitative analysis, the classification of the invariant curves in parameter space can be obtained.

A Simplified Proof to a Theorem by DINH Tongren on Periodic Solutions of Duffing Equations

DONG Yu-jun

2001, 22(9): 997-1000.

Abstract(2202) PDF(561)

Abstract:
In 1982, DING Tongren gave a basic theorem about existence of periodic solutions of Duffing equations with double resonance. A simplified proof will be given by making use of the Leray-Schauder principle.