ON EXACT SOLUTION OF KRMN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

It is extremely difficult to obtain an exact solution of von Kármán’s equationsbecause the equations are nonlinear and coupled.So far many approximate methods havebeen used to solve the large deflection problems except that only a few exact solutions havebeen investigated but no strict proof on convergence is presented yet.In this paper,first ofall,we reduce the von Kármán’s equations to equivalent integral equations which arenonlinear,coupled and singular.Secondly the sequences of continuous function withgeneral form are constructed using iterative technique.Based on the sequences to beuniformly convergent,we obtain analytical formula of exact solutions to von Kármán’sequations related to large deflection problems of circular plate and shallow spherical shellwith clamped boundary subjected to a concentrated load at the centre.     

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper,a kind of rationalism theory of shell is established which is of differentmechanic characters in tension and in compression,and the finite element numericalanalysis method is also described.     

THE PROPERTIES AND APPLICATIONS OF THE INTEGRATING FACTOR IN THE OUALITATIVE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

In this article, we indicated that all the problems. such as theclassification of the singular point and the determination of thestability of limit cycle, can be solved by the application of the in-tegral factor. Especially we gave a criterion for deciding the cen-ter and the focus, Which is appropriate for the singular point ofthe first order as well as that of the higher order.In the qualitative theory of ordinary differential equations,allthe problems, such as the classification of singular point of thefirst order and higher order, and the determination of stability oflimit cycle, are important problems to be solved by different ways,the distinction between a focus and a center of singular point of thehigher order is an unsolved problem. In this paper, we show that allthe problems mentioned above can be solved by the use of the integra-ting factor. A criterion is given to decide the center and the fo-cus, and this criterion is applicable to the singular point of thefirst order as well as the higher o     

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)-LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot’s equations for saturated porous media. The Darcy’s laws of unsaturated soil were proved. It is shown that Biot’s equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)-NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed. Foundation items: the National Natural Science Foundation of China (59678003); Special Research Plan of the Education Department of Shaanxi Province (01JK178) Biographies: HUANG Yi (1936-) ZHANG Yin-ke (1964-)     

THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into ModeⅢ quasistatically propagating crack in an elastic-perfectly plastic material.Thesignificance of this paper is that the usual small scale yielding theory has been brokenthrough.By obtaining the general solutions of the stresses and the displacement rate ofthe near crack line plastic region,and by matching the general solutions with theprecise elastic fields(not the usual elastic K-dominant fields)at the elastic-plasticboundary,the precise and new solutions of the stress and deformation fields,the sizeof the plastic region and the unit normal vector of the elastic-plastic boundary havebeen obtained near the crack line.The solutions of this paper are sufficiently precisenear the crack line region because the roughly qualitative assumptions of the smallscale yielding theory have not been used and no other roughly qualitative assumptionshave been taken,either.The analysis of this paper shows that the assumingly“steady-state cas     

VARIATIONAL PRINCIPLE OF HYBRID ENERGY AND THE FUNDAMENTALS OF 3-D LAMINATE THEORY—A NEW APPROACH FOR THE ANALYSIS OF INTERLAMINAR STRESSES IN COMPOSITE LAMINATES

This paper discusses the discuntinuity of stresses and strains at interlaminar surfaces of the eomposne laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of clastic energy based on the globally continuous variables in laminates, different from the traditional potemial energy and complementary energy. Then. a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D lamimte theory and deterplining the interlaminar stresses mear the free edges.     

AN IMPROVED ARC-LENGTH METHOD AND APPLICATION IN THE POST-BUCKLING ANALYSIS FOR COMPOSITE STRUCTURES

Based on the conventional arc- length method, an improved arc- length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc- length . An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and sheik structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)—NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

IntroductionSoilisthemostcommonlyusedconstructionmaterialincivilengineeringandhydraulicengineering .Thecharacteristicsofsoilhavebeeninvestigatingfornearlyonehundredyears.Butbecauseofitscomplexstructure,changeableenvironmentandbeingsensitivetotheoutsideconditions,thesoiloftenshowsvariedproperties[1,2 ].Themaindifficultytothedevelopmentofgeotechnicalmechanicsishowtosetupconstitutiveequationswhichcouldsatisfactorilyaccountforengineeringpropertiesofsoil[3].Manyconstitutivemodelshavebeenformedinth…     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)—LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

IntroductionInpart(Ⅰ )ofthework[1],byuseofmixturetheory ,thenonlinearconstitutiveequationsandthefieldequationsofunsaturatedsoilwereconstructed ,andthecompleteequationsforthethermodynamicsystemofunsaturatedsoilwasformed .Inthispart,thelinearconstitutiveequationsandfieldequationsofunsaturatedsoilareobtainedthroughlinearizingnonlinearequations,andthelinearequationsarewrittenintheformssimilartoBiot’sequationsforsaturatedporousmedia .ItisprovedthatDarcy’slawissuitabletodescribethemotionofliquid…     

A NEW IHIERARCHICAL BOUNDARY ELEMENT METHOD AND ITS ADAPTIVE PROCESSES FOR PLATE BENDING PROBLEM

In this paper a new hierarchical boundary element method is introducedfor solving the problem of plate bending.Exact solutions of the governing equationsare used inside the domain together with independent deflections and rotations on theboundary.A generalized variational principle is employed to achieve the boundaryelement formulation.Further,the adaptive processes of the method are also discussed.By virtue of the error estimate technique proposed by Zienkiewicz et al.areasonable error indicator and adaptive scheme are suggested.Numerical examplesillustrate the high accuracy of the new elements and show the excellent efficiency ofthe adaptive computation described in this paper.     

THE SINGULARITY ANALYSIS OF THE STRESS AND STRAIN FIELDS FOR MODE I FRACTURE IN ELASTIC-PLASTIC STATE

The stress and strain singularities of power hardening material for Mode I fracrure areanalysed according to the fundamental equations of elastic-plastic mechanics. It is foundthat the singularities of all stress and strain components do not change in the thick direction,and neither the six stress components nor the six strain components have the samesingularity.     

THE CALCULATION OF BENDING AND STABILITY OF A THIN RECTANGULAR PLATE FOR VARIABLE RIGIDITY

The subject discussed in this paper is the rectangular plate.Its two opposite edges are simply supported,while the othertwo are arbitrary,and the rigidity of the plate is variablealong the direction parallel to the simply supported edges.In order to solve the problem,the author adopts the finiteplate-strip element method,which is different from theusual finite element method or the finite strip method.Thesteps of the above method is no longer to establish a rigidi-ty matrix for elements or strips and gather them into a totalmatrix for solution.Now the relation of transfer betweenthe strain and inner force of every plate-strip is shown.Fi-nally a practical example is given and this method is foundto be easier and more effective.     

ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior ofa Griffith permeable crack under harmonic anti-plane shearwaves in the piezoelectric materials is investigated by use of the non-local theory.To overcome themathematical difficulties,a one-dimensional non-local kernel is used instead of a two-dimensionalone for the anti-plane dynamic problem to obtain the stress and the electric displacement near thecrack tips.By means of Fourier transform,the problem can be solved with a pair of dual integralequations that the unknown variable is the jump of the displacement across the crack surfaces.These equations are solved with the Schmidt method and numerical examples are provided.Con-trary to the previous results,it is found that no stress and electric displacement singularities arepresent at the crack tip.The finite hoop stress and the electric displacement depend on the cracklength,the lattice parameter of the materials and the circle frequency of the incident waves.Thisenables us to employ the maximum stress hypothesis to deal with fracture problems in a naturalway.     

THE GENERALIZED BOUSSINESQ EQUATIONS AND OBLIQUELY INTERACTING SOLITARY WAVES IN A STRATIFIED FLUID

In this paper, on the basis of Boussinesq's shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, give the secondorder approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.     

LUBRICATION THEORY FOR MICROPOLAR FLUIDS AND ITS APPLICATION TO A JOURNAL BEARING WITH FINITE LENGTH

In this paper,the field equation of micropolar fluid with general lubrication theoryassumptions is simplified into two systems of coupled ordinary differential equation.Theanalytical solutions of velocity and microrotation velocity are obtained.Micropolar fluidlubrication Reynolds equation is deduced.By means of numerical method,thecharacteristic of a finitely long journal bearing under various dynamic parameters,geometrical parameters and micropolar parameters are shown in curve form.Thesecharacteristics are pressure distribution,load capacity,coefficient of flow flux andcoefficient of friction.Practical value of micropolar effects is shown,so micropolar fluidtheory further close to engineering application.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

THE EMBEDDED THEOREM FOR FAMILY OF QUASI METRIC SPACES IN MENGER SPACE AND ITS APPLICATION

In this paper the notion of embedding for family of quasi metric spaces in Mengerspaces is introduced and its properties are investigated.A common fixed point theorem forsequence of continuous mappings in Menger spaces is proved.These mappings are assumedto satisfy some generalizations of the contraction condition.The proving technique hereinseems to be new even for mappings in Menger spaces.     

A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS

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