THE FLOQUET THEORY FOR QUASI-PERIODIC LINEAR SYSTEMS

In this paper we establish the Floquet theory for the quasi-perio-dic systemwhere A(u_1,u_2,…,u_m)is an n×n periodic matrix function of u_1,u_2.…,u_mwith period 2π,and it is of C~τ,τ=(N 1)τ_0,τ_0=2(m 1).N=(1/2)n(n 1).Meanwhile,we define the characteristic exponential roots β_1,β_2,…,β_nof(0.1),and assume thatwhere K(ω),K(ω,β)>0.k_μ,j_v.are integers,all the integers k_1,k_2,…,k_m.are not zero,i~2=-1,Then there exists aquasi-periodic linear transformation,which carries(0.1)into a li-near system with constant coefficients.     

THE THEORY OF RELATIVISTIC ANALYTICAL MECHANICS OF THE ROTATIONAL SYSTEMS

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

THE DISPLACEMENT WAVE THEORY OF BLOOD VESSEL

On the basis of the medical and mechanical analysis and explanations in this paper thevisco-elastic simply supported beam model is proposed to treat the displacement wave of theblood vessels.The relationships between the displacement wave and blood vessel elasticityas well as the viscous dissipation of the blood and blood vessel are obtained.Thecorresponding relations of such kinds of pulses in the traditional Chinese medicine assmooth pulse,surface pulse and deep pulse to the displacement waves of blood vessels arealso found.The computational results are in good agreement with those acquired in theexperiments with ultrasonic wave.     

THE RE-EXAMINATION OF THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY

The weakly nonlinear theory has been widely applied in the problem of hydrodynamicstability and also in other fields.However,although its application has been successful forsome problems,yet,for other problems,the results obtained are not satisfactory,especiallyfor problems like transition or the evolution of the vortex in the free shear flow,for whichthe goal of the theoretical investigation is not seeking for a steady state,but predicting anevolutional process.In this paper,we shall examine the reason for the unsuccessfulness andsuggest ways for its amendment.     

SOME COMMENTS ON THE ORIGINAL KALUZA-KLEIN THEORY

In this note the basis of the Kaluza-Klein theory is examined critically and it is pointedout that the five-dimensional version can’t work in the way that was originally intended.Thereason why the problem was not noted originally is elucdated.     

THE THEORY AND APPLICATIONS OF GENERALIZED H-SPACE

This paper brings forward the concept of generalized H-spaces which extends the concepts of H-spaces and almost probabilistic metric spaces.In this paper,the uniformity and properties far generalized H-space are considered.The conditions of metrization and the form of metric functions for generalized H-spaces,H-spaces and Menger PM-spaces are given and the characteristics of completeness and compactness for generalized H-spaces are presented.The results of this paper generalize and unify some recent results of[1-2,8,10].     

CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅱ)

The present paper uses the mathematics model for consolidation of unsaturatedsoil developed in ref.[1]to solve boundary value problems.The analytical solutionsfor one-dimensional consolidation problem are gained by making use of Laplacetransform and finite Fourier transform.The displacement and the pore water pressureas well as the pore gas pressure are found from governing equations simultaneously.The theoretical formulae of coefficient and degree of consolidation are also given inthe paper.With the help of the method of Galerkin Weighted Residuals,the finiteelement equations for two-dimensional consolidation problem are derived.A FORTRANprogram named CSU8 using8-node isoparameter element is designed.A plane strainconsolidation problem is solved using the program,and some distinguishing features onconsolidation of unsaturated soil and certain peculiarities on numerical analysis arerevealed.These achievements make it convenient to apply the theory proposed by theauthor in engineering practice.     

THE THEORY OF FRACTAL INTERPOLATED SURFACE AND ITS APPLICATIONS

I.IntroductionFI.actillilltcrpolationwastlrstpEltforwardbyunA]ncrica1llathematician,M.F.Barllsley.in1986.ItgivesanewInethodologytardataf'ittillg,whichnotonlyopedsupanewresearch11eldfol'tilnctiollappl'oachingtheory,butalsoprovidespowerfultoolsforcolnptltcrgraphicsThistool'sapplicabilityisnowfilllyappreciated.Theuseoflinearfunctions,polynomialfunctionsandSurtllcespringfunctionstoestablishvariousmeterialobjectmodelsinreallifefi-omtraditionalEuclideangeometryisnowcommonpractice.Theavailabilit…     

THE THEORY OF STATIC DECAY IN COMPUTATIONAL MECHANICS

In this paper,a new mathematical form,matrix,continued fraction(MCF)isintroduced to describe the decay of effects of an equilibrant system of forces acting on asphere of an elastic body.By this way,the famous Saint-Venant’s principle is proved oftenbut not always valid in computational mechanics.     

THE ANALYTIC THEORY OF THE TEMPERATURE FIELDS OF BITUMINOUS PAVEMENT OVER SEMI-RIGID ROADBASE

Projectofthe'Eight-Fi\e-NationalMajorScienceal1dTechnoIog}'.85-403-02-02I.IntroductionPavementstructureisexposedtonaturalenvironment,andisweatheredbycontinuousatmosphereinfluencesuchasthesolarradiation,theskyradiationandtheexternalairtemperature.Apartofth…     

线性非局部弹性理论的修正

本文通过考虑局部化残余力的影响对线性非局部弹性理论进行了修正，由修正后的理论所导出的应力边界条件包含了物体微观结构的长程力的作用，这个结果不仅解释了在裂纹混合边界值问题中线性非局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以自然地得到裂纹尖端的Ｂａｒｅｎｂｌａｔｔ分子内聚力模型。     

NEW POINTS OF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS (Ⅰ)──FUNDAMENTAL THEORY

In the linear nonlocal elasticity theory, the solution to the boundary-value problem of the crack with a constant stress boundary condition does not exist. This problem has been studied in this paper. The contents studied contain of examining objectivity of the energy balance, deducing the constitutive equations of nonlocal thermoelastic bodies, and determining nonlocal force and the linear nonlocal elasticity theory. Some new results are obtained. Among them, the stress boundary condition derived from the linear theory not only solves the problem mentioned at the beginning, but also contains the model of molecular cohesive stress on the sharp crack tip advanced by Barenblatt.     

关于线性非局部弹性理论的应力边界条件

应力边界条件的提法是线性非局部弹性理论尚未解决的一个理论问题。文中针对这一问题进行了研究，所导出的应力边界条件包含了物体微观结构的长程相互作用，这个结果不仅解释了在裂纹混合边界值问题中非线性局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以自然地得到裂纹尖端的分子内聚力模型。     

关于非局部场论的两点注记

研究了非局部场论中尚未完全解决的两个基本问题：其一为局部化体力，力矩残余之间的相关性，由此得到了一个描述两者关系的定理；其二为线性非局部弹性理论的应力边界条件的提法；文中所得到的应力边界条件不仅解释了在裂纹混合边界值问题中线性非局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以给出裂纹尖端的分子内聚力模型。     

Two notes on nonlocal field theory

In this paper, two fundamental problems completely unsolved in nonlocal field theory are studied. The first is the dependence of nonlocal residuals. By studying this problem, a theorem concerning the relationship between the residuals of nonlocal body force and nonlocal moment of momentum is given and proven. The other problem is how to give the stress boundary conditions in the linear theory of nonlocal elasticity. The stress boundary conditions obtained in this paper can not only answer why the nonlocal stress solution satisfying the boundary conditionst _ji ^(s) n _j ¦O ₂ =p _i (p _i is a constant) on the surface of crack does not exist but also give a model of the molecular cohesive stress on the crack tip.     

Bond-based peridynamic modelling of singular and nonsingular crack-tip fields

A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension.     

The scattering of harmonic elastic anti-plane shear waves by two collinear cracks in anisotropic material plane by using the non-local theory

In this paper, the dynamic behavior of two collinear cracks in the anisotropic elasticity material plane subjected to the harmonic anti-plane shear waves is investigated by use of the nonlocal theory. To overcome the mathematical difficulties, a one-dimensional nonlocal kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress field near the crack tips. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near crack tips. The nonlocal elasticity solutions yield a finite hoop stress at the crack tips, thus allowing us to using the maximum stress as a fracture criterion. The magnitude of the finite stress field not only depends on the crack length but also on the frequency of the incident waves and the lattice parameter of the materials.     

Stress concentration at the tip of crack

By means of the theory of nonlocal elasticity, the stress concentration is determined at the tip of crack subjected to a uniform tension perpendicular to the line of crack at infinity. The stress concentration is found to be finite and depends on the length of the crack.     

Nonlocal theory solution of two collinear cracks in the functionally graded materials

In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials.     

用非局部弹性场论研究圆盘状裂纹问题

本文采用非局部弹性理论。用Love位移函数导出三维轴对称问题的非局部弹性应力的一般形式解,并求解了圆盘裂纹问题。得到了裂纹尖端区的应力是有界的,再次证实了非局部理论模型求解断裂力学问题的正确性。