ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES(I)──MODELLING

ＡＮＩＳＯＴＲＯＰＩＣＥＦＦＥＣＴＳＯＦＱＵＡＳＩ－ＩＳＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＳ（Ｉ）──ＭＯＤＥＬＬＩＮＧＺｈｅｎｇＱｕａｎｓｈｕｉ（郑泉水），ＦａｎｇＨｕｉｙｕ（方辉宇）（ＤｅｐａｒｔｍｅｎｔｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈａｎｉｃｓ...     

ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES(I)──MODELLING

Experimental observations show that quasi-isotropic materials, such as N-axial fibre-reinforced composites and woven materials, exhibit various degrees of anisotropy in elasticity and strength, and the anisotropy in strength is normally stronger than that in elasticity. In view of some available experimental data and based on the general formulation of the constitutive equations and failure criteria of quasi-isotropic materials established by using the theory of representations for tensor functions, we postulate several applicable models of the constitutive equations and strength for 3-and 4-axial quasi-isotropic materials to reveal the anisotropic effects. In a continued work (Part II), the anisotropic effect in strength of an infinitely large plate with a single elliptical hole or crack is studied, and the proposed stiffness and strength models are verified in terms of micro-mechanical analyses.Project supported by the National Natural Science Foundation of China and the State Education Commission Foundation of China     

ANISOTROPIC EFFECTS OF QUASI－ISOTROPIC COMPOSITES（II）──APPLICATIONS AND MICRO－MECHANICAL ANALYSIS

ＡＮＩＳＯＴＲＯＰＩＣＥＦＦＥＣＴＳＯＦＱＵＡＳＩ－ＩＳＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＳ（ＩＩ）－－ＡＰＰＬＩＣＡＴＩＯＮＳＡＮＤＭＩＣＲＯ－ＭＥＣＨＡＮＩＣＡＬＡＮＡＬＹＳＩＳＦａｎｇＨｕｉｙｕ（方辉宇），ＺｈｅｎｇＱｕａｎｇｓｈｕｉ（郑泉水）（...     

ANALYSIS ON BUCKLING AND POSTBUCKLING OF DELAMINATION IN 3D COMPOSITES

In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterativeprocedure based on Taylor's series expansion is used to generate a family of nondimensionalized post-buckling solutions of the above problem by yon Karman's nonlinear plate theory. Attention is fo-cused, herein, on the effects of the bridge force of through-thickness fibers on the buckling and post-buckling behavior of the delamination. It is found that fiber bridge not only increases the ability of re-sisting delamination buckling and postbuckling, but also brings on the jump of the delamination deflec-tion mode during the postbuckling phase. Consequently the behavior of the composite structure with de-lamination is greatly improved, such as increasing the residual strength and prolonging the service life.     

CONSTITUTIVE RELATION AND STIFFNESS DEGRADATION OF CRACKED ANISOTROPIC COMPOSITE LAMINATES(II)─DETERMINATION OF RESOLVED STIFFNESS AND INVESTIGATION OF STIFFNESS DEGRADATION

The study on properly degradation of damaged,.onlj,osile laminates is extendedto anisotropic laminates with matrix cracking. In (II) of the paper, a solution forpartitioned stiffness is given to complete the constitutive relations developed in (I) Thestiffness degradation in (θ_m/90_n)_s cracked laminates is calculated and the results arediscussed.     

A MICRO-MECHANICAL MODEL OF KNITTED FABRIC AND ITS APPLICATION TO THE ANALYSIS OF BUCKLING UNDER TENSION IN WALE DIRECTION： MICRO-MECHANICAL MODEL

The typical micro-knitting structure of knitted fabric, which makes it very different from woven fabric, is described. The tensile tests of knitted fabric are reported. The deformations of the micro-knitting structures are carefully studied. The study indicates that when a knitted fabric sheet is subjected to a tension along w-direction an extra compressive stress field inside loop in c-direction is induced. The extra stress field is also determined through analysis. Finally, a micro-mechanical model of knitted fabric is proposed. This work paves the way for the simulations of buckling modes of a knitted fabric sheet as are observed in experiments. The project supported by the National Natural Science Foundation of China (10272079)     

THE REMAINDER－EFFECT ANALYSIS OF FINITE DIFFERENCE SCHEMES AND THE APPLICATIONS

ＴＨＥＲＥＭＡＩＮＤＥＲ－ＥＦＦＥＣＴＡＮＡＬＹＳＩＳＯＦＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＳＬｉｕＲｕ－ｘｕｎ（刘儒勋）ＺｈｏｕＺｈａｏ－ｈｕｉ（周朝晖）（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｕｎｉｖｅｒｓｉｔｙｏ...     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅱ)

Forming a connecting link between what goes before and comes after,this papersummarizes the general framework of pansystems methodology and related mathematicalmodelling of fundamental concepts including generalized systems,structure,function,entirety principle of system,pansystems relations,pantransformations,panderivatives,pansymmetries,generalized quantization,etc.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS (Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅰ)

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces. Projects supported by the Science Fund of the Chinese Academy of Sciences.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES(Ⅱ)

This paper is a continuation of the author's previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.     

CONSTITUTIVE RELATION AND STIFFNESS DEGRADATION OF CRACKED ANISOTROPIC COMPOSITE LAMINATES(II)─DETERMINATION OF RESOLVED STIFFNESS AND INVESTIGATION OF STIFFNESS DEGRADATION FOR CRACKED LAMINATES

I.IntroductionTheconstitutiverelationsofacracked(omm.),laminatearedevelopedin(l)ofthispaper.Forthecrackedanisotropiclaminateswithsymmetricconstrainedcracking,themethodofstiffnesspartionisusedtosolvethecoupled'problemandtheeffectivestiffnessesofthelaminatesareexpressedasfunctionsofcrackdensity.Duringthestiffnesspartition,thein-planestiffnessmatrixesandtheout-of-planestiffnessmatrixesforthecrackedplyandtheconstraintplyshouldberesolvedintotwoparts.Fortheconstraintply(2),allcouplingstiffnesseleme…     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES(Ⅰ)

This paper is devoted to the study of the basic theory and applications of probabilistic metric spaces (PM-space). In this paper the topological structure and properties for PM-space are considered. The conditions of metrization and the form of metric functions for PM-spaces. Menger PM-spaces and probabilistic normed linear spaces (PN-space ) are given and the characterizations of various probabilistically bounded sets are presented. As applications we utilize these results obtained in this paper to study the linear operator theory and fixed point theory on PM-spaces.     

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅱ)

This paper is a continuation of the author’s previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.     

PLASTIC ANALYSIS OF THIN PLATES WITH ANISOTROPIC HARDENING

In this paper we discuss the adoption of the anisotropic hardening model due to theexistence of Bauschinger effect when thin plate is applied by repeated loading.The loadingcondition of thin plates for linear kinematic hardening has been deduced in terms ofgeneralized forces and generalized plastic deformation.And it can be extended to nonlinearkinematic hardening and mixed hardening.Finally as an example the numerical results areobtained for a circular plate.     

OPTIMIZATION AND APPLICATIONS OF REVERSE-FLOW CYCLONES

An optimum design approach to reverse-flow cyclones based on the concept of optimizing cyclone dimensions is introduced in this paper. This approach involves optimizing cyclone dimensions by categories, calculating cyclone performance by correlating similitude numbers and optimizing the combination of four cyclone parameters, D1 KA1 dr^- and vi, which has been proven to be applicable not only for single-stage cyclone, but also for multistage cyclone separators. Applications of the designed cyclones in FCC units and acrylonitrile reactors are also presented.     

EFFECTS OF MICROSTRUCTURE ON THE MACROSCOPIC ELASTO-PLASTIC PROPERTIES OF METAL MATRIX COMPOSITES

The generalized self-consistent finite-element iterative averaging method was adopted toanalyze the elasto-plastic tensile properties of SiC whiskers reinforced aluminum matrix composites.The effects of varying fiber's aspect ratio and volume fraction on the macroscopic elasto-plastic defor-mation of the composites were studied.By the analysis of microscopic stress fields,the relation be-tween the propagation of the elasto-plastic region in the matrix and the macroscopic elasto-plastic de-formation of composites was discussed.It was found that the propagation of the plastic region in thematrix between the fiber's ends would affect prominently the elasto-plastic tensile behaviour of thecomposites.It was shown that the characterization of the stress-strain response in terms of the 0.2%offset yield strength is incomplete.     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅰ)

A new notion of finite continuous topological space (in short, FC-space) with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.