TRANSFER OPEN OR CLOSED SETVALUED MAPPING AND GENERALIZ－ATION OF H－KKM THEOREM WITH APPLICATIONS

ＴＲＡＮＳＦＥＲＯＰＥＮＯＲＣＬＯＳＥＤＳＥＴＶＡＬＵＥＤＭＡＰＰＩＮＧＡＮＤＧＥＮＥＲＡＬＩＺ－ＡＴＩＯＮＯＦＨ－ＫＫＭＴＨＥＯＲＥＭＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＬｉＢｉｎｇ－ｙｏｕ（李秉友）；ＳｕＪｉａ－ｂａｏ（苏家宝）（Ｄｅｐａｒｔｍｅｎｔ...     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬ．ＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（ＩＩ）ＨｕａｎｇＪｉａｙｉｎ（黄家寅）；ＱｉｎＳｈｅｎｇｌｉ（秦圣立）；Ｘｉ...     

JORDAN CANONICAL FORMS OF MATRICES OVER QUATERNION FIELD

ＪＯＲＤＡＮＣＡＮＯＮＩＣＡＬＦＯＲＭＳＯＦＭＡＴＲＩＣＥＳＯＶＥＲＱＵＡＴＥＲＮＩＯＮＦＩＥＬＤ￥ＣｈｅｎＬｏｎｇｘｕａｎ（陈龙玄）ＨｏｕＲｅｎｍｉｎ（侯仁民）ＷａｎｇＬｉａｎｇｔａｏ（王亮涛）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｙａ...     

EAPPROXIMATE INERTIAL MANIFOLDS FOR THE SYSTEM OF THE J-J EQUATIONS

ＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳ￥ＣａｉＲｉｚｅｎｇ（...     

THE LAW OF THE ITERATED LOGARITHM OF RANDOM WEIGHTING APPROXIMATION FOR MEAN ERROR──NON．I．I．D．SITUATION

ＴＨＥＬＡＷＯＦＴＨＥＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＯＦＲＡＮＤＯＭＷＥＩＧＨＴＩＮＧＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＭＥＡＮＥＲＲＯＲ──ＮＯＮ．Ｉ．Ｉ．Ｄ．ＳＩＴＵＡＴＩＯＮＷａｎｇＢｉｎｇｚｈａｎｇ（王炳章）ＰｅｎｇＪｉａｎｐｉｎｇ（彭建平...     

The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

（黄家寅）（秦圣立）ＴＨＥＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＢＥＮＤＩＮＧＦＯＲＯＲＴＨＯＴＲＯＰＩＣＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳ￥ＨｕａｎｇＪｉａｙｉｎ;ＱｉｎＳｈｅｎｇｌｉ（ＱｕｆｕＮｏｒｍａｌＵｎ...     

THE MATHEMATICAL MODELS AND GENERALIZED VARIATIONAL PRINCIPLES OF NONLINEAR ANALYSIS FOR PERFORATED THIN PLATES

ＴＨＥＭＡＴＨＥＭＡＴＩＣＡＬＭＯＤＥＬＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＮＯＮＬＩＮＥＡＲＡＮＡＬＹＳＩＳＦＯＲＰＥＲＦＯＲＡＴＥＤＴＨＩＮＰＬＡＴＥＳＣｈｅｎｇＣｈａｎｇｉｕｎ（程昌钧）；ＹａｎｇＸｉａｏ...     

THE BOUNDED EXTERMINATION AND STABILITY OF MUTUAL INTERFERENCE SYSTEM OF FOUR－DIMENSIONAL SPECIES

ＴＨＥＢＯＵＮＤＥＤＥＸＴＥＲＭＩＮＡＴＩＯＮＡＮＤＳＴＡＢＩＬＩＴＹＯＦＭＵＴＵＡＬＩＮＴＥＲＦＥＲＥＮＣＥＳＹＳＴＥＭＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＳＰＥＣＩＥＳＨｏｕＧａｎ－ｓｈｅｎｇ（侯赣生）（Ｄｅｐｌ．ｏｆＰｈｙｓｉｃｓ，Ｊｉａｎｇｘ...     

AN APPLICATION OF SCHAUDER’S FIXED POINT THEOREM TO THE EXISTENCE OF SOLUTlONS OF IMPULSIVELY DIFFERENTIAL EQUATIONS

ＡＮＡＰＰＬＩＣＡＴＩＯＮＯＦＳＣＨＡＵＤＥＲ’ＳＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＴＯＴＨＥＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴｌＯＮＳＯＦＩＭＰＵＬＳＩＶＥＬＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＤｏｎｇＹｕ－Ｊｕｎ（董玉君），ＺｏｕＥｒ－ｘｉ...     

ON THE SECOND ORDER WAVE DIFFRACTION IN TWO LAYER FLUIDS

ＯＮ　ＴＨＥ　ＳＥＣＯＮＤ　ＯＲＤＥＲ　ＷＡＶＥ　ＤＩＦＦＲＡＣＴＩＯＮ　ＩＮ　ＴＷＯ　ＬＡＹＥＲ　ＦＬＵＩＤＳＷｕＪｉａｎｈｕａ（吴建华）；ＦａｎｇＹｉｎｇ（方颖）（ＲｅｃｅｉｖｅｄＭａｙ４，１９９５；ＲｅｓｉｖｅｄＪｕｎ．２１，１９９６；Ｃｏｍｍ...     

Analytic Sensitivity Analysis for Shape Optimization

ＩｎｔｒｏｄｕｃｔｉｏｎＳｈａｐｅｏｐｔｉｍｉｚａｔｉｏｎｆｏｒｅｌａｓｔｏｍｅｒｉｓａｎｉｍｐｏｒｔａｎｔｍｅａｓｕｒｅｔｏｒｅｌｉｅｖｅｓｔｒｅｓｓｃｏｎｔｒｉｔｉｏｎ ,ｐｒｅｖｅｎｔｂｒｅａｋｉｎｇ ,ｉｍｐｒｏｖｅｌｏａｄ＿ｂｅａｒｉｎｇｃａｐａｃｉｔｙ .Ｓｔｒｕｃｔｕｒａｌｒｅｐｅｔｉｔｉｏｎａｎａｌｙｓｉｓ,ｓｅｎｓｉｔｉｖｉｔｙａｎａｌｙｓｉｓａｎｄｏｐｔｉｍａｌａｌｇｏｒｉｔｈｍａｒｅｔｈｒｅｅｉｍｐｏｒｔａｎｔｌｉｎｋｓｏｆｓｈａｐｅｏｐｔｉｍｉｚａｔｉｏｎ .Ｉｎｔｈｅｃｏｕｒｓ…     

Neck development in metal/elastomer bilayers under dynamic stretchings

Dynamic stretching of bilayer plates comprised of an elastomer layer bonded to a metal layer is studied with emphasis on neck development under plane strain. Neck retardation and multiple necks in the metal layer are promoted by the elastomer layer under quasi-static conditions and also by inertia in the all-metal layer under dynamic stretching. The present study explores the interaction of these two effects under the assumption that ductility is unlimited. The study reveals the roles of the elastomer modulus, the metal strength and the rate of stretching in giving rise to necking retardation.     

Effects of Mean pressure on the behavior of a filled elastomer

The rheological behavior of an elastomer composed of a polyurethane rubber filled with granular potassium chloride is studied on the basis of a series of compression tests with superimposed hydrostatic pressure. It is suggested that behavior may be approximated by a linear anelastic response for relatively small strains until a marked change in structure occurs, and that further deformation involves shear-dependent dilatation which is strongly influenced by mean pressure. Theories are suggested which describe the experimentally observed behavior.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension

Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials(～1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface(with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.     

Dynamic Analysis of the Non-Linear Behavior of a Composite Sandwich Beam with a Magnetorheological Elastomer Core

This work deals with the active control of the vibrations of mechanical structures incorporating magnetorheological elastomer. The damping coefficient and shear modulus of the elastomer increase when exposed to a magnetic field. Compared with the vibration control where the elastomer is permanently exposed to a magnetic field, the control of this process through time reduces vibrations more effectively. The experimental study for the vibrations of a sandwich beam filled with an elastomer is conducted, followed by a numerical study using the Abaqus code.The vibration damping is found to be dependent on the loading rate of micro-size ferromagnetic particles in the elastomer.     

光敏液晶高弹体梁光致弯曲的特性研究

光敏液晶高弹体是一类新型智能材料,它兼有液晶和橡胶的特性,可以同时由光、热实现驱动,具有广阔的应用前景.本文着重研究了光敏液晶高弹体梁的光致弯曲特性,根据该材料的一维线性化本构关系,在小变形假设下,用简单梁理论得到了光致弯曲模型.将光照的效应等价为一等效力矩,分析了各种参数对其的影响规律,得到了自由梁弯曲曲率和超静定梁约束反力的解析表达式,并计算了梁内应力分布及中性面的个数.结果表明,各种参量对弯曲的影响相互耦合,显现出非线性性;液晶高弹体光致弯曲存在两个或三个中性面,应力分布与通常的梁弯曲有很大不同.     

Mullins effect in elastomers filled with particles aligned by a magnetic field

Magnetorheological elastomers (MRE) are particulate composite materials, whose fillers are structured by a magnetic field during curing. These particles are brought in quasi-contact by the field, in a chain-like unidirectional structure. Due to this organization the local stresses between the particles is high and debonding between particles and elastomer occur at low strain. We have experimentally studied and analytically modeled the progressive breaking of the polymer-to-particle bonds. The two cases of strong and weak bonds between elastomers and particles have been studied. The analytical model correctly reproduces the stress strain curve in the presence of a debonding process although overestimating the size of the debonding cavity which is obtained by comparison between experiments and FEM simulations. The extension of the model to a chain of spheres allows to well explain the Mullins effect on MRE. Furthermore it is shown that the quality of the bonds between the particles and the elastomer does not influence the change of stiffness brought by the application of a magnetic field.     

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction free layer, which is an extension of the Rayleigh–Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch. These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field.     

The Stability of Laminated Elastomer Coatings Under Surface Loading

The stability of laminated elastomer coatings at normal and high temperatures is considered in a three-dimensional formulation. The problem is formulated and the basic characteristic equations are derived. Graphs of the physicomechanical parameters of some elastomers against temperature are experimentally obtained. Specific examples for a three-layer coating are considered