On Bending–Tension Coupling of Laminates

This paper deals with the evaluation of coupling between the in and out of plane behaviours of a laminate composed of identical anisotropic layers. The subject has been motivated by problems arising from coupling in modern practical industrial applications. Coupling is an effect which is often undesired by laminate designers, and some rules and solutions, recalled in the paper, are known today to counter it. Two subjects are analysed in the article: firstly, it is considered the problem of finding the stacking sequence angles which determine the maximum coupling of a laminate whose number of plies and elementary layer properties are known. Secondly, the sensitivity of uncoupling to an orientation defect is analysed, that is, how coupling changes when an error in the orientation of one layer is made: a simple and exact formula assessing the degree of coupling, which is the ratio of the real coupling with respect to the possible maximum, is given. The polar method, proposed by G. Verchery, has been used to develop the research, which is made in the theoretical framework of the Classical Laminated Plate Theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

受弯脱层层板的局部失稳临界载荷的有限元分析

含脱层的复合材料层板承受弯曲载荷作用会产生跳跃失稳，还常常引起脱层扩展，从而导致结构失效。本文用基于一阶剪切层板理论的几何非线性有限单元法分析了受弯曲曲载荷作用下含脱层板的人稳的临界载荷。本文指出分叉失稳产生了跳跃失稳，而该跳跃失稳与浅圆拱或薄圆柱壳受向心压力作用下的跳跌 同，在整体平衡路径上没有一个极限点。本文对临界载计算结果比使用能量准则的结果要小，文中给出了原因。     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(II)—THE ANALYSES OF THE STRESS STRUCTURE

Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper. The characteristics of the stress structure in the smooth region have been found that the variable z can separated out; the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree. A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.     

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation. The project supported by the Foundation of the Laboratory for Nonlinear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.     

一种计算复合材料等效弹性性能的有限元方法

在最小二乘意义下提出了一种计算复合材料等效弹性性能的有限元方法.这种方法由于考虑了等效弹性张量各分量之间的耦合关系,所求得的等效弹性常数比传统方法更可靠,可适用于求解含任意形状的夹杂和夹杂物问题.通过算例计算了在不同弹性模量对比度下两相复合材料的等效弹性性能,并与相关的理论及数值结果进行了比较,结果表明,利用该方法计算含夹杂复合材料等效弹性常数是可行的.     

Invertibility and dichotomy of differential operators on a half-line

A linear ordinary differential operator with bounded coefficients satisfying certain homogeneous initial conditions is shown to be invertible onL _n ² (0, ) if and only if the underlying system of differential equations has a dichotomy. Moreover, in that case the operator is proved to be a direct sum of two infinitesimal generators ofC ₀-semigroups, one of which has support on the negative half-line and the other on the positive half-line. The effect of perturbations of the initial values on the dichotomy is also described.     

核壳结构PS/CeO2复合微球弹性模量的AFM测定

利用原子力显微镜测定了聚苯乙烯(Polystyrene, PS)微球和核壳结构PS/CeO₂复合微球的力-位移曲线,并根据Hertz接触理论计算了微球样品的弹性模量.结果表明:粒径在120 nm左右的PS微球的平均弹性模量约为2.80 GPa,其数值略低于聚苯乙烯块体材料的弹性模量.复合微球的弹性模量随CeO₂壳层厚度的增加而增大,当CeO₂壳厚分别约为8、12和16 nm时,其平均弹性模量依次约为7.93、8.25和10.67 GPa.与纯氧化铈相比,PS/CeO₂复合微球的弹性模量更接近于聚苯乙烯微球.     

A novel method for measuring and characterizing dynamic fracture-initiation toughness of elastic-plastic materials

The characterization and testing methods of the dynamic fracture initiation toughness of elastic-plastic materials under tensile impact are studied. By using the self-designed bar-bar tensile impact apparatus, a novel test method for studying dynamic fracture-initiation has been proposed based on the one-dimensional test principle. The curve of average loadv. s. displacement is smooth until unstable crack propagation, and the kinetic energy which does not contribute to the crack growth can be removed from total work done by external-force to the specimen. The fracture-initiation point is determined by compliance-changing rate method. The results show that these methods are feasible and effective. Through the analysis of the conversion between work and energy of a fracture specimen, the dynamicJ-integral is adopted as a characteristic parameter for elastic-plastic materials under impact loading. TheJ-integral is calculated from and curves by using the formula proposed, by Rice. TheJ-integral at fracture initiation is employed to describe the dynamic fracture-initiation toughness of elastic-plastic materials and the experimental results indicate thatJ _ID can be regarded as a material constant.     

裂纹尖端张开角准则的稳态裂纹扩展实验研究

ASTM和ISO已发布获得低约束条件下断裂性能和裂纹稳态扩展阻力曲线的标准,标准中采用多种试验方法确定临界裂纹张开角度来表征板材的裂纹稳态扩展。本文采用准静态裂纹扩展试验方法,通过摄像技术测定裂纹尖端张开角(CTOA),验证标准对1mm厚度2024-T3铝合金板稳态裂纹扩展行为的有效性。研究了试样构型、裂纹尺寸和是否疲劳预制裂纹对裂纹稳态扩展过程中CTOA的影响。试验结果表明:裂纹扩展2mm后,距离裂纹尖端1mm处的CTOA趋于一个恒定值6°,这个值与试样构型和裂纹长度无关;同时,不预制疲劳裂纹对CTOA值和试样的最大剩余强度影响较小。     

Anisotropy of Seismic Attenuation in Fractured Media: Theory and Ultrasonic Experiment

This is a study on anisotropy of seismic attenuation in a transversely isotropic (TI) model, which is a long-wavelength equivalent of an isotropic medium with embedded parallel fractures. The model is based on Schoenberg’s linear-slip theory. Attenuation is introduced by means of a complex-valued stiffness matrix, which includes complex-valued normal and tangential weaknesses. To study the peculiarities of seismic attenuation versus wave-propagation direction in TI media, numerical modeling was performed. The model-input data were the complex-valued weaknesses found from the laboratory ultrasonic experiment made with a Plexiglas plate-stack model, oil-saturated (wet) and air-filled (dry). The laboratory experiment and the numerical modeling have shown that in the vicinity of the symmetry axis, in the wet model, P-wave attenuation is close to S-wave attenuation, while in the dry model, P-wave attenuation is much greater than S-wave attenuation. Moreover, the fluid fill affects the P-wave attenuation pattern. In the dry (air-saturated) model, the attenuation pattern in the vicinity of the symmetry axis exhibits steeper slope and curvature than in the wet (oil-saturated) model. To define the slope or the curvature, a QVO gradient was introduced, which was found to be proportional to the symmetry-axis Q _S/Q _P-ratio, which explains the differences between dry and wet models. Thus, depending on the Q _S/Q _P-ratio, the QVO gradient can serve as an indicator of the type of fluid in fractures, because the QVO gradient is greater in gas-saturated than in liquid-saturated rocks. The analysis of P-wave attenuation anisotropy in seismic reflection and vertical seismic profiling data can be useful in seismic exploration for distinguishing gas from water in fractures.     

纵向剪切三相共焦点椭圆模型的精确解及其应用

推广夹杂问题的三相同心圆模型,提出了三相共焦点椭圆模型,从而计及了夹杂形状变化的重要因素。利用保角变换结合罗朗级数展开技术获得了纵向剪切载荷下的封闭形式解。本模型和解答对夹杂、界面层附近的细观应力场分析、对复合材料和含缺陷材料的有效弹性模量预测有重要实用价值,获得了比经典公式更精确的结果。对特殊模型,可以得到许多有意义的问题（如二相模型）的解答。     

THE SOLUTION TO THE DESTABILIZING CRITICAL LOAD OF CIRCULAR DOUBLE ARTICULATED ARCH UNDER GOING VERTICAL DISTRIBUTIVE LOAD g0/cos2θ

In this paper, after taking the effect of axis force on bending into consideration, the general potential energy for the circular double articulated arch is established undergoing vertical distributive load g₀/cos²θ. With sufficient engineering precision, the fourth approximations to the destabilizing critical load of the arch under t his load are obtained by Ritz method. The approximations to the critical load ta ble are listed for various center angles of arch, and are contrasted with the critical load circular arch undergoing radial uniform load. Some reference results have been obtained.     

Some bounded results of θ(t)-type singular integral operators

Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ(t)-type singular integral operators in L _B ^p (R ⁿ), (1≤p<+∞) and H _B ¹ (R ⁿ) spaces are discussed. Foundation item: the Education Commission of Shandong Province (J98P51) Biography: Zhao Kai (1960-)     

Green's function,continual weighted composition operators along trajectories,and hyperbolicity of linear extensions for dynamical systems

The hyperbolicity of linear skew-product flows with infinite-dimensional fibersE over a dynamical system on a compact metric spaceX is described in terms of the existence and uniqueness of Green's function and in terms of the spectra for family of the semigroups of weighted composition operators acting inL ₂(R;E) and parametrized by the points ofX.     

A study ofJ-integral of the orthotropic composite material

The relation between J-integral near model I crack tip in the orthotropic plate and displacement derivative is derived in this paper. Meanwhile, the relation between stress intensity factor K _I and displacement is also given in this paper. With sticking film moire interferometry method, the three-point bending beam is tested, thus the values of J-integral and K _I can be obtained from the displacement field, and then the truth of relation formula between J-integral and K _I in the orthotropic composite materials is experimentally verified.     

OnJ-integrals in the plane fracture of composite materials

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.     

Maximal Elements and Equilibrium of Abstract Economy

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Pseudo Almost Periodic Solutions to a Class of Semilinear Differential Equations

This paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to a class of semilinear differential equations involving the algebraic sum of two (possibly noncommuting) densely defined closed linear operators acting on a Hilbert space. Sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those semilinear equations are obtained. An erratum to this article is available at .     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.