Numbering homoclinic points of diffeomorphisms in the plane

In this paper we introduce a numerical conjugacy invariant for planar maps with homoclinic points. This invariant can be estimated based on partial information about the location of compact pieces of the stable and unstable manifolds of the system. The invariant is also related to topological entropy, and we indicate a method by which good bounds on the entropy of a system can be obtained.     

弹塑性板壳结构非线性有限元分析

本文根据塑性流动理论的基本公式，由隐式积分导出了与路径无关的变量更新算法和一致切线模量。采用单元广义应力应变直接离散塑性流动定律，构造了杂交应力单元一致切线刚度矩阵的显式表达式，编制了结构有限元程序ＳＡＦＥ，数值算例表明：本文的计算方法和计算程序是正确可靠的，可用于弹塑性板壳结构的非线性分析，计算结果屈曲临界载荷和极限承载能力。     

EFFECT OF VERTICAL BAFFLES ON PARTICLE MIXING AND DRYING IN FLUIDIZED BEDS OF GROUP D PARTICLES

This study reports the effect of vertical baffles on the group D powder mixing and drying characteristics in a batch fluidized bed dryer. Results obtained in this study showed that operating the fluidized bed dryer with vertical baffles gave better particle mixing. This is due to the fact that the vertical baffles acted to limit the growth of small bubbles into large bubbles and the small bubbles caused more vigorous mixing in the bed of particles before finally erupting at the bed surface. Thus, insertion of vertical baffles is a useful way to process group D particles in a fluidized bed, especially when the fluidized bed is large.     

VERIFICATION OF SMOM AND QMOM POPULATION BALANCE MODELING IN CFD CODE USING ANALYTICAL SOLUTIONS FOR BATCH PARTICULATE PROCESSES

For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simulation. In this work, a CFD based population balance model is tested using a batch crystallization reactor. In this CFD model, the population balance is solved by the standard method of moments （SMOM） and the quadrature method of moments （QMOM）. The results of these simulations are compared to analytical solutions for the population balance in a batch tank where 1） nucleation, 2） growth, 3） aggregation, and 4） breakage are taking place separately. The results of these comparisons show that the first 6 moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage at all times.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

Approximate solutions for the shear center of plates of variable thickness

Summary In a plate-theoretical formulation of the shear center problem, the relevant boundary-value problem is for a cantilevered rectangular plate of variable thickness with two free opposite edges and with the edge opposite to the clamped end subject to a rigid vertical displacement and free of bending moment. For plates with Poisson's ratiov equal to zero, there is an exact elementary solution for this boundary-value problem from which the exact location of the shear center can be calculated. When Poisson's ratio is not zero, an approximate elementary solution may be obtained within the framework of a Saint-Venant flexure solution for plates by satisfying the displacement boundary conditions at the clamped edge approximately. Different forms of this approximation are discussed in [7], some with rather marked Poisson's ratio effects. Among these, the minimum complementary energy approach of [6] gives a shear center location identical to the exact solution forv=O.A generalized beam theory developed in [6] is implemented here to delineate the effect ofv without altering the edge conditions by ad hoc approximations. The results show that the Poisson's ratio effect is rather moderate and the shear center location is nearly the same as that for zero Poisson's ratio. A finite element solution for the plate theory boundary-value problem confirms this finding.The generalized beam equations are also used to study the effect of the aspect ratio of the plate and orthotropy on the location of the shear center.

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Näherungslösungen für den Schubmittelpunkt von Platten veränderlicher Dicke

Übersicht In der plattentheoretischen Formulierung des Schubmittelpunktproblems [6] betrifft die relevante Randwertaufgabe eine rechteckige Kragplatte mit veränderlicher Dicke in Querrichtung, mit einer Lastverteilung, welche eine gleichförmige Durchbiegung am belasteten Rand erzeugt.Die vorliegende Arbeit implementiert eine Näherungslösung dieses Problems in der Form einer verallgemeinerten Balkentheorie zwölfter Ordnung, welche Verwölbung sowie auch anticlastische Krümmung berücksichtigt [6]. Das Ziel ist, den quantitativen Einfluß der Poissonschen Zahl und auch den der Orthotropie zu bestimmen.Die Resultate zeigen, daß der Einfluß der Poissonschen Zahl, welcher in der bekannten näherungsweisen Bestimmung mit Hilfe des Variationsprinzips für Spannungen vollkommen verschwindet, in der Tat sehr gering ist, insbesondere im Vergleich mit den Folgen einer Anwendung der St.-Venantschen Biegetheorire zusammen mit einer klassischen Stipulierung bezüglich des Verschiebungsfeldes am Schwerpunkt der Querschnittsfläche. Darüber hinausgehend wird gezeigt, daß die numerischen Werte nur unwesentlich von Unterschieden zwischen Isotropie und Orthotropie beeinflußt sind.Die obigen Resultate werden durch die Ableitung und Anwendung einer Balkentheorie sechzehnter Ordnung und durch Rechnungen mit Hilfe von Finiten Elementen bestätigt.

     

动态系统最优滤波的可靠性

—本文以静态测量的可靠性理论为基础，研究了动态系统最优滤波的可靠性及其特性，以ＧＰＳ动态定位为例，对其可靠性指标进行了初步分析。动态系统的可靠性理论对于研究动态系统的粗差剔除、容错技术、可靠性分析等具有重要意义     

ANISOTROPIC STRENGTH CRITERION BASED ON T CRITERION AND THE TRANSFORMATION STRESS METHOD 1)

岩土材料通常呈现出成层水平分布特点, 即可将其视为横观各向同性材料, 横观各向同性对于岩土材料的变形以及强度值都会产生显著的影响. 基于已提出的t强度准则, t强度准则是基于各向同性单元体中存在有效滑移面来构建的, 并根据该空间有效滑移面上主剪应力与主法向应力的比值达到一定阈值为破坏条件. 在空间中存在有效滑移面与物理沉积面, 基于上述两个面在空间的位置关系, 用两面夹角作为表征横观各向同性对剪切强度影响程度的参量, 并假定当该夹角值越大, 则各向异性对强度贡献程度越大, 对应更大的应力比强度值, 反之, 则对应更小的应力比强度值. 基于上述思路并类比将其推广为正交三维各向异性准则, 基于三维各向异性材料的三维沉积面, 提出了三维特征沉积面的概念, 并基于空间滑移面与三维特征沉积面之间的夹角作为度量各向异性程度的变量, 提出了基于两面角作为参量考虑原生各向异性的应力比强度公式, 并利用该应力比强度公式来修正已提出的t强度准则, 最终建立了考虑各向异性影响的t准则公式. 在上述准则基础上, 考虑将各向异性应力空间转换为各向同性应力空间的思路, 在各向异性t准则基础上, 推导得到了基于各向异性强度t准则的变换应力公式, 利用变换应力公式可以将传统的以p, q为变量的各向同性本构模型转变为可考虑各向异性的三维本构模型. 通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测, 验证了所提的各向异性t准则及其变换应力公式的有效性及适用性.     

Experimental and theoretical study of the nonlinear response of agiant magnetostrictive rod

In this paper, a magnetomechanical coupling constitutive relation of the giant magnetostrictive material was investigated experimentally and theoretically. A grain-oriented magnetostrictive rod of iron and rare earth was tested under a combined magnetomechanical loading. Two types of experimental curves were obtained, i.e., the magnetostrictive curve of the extensional strain vs the magnetic field, and the curve of the magnetic polarization intensity vs the pre-stress. A new theoretical constitutive model, based on the density of domain switching, is developed. Comparison of the theoretical predictions with the experimental results indicates that this model can capture the main characteristics of the magnetoelastic coupling deformation of a giant magnetostrictive rod. The project supported by the National Natural Science Foundation of China (10025209, 10132010, 10102007)     

Non-linear constitutive relations for magnetostrictive materials

In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.