微结构固体中钟型与扭结孤立波的演化

根据Mindlin理论和Murnaghan模型,首先建立了描述耗散、频散及非线性微结构固体中一维纵波传播的一种简单模型.然后利用有限差分方法,数值模拟了微结构效应对钟型与扭结孤立波演化的影响. 结果表明,随着微结构效应的减弱,钟型孤立波的幅度衰减以及非对称特征变得越来越明显;随着微结构效应的增强,扭结孤立波顶部出现的“帽子”状变化以及由此产生的非对称特征变得越来越明显.      

Using quaternion matrices to describe the kinematics and nonlinear dynamics of an asymmetric rigid body

A set of four quaternion matrices is used to represent the equations of finite rotation theory and to describe the kinematics and nonlinear dynamics of an asymmetric rigid body in space. The results obtained are tested in setting up direction-cosine matrices, calculating three-index symbols, establishing the relationship between the components of angular velocity in body-fixed and space-fixed frames of reference, and using a set of three independent rotations. Euler–Lagrange equations and a set of four quaternion matrices are used to construct a block-matrix model describing the nonlinear dynamics of a free asymmetric rigid body in three-dimensional space. The model gives the matrix Euler’s equations of motion and other special cases. Algorithms adapted to use in a numerical experiment are developed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 133–143, February 2009.     

非局部—非对称拟连续统理论

本文基于原子点阵模型,应用广义函数论,建立了非局部一非对称拟连续统理论.并讨论了非对称应力的物理—力学模型,即微观—宏观相结合的模型理论.     

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs＇ parameter 13 or the larger the pulling angle O, the more reasonable the symmetric model would be to approximate the asymmetric one.     

Construction of irregular particles with superquadric equation in DEM

Non-spherical particles are widely present in industrial production, and significantly affect the macro and micro characteristics of granular materials. Although the superquadric equation can be used to construct non-spherical particles, its disadvantage is that the particle shape is geometrically symmetric and strictly convex. In this study, two composed approaches are used to describe geometrically asymmetric and concave particle shapes, including a multi-superquadric model and a poly-superquadric model. The multi-superquadric model is a combination of several superquadric elements, and can construct concave and geometrically asymmetric particle shapes.The poly-superquadric model is a combination of eight one-eighth superquadric elements, and can construct convex and geometrically asymmetric particle shapes. Both composed models are based on superquadric equations, and Newton's iterative method is used to calculate the contact force between the elements. Furthermore, superquadric elements, multi-superquadric elements,and poly-superquadric elements are applied for the formation of complex granular beds, and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.     

A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model

A new modified couple stress theory for anisotropic elasticity is proposed. This theory contains three material length scale parameters. Differing from the modified couple stress theory, the couple stress constitutive relationships are introduced for anisotropic elasticity, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. However, under isotropic case, this theory can be identical to modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The differences and relations of standard, modified and new modified couple stress theories are given herein. A detailed variational formulation is provided for this theory by using the principle of minimum total potential energy. Based on the new modified couple stress theory, composite laminated Kirchhoff plate models are developed in which new anisotropic constitutive relationships are defined. The First model contains two material length scale parameters, one related to fiber and the other related to matrix. The curvature tensor in this model is asymmetric; however, the couple stress moment tensor is symmetric. Under isotropic case, this theory can be identical to the modified couple stress theory proposed by Yang et al. (Int J Solids Struct 39:2731–2743, 2002). The present model can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model of couple stress theory including only one material length scale parameter for modeling the cross-ply laminated Kirchhoff plate is suggested. Numerical results show that the proposed laminated Kirchhoff plate model can capture the scale effects of microstructures.     

A multi-axial constitutive model for metal matrix composites

Metal matrix composites (MMCs) generally do not follow the classical plasticity theory, even though the matrix metals do deform plastically. A tension-compression yield asymmetry is typically observed in MMCs. For particulate-reinforced MMCs, this non-classical response is mainly due to the variation of damage evolution with loading modes. In this paper, a viscoplastic multi-axial constitutive model for plastic deformation of MMCs is constructed using the Mises-Schleicher yield criterion. The subsequent plastic flow is characterized by an associated and decomposed flow rule considering effects from both deviatoric and hydrostatic stresses. This model is capable of describing the multi-axial yield and flow behavior of MMCs by using simulated or measured asymmetric tensile and compressive stress-strain responses as input. As an example, the influence of damage evolution in terms of interfacial debonding in MMCs (obtained from FEM simulations) is incorporated through the different tensile and compressive stress-strain behaviors. Applying this model to predict the torsion and the pressure-dependant tensile responses of some commonly used MMCs provides good agreement with experimental data.     

The structure of shock layers in elastic-plastic media: Micro-plastic regime

The Granato-Lücke theory of internal friction is used as the basis of a model of shock-wave formation and propagation in elasto-plastic solids below the general yield point. The structure of shock layers in such a model is shown to be in general asymmetric and, at sufficiently large jumps in strain, to exhibit oscillations in the strain at its trailing edge.     

Investigation of convection in a horizontal cylindrical layer of a saturated porous medium

The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness.     

Numerical investigation of the mechanism of asymmetric vortex flows

A robust iterative method suitable for the numerical simulation of high angle of-attack vortex flows is established based upon the multiple line vortex model (MLVM). With symmetric or asymmetric positions of separation lines given, the first converged solution at an angle of attack as high as 60 degree is obtained by means of the present method. Numerical experiments for a tangent-ogive forebody indicate the viscous onset mechanism of asymmetric vortex flows over a body of revolution at high angles of attack and zero sideslip.     

Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides

Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered.The theory of bifurcations of the fixed point is applied to such model,and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincarémap.The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation.While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences,and bring about two antisymmetric chaotic attractors subse- quently.If the symmetric system is transformed into asymmetric one,bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.     

基于3自由度的新月形覆冰输电线舞动稳定性研究

针对覆冰输电线舞动问题提出了一种基于非对称空气动力系数矩阵的临界风速计算方法．基于拟静态理论得到覆冰输电线的气动载荷，该气动载荷考虑了横向运动以及扭转运动对相对风攻角的影响，最后建立等效的3自由度覆冰输电线舞动模型．在初始风攻角处对气动载荷进行泰勒展开，得到非对称的线性空气动力系数矩阵．结合3自由度振动方程以及非对称空气动力系数矩阵，采用Rourh-Hurwitz准则计算覆冰输电线舞动发生的临界风速．通过风洞实验测得新月型覆冰单导线的空气动力系数，根据本文提出的理论分析了竖向振动频率、面外振动频率以及扭转振动频率对临界风速的影响，最后与DenHartog理论得到的临界风速进行了对比．本文研究成果对于指导覆冰输电线路防舞设计具有理论意义．     

Generalized closed-form model for analysis of asymmetric shaped charges

This paper presents a model that has less constraints than similar models and explains the collapse phenomenon in any desired order of geometrical asymmetries and in the presence of symmetric and asymmetric general-form wave fronts. It seems that, in this model, a complete generalized form of the classical jet formation theory has been developed. Available models that describe the symmetric jet and slug formation phenomenon are very good in such conditions. But the liner and confinement asymmetries, detonation wave front asymmetries, and other specifications, such as manufacturing tolerances, can affect the collapse and the behavior of the jet and slug. Some proposed models that describe asymmetric cases are not closed-form models or are only applicable for limited conditions, such as small asymmetries and a planar wave front. With the presented model, effects of concave, plane, and convex wave fronts on the off-axis velocity of the jet, other parameters of the jet and slug, and effects of an asymmetric wave front on jet formation for a completely symmetric liner and confinement geometry can be evaluated.     

An asymmetric theory of nonlocal elasticity—Part 1. Quasicontinuum theory

In this article, an asymmetric theory of nonlocal elasticity is developed on the basis of three dimensional atomic lattice model, the Galileo invariance for constitutive equations and by use of Fourier transformation of generalized function and energy method. It is shown that nonlocal characteristic functions (or constitutive parameters of internal elastic energy) can be explicitly expressed in terms of interacting forces connecting atoms, and the general model of nonlocal theory with rotation effects is asymmetric. Both symmetric stress and anti-symmetric stress is a nonlocal function of strain and local rotation for anisotropic materials. For isotropic materials, symmetric stress is only a nonlocal function of strain, while antisymmetric stress is only a nonlocal function of local rotation.     

T-Y tube model of human ascending aortic input impedance

Arterialimpedancehasitsparticularsignificancebecauseitdescribesthephysicalandgeometricalcharactersofthewholearterialsystem.Moreover.itisagoodmeasureoftheleftventricleafterload.Numerousexperimentalandtheoreticalresearchesha\'ebeendoneinthisarea.Itisshownth…     

不可压缩湍流非对称脱体涡流场数值分析

采用拟压缩性方法，Ｂｅａｍ－Ｗａｒｍｉｎｇ近似因式分解格式数值求解三维定常不可压Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程。对Ｂａｌｄｗｉｎ－Ｌｏｍａｘ代数湍流模型，采用Ｄｅｇａｎｉ－ｓｃｈｉｆｆ修正。计算绕尖头正切拱型旋成柱体的大迎角大雷诺数脱体涡流场，计算结果中的非对称脱体涡与实验相符．     

剥蚀引起的球锥体两相绕流效应

基于多学科理论建立了极端环境下球锥体烧蚀、剥蚀的数理模型。利用离散涡方法计算流场与球锥表面压力分布,采用三方程烧蚀模型计算热化学控制机制下的烧蚀速率;引入颗粒轨道模型求解剥蚀颗粒的运动,编程计算高温高压燃烧室内球锥形烧蚀试件的绕流场及剥蚀颗粒的运动轨迹。研究表明：烧蚀对球锥体的绕流影响显著,球锥体的涡云较快地转变为不对...     

Theory of nonlocal asymmetric elastic solids

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum fieM theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic fiteld theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation, We show that there is the nonlocal body moment in the nonlocal elastic solids. The noniocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.     

基于强度与稳定性的端头加固理论模型及敏感性分析

为确保盾构始发与到达的顺利进行,避免施工过程中发生端头土体失稳,引发地表沉陷、塌方等工程事故,基于土体强度与稳定性的基本理论,作者就如何确定端头土体纵向加固范围和建立砂土复合地层端头滑动模型进行了研究。在具体分析了现有端头加固理论模型的优缺点后,提出一种基于强度理论的荷载等效模型和基于稳定性理论的砂性土端头滑动模型。该端头加固理论模型,与已有的计算模型相比,更真实地反映了端头土体的受力状况,因而与工程实际情况更为接近,且具有地层适应性。同时,为了检验新强度理论模型的合理性,分别对新旧模型进行实例比算,并对2种模型的主要影响因素进行了敏感性分析。研究结果表明:当盾构隧道直径较小时,已有模型和新提出模型的计算结果误差较小,计算结果较为接近; 随着盾构隧道直径的不断增大,已有模型的荷载简化会引起较大的计算结果误差,如将其结果应用于工程,可能会引发较严重的工程事故; 对于大直径盾构,特别是盾构隧道直径大于10m时,建议采用本文提出的改进理论模型进行端头加固设计和验算,由此得出的加固范围更加符合工程实际情况,对工程有很强的指导意义。同时基于强度理论提出的荷载等效模型为非对称荷载问题的研究提出了一种新的研究方法和求解思路,对今后类似问题的求解具有较好的借鉴意义。     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。