非线性弹性杆中纵波传播过程的数值模拟

基于Hamilton空间体系的多辛理论研究了包含材料非线性效应和几何弥散效应的非线性弹性杆中纵波传播问题。导出了其Bridges意义下的多辛形式及其多种守恒律,并构造了等价于Box多辛格式的隐式多辛格式对不考虑材料非线性效应和几何弥散效应、只考虑材料非线性效应、只考虑几何弥散效应、同时考虑材料非线性效应和几何弥散效应四种情况下不同截面参数的圆杆中的纵波传播过程进行数值模拟,模拟结果不仅全面地反映了非线性效应和几何弥散效应对纵波传播的影响,而且也反映了多辛方法的两大优点:精确的保持多种守恒律和良好的长时间数值行为。     

简单刚架中的纵横弯曲效应问题

以一个简单刚架为例, 详细讨论了拉、压两种纵横弯曲效应对位移计算结果的影响; 并得出了拉力加强而压力削弱了梁的抗弯曲能力, 两种效应并不对称等结论.     

不锈钢材料的动态力学性能及本构模型

利用带有温度调控系统的SHPB实验装置测定了0Cr17Mn5Ni4Mo3Al不锈钢在3种应变率(300、1 000、2 700 s-1)、4种环境温度（25、300、500和700 ℃）下的应力应变关系;在液压伺服材料试验机(MTS)上进行了3种温度下的准静态（0.0005 s-1）压缩实验。实验结果表明:该不锈钢有明显的应变率强化效应和温度软化效应,并且随着环境温度的升高,应变率强化效应减弱。对Johnson-Cook模型进行了修正,考虑了冲击过程中绝热温升引起的软化效应。修正后的Johnson-Cook模型与实验结果吻合较好。     

基于应变梯度理论的微尺度蜂窝等效模量计算方法

本文提出了一种新的能够计及尺度效应的微纳米蜂窝等效模量的计算方法。将一种单参数应变梯度理论引入到本构方程当中,并基于能量等效原理推导了蜂窝面内等效模量地计算公式。算例分析表明,本文方法能够有效地计及尺度效应对蜂窝等效模量的影响。尺度效应与胞壁厚度和长度的值都有关,当胞壁厚度较小时,尺度效应显著,本文方法预测的模量会明显高于传统方法;而当胞壁厚度较大时,尺度效应变得微弱乃至可以忽略不计。但如果胞壁的长度/厚度比很大,则面内等效模量会趋近于0,此时是否考虑尺度效应意义不大。     

金属材料两种常用本构模型的比较

介绍了两种常用的本构模型，即J－C模型和Z－A模型，就两种模型各自对应变率强化效应、温度软化效应和不同温度或应变率下应变强化行为的不同描述方式进行了比较与分析，讨论了两种模型的适用范围。     

有限单元质量质心集中方法的探讨

提出利用单元质量质心集中方法来优化单元惯性效应表征、改善单元力学效应匹配的 思想: 将单元质量质心集中能够建立精确描述单元质点系惯性效应的动力学方程, 进而达到 优化单元惯性效应表征以及改善单元惯性和变形两种力学效应匹配的目的. 本文通过一维问 题的频散效应分析等对该方法的有效性进行了详细的分析和验证.     

端面摩擦效应对两种含能材料破坏特征的影响

针对Comp.B、PBX-HMX(97%)两种含能材料试样进行了SHPB端面摩擦效应实验,得到了两种材料在不同端面条件下的应力应变曲线.结果表明:端面摩擦效应对实验结果影响很大。通过对回收试样的观察,发现两种材料在不同端面条件下呈现出不同的破坏特征,并对其原因进行了简单分析。     

结构破坏的尺度律

文中综述了结构破坏的尺度律和尺寸效应的研究进展,尤其将重点放在准脆性材料的分析上,因为它们的尺寸效应是重要和复杂的．在回顾了尺寸效应研究的悠远发展史以后。着重讨论了三种主要类型的尺寸效应,即由于强度随机性引起的统计尺寸效应、能量释放的尺寸效应和由于微裂纹或断裂的分形特性可能引起的尺寸效应．得出了这些理论应用的明确结论．之后讨论了如何运用已知的尺寸效应律来测量材料的断裂特性,并采用内聚裂纹模型（cohesivecrackmodel）、非局域化有限元模型和离散元模型等对尺寸效应进行模化．文中还进而分析了尺寸效应在压缩失效和车相关材料行为下的有关问题,并讨论了在断裂扩展区描述含微裂纹材料所需的损伤本构关系．最后也讨论了尺寸效应对准脆性材料的多种应用,这些材料包括,如混凝土、海冰、纤维复合材料、岩石和陶瓷等．本文包含了参考文献377篇     

固体电介质中的挠曲电效应

挠曲电效应通常描述为非均匀变形如应变梯度引起的电极化或者电场梯度引起的变形。由于应变梯度能够局部破坏晶体的反演对称从而在材料中诱导电极化,因此挠曲电效应是固体电介质材料中普遍存在的一种力电耦合效应。由于应变梯度和电场梯度均随材料尺寸的减小而迅速增大,在宏观尺度通常被忽略的挠曲电效应在微纳尺度反而起着非常重要的作用,会显著影响材料的物理性能。与压电效应和电致伸缩效应相比,挠曲电效应具有独特的尺寸依赖特征,其不受材料对称性和铁电材料居里相变温度的限制。本文综述了固体电介质中的挠曲电效应,并重点从理论、材料和应用方面综述了固体电介质中挠曲电效应的研究进展,对挠曲电效应的独特性能进行了详细地讨论,最后本文展望了固体电介质中挠曲电效应相关研究的开放性问题和发展方向。     

冻土动态力学性能的实验研究

利用分离式霍布金森压杆(SHPB)对4种低温下的冻土进行了4种高应变 率的动态压缩实验. 实验结果表明：冻土不仅具有温度效应，还具有应变率效应，两种效应 反映出冻土材料的时温等效性. 另外这种时温等效性在分析冻土材料的破坏过程时还体现在 它的冻脆性和动脆性. 冻土材料动态应力应变曲线的汇聚现象和振荡现象均起源于这种冻脆 性和动脆性.     

DNS study of passive plume interference emitting from two parallel line sources in a turbulent channel flow

Turbulent mixing of dual plumes emitting simultaneously from line sources in a turbulent channel flow has been studied using direct numerical simulation (DNS). Three test cases have been compared to investigate the effects of the source separation on turbulent mixing of the two instantaneous plumes. The dispersion and interference of dual plumes are investigated in both physical and spectral spaces, which include an analysis of statistical moments of the concentration field, cross-correlation between the two instantaneous plumes, pre-multiplied spectra of the velocity and concentration fields, and co-spectrum and coherency spectrum of the dual plumes. As the downstream distance from the line source increases, the plume development associated with a single source emission transitions from a turbulent convective stage to a turbulent diffusive stage. It is observed that a plume released from a ground-level source reaches the turbulent diffusive stage faster than that released from an elevated source. It is also observed that a smaller separation between the two line sources tends to facilitate a more rapid growth in the cross-correlation coefficient of two instantaneous plumes. In the near-source region, the maximum coherency spectrum is produced at lower frequencies indicating that dual-plume mixing is dominated by the external flapping effects of large-scale eddy motions. However, in the far downstream region of the sources, the coherency spectrum in the higher frequency range increases significantly, indicating that the spread of the total plume is larger than all scales of turbulent eddies, such that they all contribute to the in-plume mixing of the dual plumes.     

Instability of fully developed mixed convection with viscous dissipation in a vertical porous channel

Flow driven by an externally imposed pressure gradient in a vertical porous channel is analysed. The combined effects of viscous dissipation and thermal buoyancy are taken into account. These effects yield a basic mixed convection regime given by dual flow branches. Duality of flow emerges for a given vertical pressure gradient. In the case of downward pressure gradient, i.e. upward mean flow, dual solutions coincide when the intensity of the downward pressure gradient attains a maximum. Above this maximum no stationary and parallel flow solution exists. A nonlinear stability analysis of the dual solution branches is carried out limited to parallel flow perturbations. This analysis is sufficient to prove that one of the dual solution branches is unstable. The evolution in time of a solution in the unstable branch is also studied by a direct numerical solution of the governing equation.     

梁在固有振动中的对偶关系

本文研究具有齐次边界的Euler-Bernoulli梁在固有振动中的对偶关系.将两种截面变化不同、但固有频率完全相同的梁定义为异截面对偶梁.通过位移描述和弯矩描述,指出具有齐次边界条件的变截面梁共有如下7类异截面对偶:一是自由-自由梁与固支-固支梁,二是滑支-自由梁与滑支-固支梁(及其镜像),三是铰支-自由梁与铰支-固支梁(及其镜像),四是铰支-滑支梁与铰支-滑支梁(及其镜像),五是滑支-滑支梁与滑支-滑支梁,六是铰支-铰支梁与铰支-铰支梁,七是固支-自由梁与自由-固支梁.在此基础上,将两种截面变化相同、固有频率也相同的梁定义为同截面对偶梁.研究表明,当且仅当梁的截面积函数和截面惯性矩函数具有特定指数函数形式时,前4类异截面对偶梁能成为同截面对偶梁.对于等截面梁,上述前3类同截面对偶仍可保持,而第4类同截面对偶退化为彼此镜像.此时,通过引入转角描述可发现等截面梁产生新对偶,即滑支-滑支梁与铰支-铰支梁对偶.上述等截面梁的对偶均具有如下特征,即对偶中的一种梁具有静定约束,另一种梁具有静不定约束.      

Multi-scale modelling and canonical dual finite element method in phase transitions of solids

This paper presents a multi-scale model in phase transitions of solid materials with both macro and micro effects. This model is governed by a semi-linear nonconvex partial differential equation which can be converted into a coupled quadratic mixed variational problem by the canonical dual transformation method. The extremality conditions of this variational problem are controlled by a triality theory, which reveals the multi-scale effects in phase transitions. Therefore, a potentially useful canonical dual finite element method is proposed for the first time to solve the nonconvex variational problems in multi-scale phase transitions of solids. Applications are illustrated. Results shown that the canonical duality theory developed by the first author in nonconvex mechanics can be used to model complicated physical phenomena and to solve certain difficult nonconvex variational problems in an easy way. The canonical dual finite element method brings some new insights into computational mechanics.     

Evaluation and correction of perspective errors in endoscopic PIV

Results are presented from a single and dual lens endoscopic PIV imaging system with a view to application of PIV where optical access is restricted, such as internal combustion engines and other internal flows. PIV images taken from the single lens system were processed using cross-correlation and a quadratic distortion-mapping function. The dual lens images were processed using cross-correlation, a cubic mapping function, and standard stereoscopic relationships. Comparisons between the single and dual lens systems show the single lens system to have in-plane errors, caused by perspective effects, of an order of magnitude greater than the stereoscopic dual lens endoscopic PIV system. The stereo arrangement is recommended wherever quantitative velocimetry is required, and may also prove useful in general endoscopic inspection where dimensional measurements are to be estimated.     

求解一类可分离凸规划的对偶显式模型DP-EM方法

推导对偶目标函数的精确显式表达式,可选用更多成熟高效的求解方法,从而进一步提高了非线性规划对偶理论求解结构拓扑优化问题的效率.研究工作来源于非线性凸规划同其对偶规划的间隙为零,可以等价转化为对偶问题求解,通常可以大大地缩小问题的规模,可是二者不具有显式关系却影响了对偶解法的应用.所幸的是,结构优化当中一大类问题包括连续体结构拓扑优化问题,不仅具有凸性,而且具有变量可分离性,于是原变量和对偶变量之间有了显式关系,因此,对偶解法成了38年来被应用的有效方法之一.然而长期以来,对偶问题的目标函数并不是显式,这缘于含参数的极小化问题导致目标函数为隐式表达,常见的显式化方法是进行二阶近似.本文突破了对偶问题难以显式化只能采用近似显式的定势,将我们提出的"对偶规划-显式模型"(DP-EM)方法应用于连续体结构拓扑优化,并与对偶序列二次规划(DSQP)算法及移动渐近线(MMA)算法为求解器的方法进行计算效率对比,结果显示:(1)MMA算法比DP-EM算法和DSQP算法的外部迭代次数均多;(2)DP-EM算法与DSQP算法外循环次数相同,而内循环数显著减少.说明了DP-EM算法具有显式对偶函数的优势.     

Analytical series solution for the fully developed forced convection duct flow with frictional heating and variable viscosity

Laminar forced convection flow of a liquid in the fully developed region of a circular duct with isothermal wall is analyzed. The effects of viscous dissipation as well as of temperature dependent viscosity are taken into account. The coupled momentum and energy equations are solved analytically by means of a power series method. Then, reference is made to the Poiseuille model for the temperature change of viscosity. For a fixed value of the axial pressure gradient along the duct, dual solutions are found for the velocity and temperature fields. Although dual solutions correspond to the same value of the axial pressure gradient, they lead in general to different values of the average fluid velocity, of the average fluid temperature and of the wall heat flux. It is shown that, for a given fluid and for a fixed duct radius, the absolute value of the axial pressure gradient has an upper bound above which no steady laminar solution can exist.     

Effects of dual jets distance on mixing characteristics and flow path within a cavity in supersonic crossflow

A rectangular open cavity with upstream dual injectors at a freestream Mach number of 1.9 was investigated experimentally. To evaluate the effect of the distance between the jets, the flow characteristics were investigated using the high-speed schlieren photography, particle image velocimetry, and surface oil flow techniques. The dual jet distances of 18 and 54 mm were used. Unstable flow occurs over the cavity in all cases and is not improved by changing the distance between the dual jets. Although the distance between the dual jets does not influence the flow stability, the flow field varies decidedly depending on the dual jets distance. The enhancement of air mixing depends on the distance between the jets. A long dual jets distance was found to yield better mixing characteristics within the cavity than a short one. When the jets are further apart, the mainstream between two counter-rotating vortex pairs behind the jets flows strongly into the cavity because of the increased blow-down occurring between the vortex pairs. Additionally, a counterflow with a low velocity magnitude occurs behind the jets. Hence, mixing is enhanced within the cavity by effects of the opposed flow. When the jet pairs are closer to each other, the counter-rotating vortex pairs are in contact; as a result, the blow-down effect does not occur between them. The flow drawn into the cavity from the mainstream is supplied from the sides of the test section into the cavity.     

Original ArticleKinematic hardening rules in finite plasticity Part II: Some examples

We consider finite plasticity laws which are represented by means of dual variables and satisfy the intrinsic dissipation inequality. Within two families of dual variables, two different formulations for a kinematic hardening rule, referred to as Model 1 and Model 2, are proposed. In order to discuss basic properties of the two models, the predicted response for some simple deformations is calculated. It turns out that e.g. with respect to the simple shear and simple torsion the two models differ mainly in the effects of second order. Received June 14, 1995     

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimental observations and the classical relation between indentation force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.