A Second-Order Solution of Saint-Venant's Problem for an Elastic Pretwisted Bar Using Signorini's Perturbation Method

We use Signorini's expansion to analyse deformations of a straight, prismatic, isotropic, stress free, homogeneous body made of a second-order elastic material and loaded as follows. It is first twisted by an infinitesimal amount and then loaded by applying surface tractions, with nonzero resultant forces and/or moments, only at its end faces. The centroid of one end face is taken to be rigidly clamped. By using a semi-inverse method, the problem is reduced to that of solving two plane elliptic problems involving six arbitrary constants that characterize flexure, bending, extension, and torsion superimposed upon the infinitesimal twist. It is shown that the Clebsch hypothesis is not valid for this problem. A second-order Poisson's effect, not of the Saint-Venant type, and generalized Poynting effects may also occur in these problems. This revised version was published online in August 2006 with corrections to the Cover Date.     

Linear Stability Analysis of Infiltration,Analytical and Numerical Solution

Linear stability analysis is applied to the Richards equation by perturbing the pressure field. An analytical solution of the stability problem of flow through stratified media is presented. It is obtained under two simplifying assumptions: the quasi-steady hypothesis and the quasi-linear hypothesis. Flow is found to be unconditionally stable. A numerical experiment and the comparison with published data supports the conclusion that upscaling capillary phenomena is crucial in order to capture the essence of finger flow by continuum models.     

One-dimensional nonuniform temperature flow with heat transfer by convection

In ref. [1], V. E. Najenov studied the conditions that when the viscosity of the liquid is an exponential function of temperature, the pipe flow, having steady heat transfer, is one dimensional and with nonuniform temperature. For plane canal and circular pipe he still studied the velocity and the temperature fields.In this paper, the author presents two new methods for solving the same problem. The method as in ref. [1] may be regarded as the natural branch of the methods of this paper. One of our new methods only can solve the same problem as in ref. [1] and the complex degree of its computing process is nearly the same as that in ref. [1]. But the other can go beyond the studying scope of ref. [1], namely, for the case that the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem may also be solved.     

Some checks of Taylor''s hypothesis in a slightly heated turbulent circular jet

Taylor's hypothesis has been examined by comparing temporal variations of the temperature fluctuation θ with the corresponding spatial variations. The comparison is made on the axis of a circular jet in the self-preserving region of the flow for streamwise separations extending to about 10 Kolmogorov microscales. The use of the hypothesis yields reliable estimates of streamwise temperature correlations and also of second- and third-order moments of streamwise temperature increments. Fourth-order moments of these increments are estimated less accurately. Departures from the hypothesis are smaller than in the plane jet; consistently, local isotropy appears to be more closely satisfied in the circular jet.     

扭转变形平面假设的讨论

在对圆轴扭转平面假设的内涵进行分析的基础上, 关联其在应力分析中 的应用, 并讨论了平面假设成立的条件以解释矩形截面翘曲现象, 可作为该部分课堂教学的 参考材料.     

动态最优滤波系统的粗差探测

观测粗差是影响动态系统最优滤波效果的重要因素，本文以静态平差理论为基础，研究了动态滤波系统粗差探测的理论和方法，简单的应用实例说明，文中介绍的粗差探测方法是有效的     

基于应变等效性假说的损伤定义的适用条件

研究了基于应变等效性假说的损伤定义方法，分析了定义中“材料损伤前后弹性模量”的物理含义。指出该方法只适用于间接描述弹（脆）性材料损伤行为，不能简单地用受荷过程中的“卸载模量”代替假说中的“受损弹性模量”来描述具有不可逆塑性变形特征的弹塑性损伤行为，否则将可能导致对损伤行为的误判。此外，本文给出了一种耦合塑性形变和损伤机制影响的弹塑性损伤定义。     

A modification of Taylor-Galerkin Finite Element Method and its application

Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper.One of them which is unreasonable is redefined.The only hypothesis becomes the standpoint of Generalized Finite Element.We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method,and give the two-step solving method,which makes the solving process more reasonable than ever before.Several computational examples reveal that the results of this new method are satisfied.     

Physical criterion study on forward stagnation point heat flux CFD computations at hypersonic speeds

In order to evaluate uncertainties in computational fluid dynamics （CFD） computations of the stagnation point heat flux, a physical criterion is developed. Based on a quasi-one-dimensional hypothesis along the stagnation line, a new stagnation flow model is applied to obtain the governing equations of the flow near the stagnation point at hypersonic speeds. From the above equations, the compatibility relations are given at the stagnation point and along the stagnation line, which consist of the physical criterion for checking the accuracy in the stagnation point heat flux computations. The verification of the criterion is made with various numerical results.     

On Aifantis’ strain gradient plasticity theory accounting for plastic spin

This paper examines the effect of codirectionality hypothesis on Aifantis’ distortion gradient plasticity theory. The system of microforces includes microstress, power-conjugate to the Burgers tensor rate. The proposed codirectionality hypothesis assumes, that the flow direction and the plastic microstress are in the same direction. It is obtained that the power expended by the microstress power-conjugate to the Burgers tensor rate, can be additively decomposed to power expended by scalar and vector microscopic stresses power-conjugate to the accumulated plastic distortion rate and gradient of plastic distortion rate respectively. Following the proposed codirectionality hypothesis, it is obtained that the microstress power-conjugate to the Burgers tensor rate is purely energetic. The obtained flow rule accounts for plastic spin and generalizes the Aifantis’ flow rule.     

A failure of a class of K-BKZ equations based on principal stretches

The invariants in the K-BKZ constitutive equation for an incompressible viscoelastic fluid are usually taken to be the trace of the Finger strain tensor and its inverse. The basis for this choice of invariants is not derived from the K-BKZ theory, but rather is due to the perception that this is the most natural choice. Research into using other sets of invariants in the K-BKZ equation, such as the principal stretches or the eigenvalues of the Finger strain tensor (i.e., the squares of the principal stretches) is relatively new. We attempt here to derive a K-BKZ equation based on the squares of the principal stretches that models the behavior of a low-density polyethylene melt in simple shear and uniaxial elongational deformation. In doing so, two assumptions are made as to the form of the strain-dependent energy function: first, that there is a function f(q) such that the energy function can be written as the sum of f(q _i ),i = 1, 2, 3, where the q _i 'sare the squares of the principal stretches, and second that f is a power law. We find that the K-BKZ equation resulting from these two assumptions is inadequate to describe both the shear and elongational behavior of our material and we conclude that the second of the above assumptions is not valid. Further investigation, including predictions of the second normal stress difference and some finite element calculations reveals that the first assumption is also invalid for our material.     

Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper

Nanoscale contact of material surfaces provides an opportunity to explore and better understand the elastic limit and incipient plasticity in crystals. Homogeneous nucleation of a dislocation beneath a nanoindenter is a strain localization event triggered by elastic instability of the perfect crystal at finite strain. The finite element calculation, with a hyperelastic constitutive relation based on an interatomic potential, is employed as an efficient method to characterize such instability. This implementation facilitates the study of dislocation nucleation at length scales that are large compared to atomic dimensions, while remaining faithful to the nonlinear interatomic interactions. An instability criterion based on bifurcation analysis is incorporated into the finite element calculation to predict homogeneous dislocation nucleation. This criterion is superior to that based on the critical resolved shear stress in terms of its accuracy of prediction for both the nucleation site and the slip character of the defect. Finite element calculations of nanoindentation of single crystal copper by a cylindrical indenter and predictions of dislocation nucleation are validated by comparing with direct molecular dynamics simulations governed by the same interatomic potential. Analytic 2D and 3D linear elasticity solutions based on the Stroh formalism are used to benchmark the finite element results. The critical configuration of homogeneous dislocation nucleation under a spherical indenter is quantified with full 3D finite element calculations. The prediction of the nucleation site and slip character is verified by direct molecular dynamics simulations. The critical stress state at the nucleation site obtained from the interatomic potential is in quantitative agreement with ab initio density functional theory calculation.     

空间网架结构在地震作用下的损伤累积分析

本文从连续介质损伤力学的基础理论出发，提出了弹性模量等价性假设，并在这一假设的基础上建立了考虑损伤累积效应的空间网架结构分析的有限元列式。最后，以空间网架结构在地震作用下的损伤累积分析为例，给出了本文方法的具体实施步骤。     

求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

基于湍流类比的金属橡胶吸声特性定量分析

金属橡胶材料从表到里都具有大量互相贯通且混乱的孔隙, 经分析认为, 这种混乱性及一定的周期性与湍流中的不规则性和准周期性极其相似. 由于金属橡胶材料内部芯材结构的不规则性, 即便此时的雷诺数很小, 波在金属橡胶中的传播仍是以湍流流动为主. 因此, 引入Kolmogorov的关于湍流的局部各向同性概念, 同时对Kolmogorov关于湍流局部各向同性的两个假设进行类比. 从湍流物理模型出发, 借鉴了湍流的统计处理方法, 对金属橡胶材料的吸声特性进行定量分析, 得到金属橡胶材料的能量耗散率与其结构参数之间的表达式. 研究结果表明, 湍流统计方法的引入, 为基于金属橡胶材料的减振器、阻尼器、消声器等的优化设计提供了可靠的理论依据, 也为超轻金属多孔材料的工程应用提供了一种有效的定量分析方法.      

A note on derivatives of function and their fourier transforms in L2

The purpose of this article is to indicate the shortcomings of a few theorems of [1]. Moreover, some interesting results are deduced.     

Analogy solutions of axisymmetrical twist problems by axisymmetrical finite element program

It used to be considered that an axisymmetrical problem and a twist problem of an axisymmetrical body cannot be simulated by each other, because the number of unknown variables in an axisymmetrical problem is greater than that in a twist problem, and the governing equations are not the same. This paper proposes a degenerated analogy method, by which the twist problems of axisymmetrical bodies can be simulated by axisymmetrical problems with finite element programs.An ordinary structural analysis method can be used to analyze an axisymmetrical problem, but a twist problem of axisymmetrical bodies is treated as a 3-dimensional problem usually. According to the method proposed in this paper, the analysis of a twist problem can be simulated by the analysis of an axisymmetrical body with a structural analysis problem. The example of analysis computation is also given. Thecomputed result is in agreement with the theoretical result.In this paper, the constitutive relation of the degenerated analogy problem is given.The authors suggest that a twist problem of a body made of any materials is simulated by an axisymmetrical problem of a body made of orthotropic material. If you have to use some program for the axisymmetrical problem to be limited to isotropic materials the penalty coefficient method can be used to solve the problem.     

Study of Pressure Sensitive Plastic Flow Behaviour of Gasket Materials

The mechanical behaviour of the materials used as compressible gasket in the ultra high pressure apparatus is investigated. Materials such as pyrophyllite and talc, showing a pressure sensitive plastic flow behaviour were considered and a testing configuration was set up for studying the dependence of their plastic response on the hydrostatic component of the stress tensor, according to the Drucker-Prager criterion. A Finite Element modelling of the test was performed to evaluate the specimen response and the local stress condition, during loading. The Finite Element results were validated by comparison with those of a specific experimental characterisation. A parametric analysis was then carried out, by varying the materials constitutive behaviour, in order to build up a data base of representative curves. In this way an algorithm was developed, with the aim of determining the material constitutive behaviours by the analysis of the experimental data. The proposed procedure was then used to study the mechanical response of different gasket materials.     

轴对称体扭转问题的轴对称有限元模拟解

轴对称体的轴对称问题与扭转问题一向被认为是两个互相不能模拟的问题.前者的未知量与方程多于后者,形式也不相同.本文提出一种退化模拟方法.能够把扭转问题模拟为轴对称问题的一类特殊情况来解.一般的结构分析程序都能够分析轴对称问题,但轴对称体的扭转问题通常作为三维问题处理.按本文提出的方法,可用结构分析程序的轴对称分析功能模拟扭转分析.本文还给出模拟计算的算例.计算结果表明与理论解完全一致.本文对退化模拟的材料本构关系进行了研究,建议在数值计算时以各向异性材料的轴对称问题模拟任何材料的扭转问题.当限定用各向同性材料的轴对称问题来模拟时,采用了罚系数法.     

Experimental investigation of the grid-generated turbulence features in a free surface flow

The present study aims to investigate the features of a grid-generated turbulence occurring in a current flow with a free surface flow. The interest is focused on the length and time scales of the turbulence. These are the macro, the micro and the Kolmogorov scales. To analyze the flow, a 2D LDV system has been used to measure , , u′ and w′. This non-intrusive and optical technique is really accurate (in terms of space and time resolution). Furthermore, it does not disturb the flow and provides a high data rate. Both horizontal and vertical velocities are recorded at the same time according to a coincidence window (τ_cw). Bias measurements are avoided by using a filtering technique during data processing. The improved homogeneity and isotropy of the turbulence downstream of the grid allows the use of the Taylor hypothesis. Thus, all length and time scales of the flow can be estimated. Results are discussed as well as the influence of the upcoming mean velocity on the turbulence properties.