拉格朗日方程应用于弹性力学两例

本文运用第二类拉格朗日方程,推导出弹性体的平衡微分方程和弹性波的传播方程。1.平衡方程的推导为使表述简洁,以下采用张量表示法。弹性静力学中,弹性体的边界条件为     

拉格朗日方程应用于弹性力学两例

本文运用第二类拉格朗日方程,推导出弹性体的平衡微分方程和弹性波的传播方程。1.平衡方程的推导为使表述简洁,以下采用张量表示法。弹性静力学中,弹性体的边界条件为...     

考虑质量耦合效应的流体饱和孔隙介质波动方程

利用混合物理论和连续介质力学的基本原理，推导了考虑质量耦合效应的流体饱和弹性孔隙介质的波动方程，并与经典的Biot波动方程进行了对比．结果表明：该文得到的方程包含了Biot波动方程的所有要素，且形式与后者基本相同．比较而言，该文推导过程具有更明确的物理意义，概念也更完整．     

用微元六面体推导流体力学基本方程时参考点的选择

用微元六面体证明流体力学基本方程是流体力学教学的基本内容,也是学生需要培养的思维方式.有些流体力学教科书中在用微元六面体推导流体力学方程时,由于参考点的选取不恰当,对推导过程的解释有的不清晰,有的有错误,不利于学生准确理解和掌握这个基本方法.本文对微元上物理量的分布进行了探讨与分析,指出参考点的选取对于正确推导流体力学方程的意义,并分析了为什么参考点选错了也能推导出正确结论的原因.     

多体系统动力学的高斯拘束分析方法

为研究高斯拘束原理下多体系统的动力学分析问题,针对一类多体开环链状结构,运用高斯拘束方法建立了动力学方程,讨论了动力学方程的符号推导过程,并给出了封闭形式的动力学方程解析表达式.以刚性和柔性结构为例,比较分析了不同分析方法、不同自由度下符号推导多体结构动力学方程的运算时间.分析结果表明,高斯拘束方法与传统的拉格朗日方法相比,更适合于多体结构动力学方程的符号推导,且结构自由度越高,其运算优势越明显.高斯拘束方法为一种较好的多体系统动力学分析方法.     

一维定常泥石流的数学模型

根据泥石流在山坡斜面的长度（Ｌ）远大于泥石流横截面的特征长度（Ｈ＿０），对连续方程，运动方程和Ｂｉｎｇｈａｍ模型的本构方程进行量级比较，忽略Ｈ＿０／Ｌ量级的量，推导出控制一维定常泥石流运动的微分方程。本文方法可应用于推导非定常一维泥石流的数学模型。     

贮腔类三维自由液面动力学问题数值研究

讨论了贮腔类三维自由液面动力学问题的数值研究,将任意的拉格朗日-欧拉运动学描述关系引入到系统的控制方程中,采用任意的拉格朗日-欧拉描述跟踪自由液面,推导了自由面上结点的法向矢量计算公式。采用Galerkin余量法推导了Navier-Stokes方程的空间离散有限元方程,采用三维自由液面上微分几何理论推导了表面张力计算公式。数值研究中考虑了接触角效应,最后进行了三维数值算例分析。     

绳索的大变形问题

根据绝对柔韧杆在大变形时应变与位移的准确关系以及平衡方程;推导出绳索在自重作用下的精确关系以及平衡方程,推导出绳索在自重作用下的精确解析解．并举例对电缆进行了分析和讨论．     

航天器挠性梁伸展动力学特性数值分析

利用动量矩定理推导出带挠性伸展梁航天器的姿态动力学方程,推导了梁质量微元的动力学方程．在梁等速伸展的情况下对动力学方程进行变换,通过Runge-Kutta积分法得出了数值解．结果表明梁等速伸展时,其振动的振幅随其长度的增长而增大;随航天器初始姿态角速率的增大而增大;随伸展速率的增大     

关于推导直杆横截面上应力及变形公式的探讨

借用弹性力学几何方程、物理方程及材料力学中常用的平面假设,静力平衡方程,一次性推导出材料力学中的常用公式,阐述了用此法进行试验性教学的体会。     

On hysteresis in elasto-plasticity and in ferromagnetism

We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl–Ishlinski models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems.

We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model.     

Heating zone dynamics in in situ combustion

The integrodifferential equation of the quasisteady regime of a moving in situ combustion front is obtained and its exact solution is constructed in a particular case; the possibility of the heat generated at the combustion front being projected into the region ahead of the front is analyzed and the heating zone dynamics in the reservoir and the surrounding rock are investigated. In a number of studies of in situ combustion it is assumed that an increase in the water-air factor or, what amounts to the same thing, an increase in convection velocity in the reservoir leads to the total transfer of the heat into the region ahead of the combustion front [1–3]. In [3] the area of the heating zone ahead of the combustion front was calculated in accordance with the Marx-Longenheim model [4]. Below, on the basis of exact solutions of model problems it is shown that in the case of quasisteady Newtonian heat transfer between the surrounding medium, when the latter is assumed to be a thermal reservoir, i.e., maintain a constant temperature, this projection of heat is possible if the convection velocity exceeds the velocity of the combustion front. In the case of unsteady heat transfer in accordance with the Leverrier model there is no total projection of heat into the region in question; in the steady-state regime a limited heating zone, proportional in depth to the square of the difference of the convection and combustion front velocities, is formed ahead of the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–172, July–August, 1987.The author wishes to thank V. M. Entov for his valuable advice and useful discussions.     

Advance in Experimental Mechanics in Asia-2006

In order to offer an opening platform for researchers in Experimental Mechanics community from Asia and other regions to communicate their achievement, the Editorial Committee of Journal of Experimental Mechanics decided to publish an international series…     

Genetic disorders in haematological practice in India

Haemoglobinopathies represent a significant national health burden in India. The distribution of specific disorders varies geographically and by community. Heterozygote frequencies of beta-thalassaemia range from 1 to 15%, resulting in an estimated 20 million carriers. HbS is mainly present in tribal and non-caste communities, with carrier prevalences of up to 40%. By comparison, alpha-thalassaemia carriers are found in both the caste and tribal communities, and can reach a frequency of >90% in the latter case. Community control of haemoglobinopathies relies mainly on out-reach education programmes and genetic counselling, with antenatal diagnosis offered in specific major centres. Only partial data are available on the prevalence of haemophilia, but it has been estimated that there are some 50,000 affected individuals nationwide, with an additional 1,500 new cases born each year. RFLP-based techniques have been established to detect mutations in the factor VIII and IX genes, enabling the limited introduction of carrier detection and antenatal diagnosis.     

Erosion in conical diffusers in particulate-laden cavitating flow

This paper highlights the serious damage that can occur in diffusing sections of pipework in which a cavitating particulate-laden fluid is flowing. The combined effects of particle erosion and cavitation are shown to remove considerably more material than would be expected from summing the effects of the individual mechanisms. It is demonstrated that, to be sure of avoiding this accelerated surface erosion, the transition from a smaller flow section to a larger one needs to be an abrupt expansion. If pressure recovery is important, a possible design solution is proposed. In the case of swirling flow, the expansion again needs to be abrupt. Evidence was also obtained which showed that, by allowing air to be entrained into the low pressure region in the flow, the cavitation and the erosion can be substantially reduced.     

Experiments in mechanical and optical coincidence in photoplasticity

In the extension of the shear-difference method to the separation of interior principal stresses in the elasto-plastic state¹, a basic question arises whether the optical isoclinics give the directions of the principal stresses, i.e., whether optical coincidence exists. Experiments are described aiming to answer this question, and preliminary results are given for cellulose nitrate as a model material. Experiments are also described dealing with mechanical coincidence.     

Turbulent transport in an inclined jet in crossflow

The present study experimentally investigates a turbulent jet in crossflow relevant to film cooling applications. The jet is inclined at 30°, and its mean velocity is the same as the crossflow. Magnetic resonance imaging is used to obtain the full three-dimensional velocity and concentration fields, whereas Reynolds stresses are obtained along selected planes by Particle Image Velocimetry. The critical role of the counter-rotating vortex pair in the mixing process is apparent from both velocity and concentration fields. The jet entrainment is not significantly higher than in an axisymmetric jet without crossflow, because the proximity of the wall inhibits the turbulent transport. Reynolds shear stresses correlate with velocity and concentration gradients, consistent with the fundamental assumptions of simple turbulence models. However the eddy viscosity is strongly anisotropic and non-homogeneous, being especially low along the leeward side of the jet close to injection. Turbulent diffusion acts to decouple mean velocity and concentration fields, as demonstrated by the drop in concentration flux within the streamtube issued from the hole. Volume-averaged turbulent diffusivity is calculated using a mass–flux balance across the streamtube emanating from the jet hole, and it is found to vary slowly in the streamwise direction. The data are compared with Reynolds-Averaged Navier–Stokes simulations with standard k − ε closure and an optimal turbulent Schmidt number. The computations underestimate the strength of the counter-rotating vortex pair, due to an overestimated eddy viscosity. On the other hand the entrainment is increasingly underpredicted downstream of injection. To capture the correct macroscopic trends, eddy viscosity and eddy diffusivity should vary spatially in different ways. Therefore a constant turbulent Schmidt number formulation is inadequate for this flow.