几种逻辑方法在理论力学课程教学中的应用

针对学生在学习理论力学课程过程中,各章知识点、解题方法、力学建模、分析和解决综合问题不容易掌握的特点,将力学竞赛辅导采用的科学方法论中3 种逻辑方法:比较-分类法、归纳-演绎法、分析-综合法,引入到理论力学的课程教学中. 实践证明,在理论力学课程教学中,采用了这几种逻辑方法,不仅提高了理论力学课程的教学质量,激发了学生的学习兴趣;而且学生也很容易掌握各章的知识点、解题方法、力学建模,并将它们熟练地应用于分析和解决综合问题.     

强化学生力学建模能力的几点思考

本文提出了以培养力学建模能力为载体, 强化力学思维方式的教学思想. 重点以固体力学主干课程为基础分析和讨论了力学模型的概念和要点, 强调了力学基本量和基本原理学习的重要性, 并对力学模型的建模方法、分类、基本原则进行了讨论. 通过理论力学和材料力学的典型例题分析, 举例说明了建模步骤. 最后, 对如何在教学中培养学生力学建模能力、学习要点、学习方法进行了探讨.     

在理论力学教学中采用协作学习的改革实践研究

 在理论力学教学中采用了协作学习方式来全面提高学生的能力. 在简单介绍协作学习方法以后,阐述了理论力学协作学习的准备工作以及具体实施办法:分散讨论课,集中讨论课,课堂测验的运作方式以及讨论课评分的方法. 改革实践表明,对于大班上课而言,协作式学习方法具有传统方法无可比拟的优越性,值得在理论力学课堂中进行推广.     

以``大科学''观进行力学教学

 阐述大学的力学教学应该将培养学生的思维方法、学习方法、学习兴趣和科学观念作为责 任，把力学当作一门承上启下的课程来进行教学实践，让学生们通过力学的学习尽快进入大 学生这一角色. 力学是大学第一门物理课程，力学教师有义务为后面的课程开辟道路，做好 铺垫，这是力学教学的任务.     

钢结构格构柱设计理论的力学问题

借助钢结构格构柱设计理论的换算长细比、横向最大剪力以及分肢承载力三个重要力学问题的解决思路和求解技巧的演绎教学,培养学生发现工程中的力学问题、寻找解决力学问题的途径、服务工程设计的能力,引导学生深刻认识力学理论在解决工程问题中的重要作用,进而激发学生学习力学理论的兴趣,实现学生探究、解决工程问题的创新思维、创新能力的培养目标.     

理论力学课程中3W1H教学法的应用

理论力学作为高等工程类专业技术基础课程,以理论分析为基础,充分培养学生理论与实际相结合的分析问题与解决问题的能力.本文结合自身教学实践和体会,给出了在理论力学课程中3W1H教学法的实施过程和应用方案,该教学法的应用对于启迪学生思维,引导学生进行力学问题分析和求解,提高学生的学习能力和工程实践应用能力具有良好效果和借鉴作用.     

弹性力学应力状态理论求解器开发及应用研究

论文基于吴家龙教授编著的《弹性力学》教材内容和课程"三难"特点,以应力状态理论部分常见题型求解任意微分斜面应力矢量、正应力、切应力、主应力和应力主方向及最大切应力为例,应用Matlab-GUI模块编制应力状态理论求解器,通过界面物理参数输入和结果显示过程,再现弹性力学求解思维,验证学生数理求解结论;把繁琐抽象的力学公式和微分斜面结果进行图形可视化,使学生的抽象思维和力学思维得到兼容;通过弹性力学应力状态理论求解器开发及应用,可为学生力学学习及力学同行教学提供借鉴。     

钢构件设计中的弹塑性力学问题

分析我国现行《钢结构设计规范》GB50017-2003,对比美、欧规范,针对钢结构常用受力构件设计的强度问题和稳定问题涉及到的弹塑性理论应用,通过课堂教学环节,讲授钢结构构件设计原理和弹塑性设计方法,让学生深刻体会弹性设计理论和弹塑性设计理论的差异,认识弹塑性理论在钢结构设计中应用的必要性. 同时也让学生学习正确运用力学知识解决工程问题的思维方法,激发学生学习力学理论的兴趣,培养学生综合应用知识解决工程问题的能力.     

A three stages teaching method of elastic mechanics course

提出了弹性力学三段式教学方法,即围绕每一知识点,按照工程背景、数理基础、力学原理进行划分,在教学实施中遵循先工程,后数理,再力学的讲解顺序. 工程背景可与材料力学知识点进行衔接;数理基础与高等数学、解析几何等数理课程衔接,实现知识点的迁移教学;最后利用力学原理构建弹性力学的基本理论. 以弹性力学中平衡方程的讲解为例,阐述了三段式教学方法的实施过程. 该方法对降低学生学习弹性力学中的畏难情绪,提高学习信心有一定的积极作用.     

弹性力学的三段式教学方法

提出了弹性力学三段式教学方法,即围绕每一知识点,按照工程背景、数理基础、力学原理进行划分,在教学实施中遵循先工程,后数理,再力学的讲解顺序.工程背景可与材料力学知识点进行衔接;数理基础与高等数学、解析几何等数理课程衔接,实现知识点的迁移教学;最后利用力学原理构建弹性力学的基本理论.以弹性力学中平衡方程的讲解为例,阐述了三段式教学方法的实施过程.该方法对降低学生学习弹性力学中的畏难情绪,提高学习信心有一定的积极作用.     

Transition process in a fluid layer in a rotating paraboloid in response to a sudden change in its angular velocity

The process of establishment of the rigid-body rotation state in a liquid layer in a rotating paraboloid upon a sudden increase in its angular velocity is studied theoretically and experimentally. The theoretical study is performed within the framework of linear shallow-water theory with account for the bottom Ekman friction. Analytical solutions describing the transition process are obtained and the dependence of the establishment time on the liquid depth and the radius of curvature of the paraboloid is investigated. It is shown that the effect of free surface deformation may lead to a significant increase in the establishment time. Good agreement with the results of special laboratory experiments is found.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

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.     

Mixing in Circular and Non-circular Jets in Crossflow

Coherent structures and mixing in the flow field of a jet in crossflow have been studied using computational (large eddy simulation) and experimental (particle image velocimetry and laser-induced fluorescence) techniques. The mean scalar fields and turbulence statistics as determined by both are compared for circular, elliptic, and square nozzles. For the latter configurations, effects of orientation are considered. The computations reveal that the distribution of a passive scalar in a cross-sectional plane can be single- or double-peaked, depending on the nozzle shape and orientation. A proper orthogonal decomposition of the transverse velocity indicates that coherent structures may be responsible for this phenomenon. Nozzles which have a single-peaked distribution have stronger modes in transverse direction. The global mixing performance is superior for these nozzle types. This is the case for the blunt square nozzle and for the elliptic nozzle with high aspect ratio. It is further demonstrated that the flow field contains large regions in which a passive scalar is transported up the mean gradient (counter-gradient transport) which implies failure of the gradient diffusion hypothesis.     

Nonlinear waves in electromigration dispersion in a capillary

We construct exact solutions to an unusual nonlinear advection–diffusion equation arising in the study of Taylor–Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave ansatz. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.     

Capillary effects in steady-state flow in heterogeneous cores

Effects of capillary heterogeneity at the macroscopic scale have previously been analyzed for static conditions or in the context of outflow end-effects. This paper presents a systematic study for the case of one-dimensional, steady-state flow, that complements recent work on transient displacement. We consider the saturation response to various forms of heterogeneity. Included are analytical results for certain model cases, some general results, and numerical solutions for variously correlated spatial variations. The sensitivity to process parameters, such as rate, heterogeneity length scale and correlation, is studied. Physical interpretations are offered and potential applications in the estimation of heterogeneity are discussed.     

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.     

Mean stress in a granular medium in dynamics

In this paper we propose to construct a mean stress tensor for a granular medium, valid in static and in dynamics, which takes into account the contact reactions and the body forces acting at the grain level. A simple analytical example shows that taking account of inertia forces is essential to insure the symmetry of the mean stress tensor in dynamics. Finally, numerical simulations illustrating this definition of the mean stress tensor are presented for a granular medium ensiled.