1988年全国青年力学竞赛复赛试题解答

材料力学部分1.一体重为W的跳水运动员站在厚2a长为L的悬臂梁跳水板之端部,已知梁的许用应力为σ_B,惯矩为J,弹性模量为E.允许他起跳的高度在()之...     

1988年全国青年力学竞赛复赛试题

材料力学部分1.一体重为 W 的跳水运动员站在厚2a 长为 L 的悬臂梁跳水板之端部,巳知梁的许用应力为 σ_B,惯矩为 J,弹性模量为 E.允许他起跳的高度在()以内.2.两端简支,长为 l 的直圆管中,定常地以速度v 流动着液体.已知管的弹性模量 E,转动惯量 J=     

跳台滑雪中运动员采用什么姿态飞得既稳且远

针对冰雪运动项目跳台滑雪,本文阐述了跳台滑雪运动员在比赛过程中助滑、起跳、飞行及着陆阶段的动作技术特点及其所蕴含的力学原理,设计制作了实验道具并开展了演示实验,说明了起跳阶段适当蹬地与飞行阶段维持特定姿态是跳台滑雪运动员取得优异成绩的关键因素.本文还探讨了相关演示实验在基础力学教学中的应用前景.     

是生物控制最优化而不是 v_1与 v_2组合最优化

文[1]讨论了急行跳远的最佳起跳角θ_(■)与腾起角α_(■),并在v_1,v_2不变的假设下求得α_(■)在20°左右;这里,v_1表示起跳瞬时水平助跑速度,v_2表示蹬地起跳速度(图1).但文[1]将运动员起跳瞬间身体质心速度说成是助跑速度v_1与起跳速度v_2的矢量和的     

是生物控制最优化而不是 v_1与 v_2组合最优化

<正> 文[1]讨论了急行跳远的最佳起跳角θ_(■)与腾起角α_(■),并在v_1,v_2不变的假设下求得α_(■)在20°左右;这里,v_1表示起跳瞬时水平助跑速度,v_2表示蹬地起跳速度(图1).但文[1]将运动员起跳瞬间身体质心速度说成是助跑速度v_1与起跳速度v_2的矢量和的     

仿青蛙机器人跳跃之力学分析与轨迹优化

目前,相比传统的轮式机器人,离散性运动的跳跃机器人具有更好的移动性能,得到了广泛的应用.本文从仿生学角度出发,选择具有优秀跳跃性能和合理运动结构的青蛙作为研究对象,建立了平面连杆机构仿青蛙机器人跳跃模型.在该模型的基础上,建立了仿青蛙机器人起跳阶段的运动学和动力学模型,得到了起跳阶段机器人各关节力矩与各关节运动轨迹,质心速度,质心加速度间的关系.结合遗传算法,对机器人在起跳阶段的跳跃轨迹进行了优化.在此基础上,从能量角度出发,对机器人在腾空阶段的跳跃轨迹进行了优化,得到了机器人最佳的跳跃轨迹.结合Matlab仿真分析,验证了方案的正确性和可行性.     

为什么大汽车的后排比前排颠簸

对一种常见的现象,即大客车的后排比前排颠簸得厉害,从力学上加以分析. 由于大客车多是后轮驱动,所以在设计时,后轮要有较大的负重,才能够加大后轮的摩擦 力. 由此,粗略分析在后轮起跳的速度比前轮小. 还由于汽车的后悬较长,对起跳有放大 的作用.     

重新审度抛体理论在体育运动中的应用

本文以跳远为例指出了抛体理论在体育运动中应用的不当之处,提出了修正意见,并给出了计算最佳起跳角和腾起角的公式.     

篮球运动员急停起跳动作踝关节生物力学特征分析

主要采用三维运动影像捕捉系统与三维测力台,对体育学院20名篮球学生,急停单脚起跳双脚落地动作进行了三维同步测试。探讨了在急停单脚起跳双脚落地动作中踝关节的生物力学特征。研究结果表明:在起跳着地最大缓冲时刻踝关节处于最大内翻和外旋状态,且男生组大于女生组;此时刻也是踝关节最容易发生损伤时刻,男生组比女生组更容易发生踝关节损伤。研究结果对于认识踝关节损伤的生物力学特征,预防和减少运动中踝关节损伤的发生具有一定的理论参考价值。     

泥石流反粒径分布的一种定性解释

假设泥石流中的粗颗粒（如石块等）以跳跃的方式前进,通过分析单个颗粒在定常充分发展的流场中的运动,给出了单一起跳速度下以及具有一定分布的起跳速度下,颗粒数密度随高度的分布,并给出了起跳粒径有分布时颗粒的平均粒径随高度的分布,定性地解释了泥石流中的反粒径分布现象。     

基于纯声子辐射模型的超薄绝缘夹层结构

在复合材料结构中起绝热、增韧作用的绝缘夹层,其加工厚度现在已达到纳米量级,原有的傅立叶热传导定律已无法描述其热能的传递行为,需从分子动力学、量子力学从发,针对不同研究对象建立相应的热传导模型．针对超薄绝缘夹层结构,将纯声子辐射模型和傅立叶热传导模型相结合数值求解热冲击条件下的温度场,并作为热载荷,用于求解结构上表面应力和夹层裂纹驱动力,其结果与只采用傅立叶热传导模型计算的结果相比较, 分析了物理参数对温度、应力和裂纹驱动力的影响．结果表明：与只采用傅立叶热传导模型计算的结果相比,按EPRT计算的热传导明显变慢,其表面剥离应力偏大,而夹层裂纹驱动力偏小．同时随着松弛时间增大和声子速度的降低,热传导减缓,表面横向剥离应力增大,超薄绝缘夹层内裂纹尖端驱动力减小．     

Augmented perpetual manifolds and perpetual mechanical systems-part II: theorem for dissipative mechanical systems behaving as perpetual machines of third kind

Perpetual points in mathematics defined recently, and their significance in nonlinear dynamics and their application in mechanical systems is currently ongoing research. The perpetual points significance relevant to mechanics so far is that they form the perpetual manifolds of rigid body motions of unforced mechanical systems, which lead to the definition of perpetual mechanical systems. The perpetual mechanical systems admit as perpetual points rigid body motions which are forming the perpetual manifolds. The concept of perpetual manifolds extended to the definition of augmented perpetual manifolds that an externally excited multi-degree of freedom mechanical system is moving as a rigid body, and may exhibit particle-wave motion. This article is complementary to the work done so far applied to natural perpetual dissipative mechanical systems with motion defined by the exact augmented perpetual manifolds, whereas the internal forces, and individual energies are examined, to understand further the mechanics of these systems while their motion is in the exact augmented perpetual manifolds. A theorem is proved stating that under conditions when the motion of a perpetual natural dissipative mechanical system is in the exact augmented perpetual manifolds, all the internal forces are zero, which is rather significant in the mechanics of these systems since the operation on augmented perpetual manifolds leads to zero internal degradation. Moreover, the theorem is stating that the potential energy is constant, and there is no dissipation of energy, therefore the process is internally isentropic, and there is no energy loss within the perpetual mechanical system. Also in this theorem is proved that the external work done is equal to the changes of the kinetic energy, therefore the motion in the exact augmented perpetual manifolds is driven only by the changes of the kinetic energy. This is also a significant outcome to understand the mechanics of perpetual mechanical systems while it is in particle-wave motion which is guided by kinetic energy changes. In the final statement of the theorem is stated and proved that the perpetual dissipative mechanical system can behave as a perpetual machine of third kind which is rather significant in mechanical engineering. Noting that the perpetual mechanical system apart of the augmented perpetual manifolds solutions is having other solutions too, e.g., in higher normal modes and in these solutions the theorem is not valid. The developed theory is applied in the only two possible configurations that a mechanical system can have. The first configuration is a perpetual mechanical system without any connection through structural elements with the environment. In the second configuration, the perpetual mechanical system is a subsystem, connected with structural elements with the environment. In both examples, the motion in the exact augmented perpetual manifolds is examined with the view of mechanics defined by the theorem, resulting in excellent agreement between theory and numerical simulations. The outcome of this article is significant in physics to understand the mechanics of the motion of perpetual mechanical systems in the exact augmented perpetual manifolds, which is described through the kinetic energy changes and this gives further insight into the mechanics of particle-wave motions. Also, in mechanical engineering the outcome of this article is significant, because it is shown that the motion of the perpetual mechanical systems in the exact augmented perpetual manifolds is the ultimate, in the sense that there are no internal forces which lead to degradation of the internal structural elements, and there is no energy loss due to dissipation.

     

油水井水泥环在冲击载荷作用下的损伤分析

 冲击整形扩径工艺是修复油水井套管损坏的常用技术，根据冲击整形的施工工艺和波 动理论，建立了套损局部位置处水泥环的损伤力学模型，以有限变形理论为基础，采用悬臂 梁力学模型，分段研究了冲击整形时钻杆屈曲的平衡位形及对套管、水泥环产生 的冲击力. 结合水泥环的应力状态, 根据脆性 材料的Mazars损伤模型，建立了水泥环的损伤力学模型. 并分析了水泥环的损伤 状态. 通过与现场测试结果对比，理论计算与实测结果误差在2.7%左右.     

固体氧化物燃料电池宏观力学效应研究进展

固体氧化物燃料电池(SOFC)是一种清洁高效且具有广泛应用前景的绿色发电装置. SOFC采用了陶瓷材料电极和电解质并在高温下工作, 力学损伤是造成其性能和寿命衰减的主要因素之一. 由于实验测试的局限性, 基于宏观力学模型的数值模拟是优化SOFC电池和电堆结构、提高其性能和耐久性的重要手段. 本文综述并评价了SOFC宏观力学效应的研究进展, 介绍了SOFC在制造、正常运行和长期工作的不同阶段受到的残余应变、阳极氧化应变、化学膨胀、工作热应变以及蠕变等力学效应. 总结了各种力学效应以及目前关注较少的电化力耦合效应的理论和数值模拟研究现状, 最后展望了SOFC宏观力学性能研究的发展前景.      

论岩体表征单元体积REV——岩体力学参数取值的一个基本问题

本文论述了岩体力学性质的尺寸效应,提出了与岩体弹性参数相应的表征单元体REV的力学描述,根据中心极限定理推导了估算裂隙岩体REV 的数学表达式。研究表明,岩体表征单元体的大小是岩体力学性质尺寸效应的客观反映。本研究成果为合理选取岩体力学参数提供了一条新途径。     

力学环境约束下剪切销可靠性分析及优化设计

剪切销是火工装置关键部件，其可靠性不仅表现为点火作用下可靠剪断，还表现为受力学环境激励不发生断裂。本文中以多项式混沌展开方法为基础，建立了力学环境约束下的剪切销分析模型，结合序贯优化与可靠性分析方法，提出了剪切销可靠性优化设计的思路。以某型火工作动装置为应用实例，依据实用的力学环境，进行了剪切销可靠性分析及优化设计，揭示了设计参数与力学环境之间的关系，并获得了影响可靠性的关键参数。最后，开展了优化后的火工作动装置实验测试，结果佐证了优化设计的有效性。     

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first-and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theo-retical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is compli-cated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.     

Modeling of pre-fracture zones for limited permeable crack in piezoelectric materials

A plane-strain problem for a limited permeable crack in an adhesive thin interlayer between two semi-infinite piezoelectric spaces is considered. The tensile mechanical stress and the electric displacement are applied at infinity. The interlayer is assumed to be softer than the connected materials; therefore, the zones of mechanical yielding and electric saturations can arise at the crack tips on the continuations of the crack. These zones are considered in this work. It was assumed that the length of electric saturation zones is larger than the length of mechanical yield zones. The zones of mechanical yielding are modeled by the crack continuations with normal compressive stresses applied at its faces. The electric saturation zones are modeled by segments at the crack continuations with prescribed saturated electric displacements. These electric displacements can linearly vary along the mechanical yielding zones. The problem is reduced to the Hilbert–Riemann problem of linear relationship, which is solved exactly. The equation for the determination of the yielding zones length, the expressions for the crack-opening displacement jump, electric potential jump, and J-integral is obtained in an analytical form. In case of finite size body, the finite elements method is used and the variation in the fracture mechanical parameters with respect to this size is demonstrated.     

论“岩体结构控制论”

经过长期实践和研究,作者于1984年提出岩体结构控制论是岩体力学的基础理论,并全面、系统地以岩体结构控制论为指导研究了岩体变形、岩体破坏及岩体力学性质的基本规律;提出岩体变形系山岩体材料变彤和岩体结构变形共同贡献的,岩体破坏系受岩体材料破坏和岩体结构破坏控制的;岩体力学性质不仅决定于岩体材料力学的性质,而且受控于岩体结构力学效应及环境因素力学效应。在此基础上,作者提出了岩体可以划分为连续介质、碎裂介质,块裂介质及板裂介质四种岩体力学介质,从而建立了完整的岩体结构力学理论体系。