圆形电流磁场的级数解

给出了圆电流磁场的级数解，讨论了解的收敛性     

非对称载荷作用的外部圆形裂纹问题

使用边界积分方程方法,研究了三维无限弹性体中受非对称载荷作用的外部圆形裂纹问题。通过使用Fourier级数和超几何函数,将问题的二维边界奇异积分方程简化为Abel型方程,获得了一般非对称载荷作用的外部圆形裂纹问题的应力强度因子精确解,比用Hankel变换法得到的结果更为一般。结果表明:边界积分方程法在解析分析方面还有很大的潜力。     

载荷和纳米MoS2添加剂含量对圆形锤头-棒料的摩擦磨损特性及其机理分析

针对精密下料中圆形锤头与棒料之间弧状接触面剧烈的摩擦磨损问题,借助WTM-2E型可控气氛摩擦磨损试验仪,利用GCr15钢块-45钢柱摩擦副在纳米MoS₂添加剂质量分数为0%、0.1%、0.2%、0.3%、0.4%、0.5%和0.7%等七种润滑工况下,重点对不同载荷下摩擦磨损试验进行分析;采用扫描电子显微镜观察了GCr15钢块磨损表面形貌,采用能量色散谱仪(EDS)分析了GCr15钢块磨损表面成分,并探讨了其润滑抗磨及自修复机理. 结果表明:随着载荷增加,摩擦接触应力变大,摩擦系数和磨损量呈上升趋势,磨损表面形态由轻微磨粒磨损转变为黏着磨损. 同时加入的MoS₂添加剂的质量分数并非越高越好,摩擦系数和磨损量随MoS₂添加剂质量分数的升高呈现先减小后增大趋势,且MoS₂添加剂质量分数在0.1%~0.3%范围内时减摩抗磨效果较好. 通过对比不同润滑条件下摩擦副因摩擦磨损而产生的噪声、振动速度和温升,进一步定量确定出纳米MoS₂添加剂质量分数为0.1%时,可以最大程度地降低摩擦副的损耗.      

降雨量预报方法评价模型

目的:给出2005年全国大学生数学建模竞赛C题的解答.方法:利用二维插值、区域圆形覆盖算法、层次分析法(AHP)中的1—9标度法和独立样本t检验,分别对非等级预报和等级预报情形建立了点降雨量和面降雨量预报方法评价模型.结果:得到了题中两种预报方法优劣的比较结果.结论:降雨量预报方法1优于方法2.     

基于竞赛输电塔结构模型的减隔振装置

以浙江省第十八届大学生结构设计竞赛“输电塔结构设计与模型制作”赛题为背景,研究输电塔结构在断线动力载荷下的受力和结构选型。方案阶段对比分析了不同结构选型的优劣;融入减隔振理念进行设计：头部与主体脱开并巧妙设置圆形压槽轨道作为减隔振装置,通过头部沿轨道转动摩擦耗能减振,独具创新性。经试验验证,并结合解析计算与SAP2000软件电算分析,得到圆形轨道减隔振装置可有效减少结构的断线动力效应、提高主体结构的安全储备的结论;旨在为类似竞赛模型和相关实际工程提供实践和理论意义上的经验指导。     

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes' dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.     

直角平面内弹性圆夹杂对入射平面SH波的散射

利用复变函数法、多极坐标移动技术及傅立叶级数展开求解二维直角平面内圆形弹性夹杂对稳态入射平面SH波的散射问题。首先写出直角平面内不含夹杂时的入射波场和反射波场;其次建立直角平面内含夹杂时夹杂外的散射波解和夹杂内的驻波解,并利用叠加原理写出问题的总波场,借助夹杂边界处应力和位移的连续条件建立求解散射波解和驻波解中未知系数的无穷代数方程组并求解,通过算例具体讨论了直角平面水平边界点的位移幅度比和夹杂边界处径向应力集中系数随不同无量纲波数、入射角及圆孔位置的变化情况,结果表明了算法的有效实用性。     

高地应力条件下隧洞开挖动态卸荷的破坏机理初探

分析了高地应力条件下静水压力场中圆形隧洞钻爆开挖时开挖边界上初始应力场动态卸荷效应及破坏机理，并计算了其破坏范围。初始应力动态卸荷时，动应力在隧洞径向表现为卸荷回弹，而在切向出现动应力集中，表现为加载。动态卸荷时间对径向应力的影响较对切向应力大，卸荷时间越短，扰动的幅度越大；初始应力动态卸荷在岩体中所造成的破坏范围较准静态卸荷情况大，卸荷时间越短，破坏范围越大。     

EXACT SOLUTION OF LARGE DEFORMATION BASIC EQUATIONS OF CIRCULAR MEMBRANE UNDER CENTRAL FORCE

Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.     

THREE-DIMENSIONAL INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources: force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.