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。     

基于复变函数的矩形巷道围岩应力与变形粘弹性分析

矩形巷道越来越多地被应用到实际工程当中，其巷道围岩稳定性理论分析具有重要的意义。本文建立了矩形巷道围岩分析的力学模型，运用复变函数理论推导，通过保角变化，得到了矩形巷道外围岩到复平面单位圆上的映射函数；在复变函数域内分析了矩形巷道围岩应力、变形的求解步骤；运用弹性力学、粘弹性理论等推导得到了巷道围岩应力变形的粘弹性解；...     

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.     

半平面内多个纳米圆形夹杂的表/界面效应

基于Gurtin-Murdoch表/界面理论,采用边界积分法,讨论了各向同性的弹性半平面中含有任意多个纳米圆形夹杂问题,得到了受表面/界面影响的纳米复合结构的应力和位移的数值解.最后,给出了半平面中含有单个纳米孔洞和纳米夹杂的数值算例,分析了纳米界面存在对整个半平面结构应力场的影响.     

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.     

有限元秩亏方程的最小范数问题

为避免因确定边界约束条件时的不同而引起的应力，位移解不一致问题，作者认为在无明显稳定边界情况下应用整体最小范数法解算有限元方程，如存在相对稳定边界，则可采用部分最小范数解，在一定条件下，最小范数解更能反映位移场的真实状态，并使计算误差分布均匀。