有限元计算中疏密网格过渡方法研究

工程计算中出于节省计算量的目的,往往需要在一个有限元模型中布置粗细不同的网格。为保证计算结果的准确性,必须保证网格突变情况下的位移协调问题。本文工作之一是在强天驰界面过渡单元的基础上,引入虚拟节点和子单元,在子单元中应用节理元思想,提出了基于最小势能原理的弹簧节理单元法。简化了积分运算,避免了精度要求极高的坐标转换,从而提高了方法的精度和实用性;二是提出了基于位移约束的主从自由度法,简便实用,只需简单的矩阵运算即可实现。两种方法均实现了不同尺寸网格间位移的协调性和刚度的匹配,从而使之满足有限元收敛准则,且生成的刚度阵具有对称性及带状性。算例证明两种方法精度良好,并可方便地应用于求解大规模工程问题。     

薄壁箱梁广义坐标法刚度矩阵的推导及应用

在符拉索夫广义坐标法初参数方程的基础上,推导出可用于均布扭转荷载作用下薄壁箱梁翘曲分析的刚度矩阵,该刚度矩阵具有较高的单元精度,可用于由较多薄壁箱梁组成的复杂结构的整体有限元分析。通过对广义坐标法刚度矩阵和乌曼斯基理论、修正乌曼斯基理论求得薄壁箱梁的位移和应力进行分析比较,为各方法在实际工程中的应用提供一定的参考。     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

Nonsmooth analysis of vector-valued mappings with contributions to nondifferentiable programming

We define order Lipschitz mappings from a Banach space to an order complete vector lattice and present a nonsmooth analysis for such functions. In particular, we establish properties of a generalized directional derivative and gradient and derive results concerning a calculus of generalized gradients (i.e., calculation of the generalized gradient of f when f = f₁ + f₂, f = f · ₂, etc.). We show the relevance of the above analysis to nondifferentiaile programming by deriving optimality conditions for problems of the form min f(x) subject to x [euro] S. For S arbitrary we state the results in terms of cones of displacement of the feasible region at the optimal point; when S ={x ? A|g(x) ? B}, we obtain Kuhn-Tucker type results.     

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.     

Box-Jenkins方法在银行业市盈率预测中的应用

试用比较先进的Box-Jenkins时间序列分析方法对上市银行市盈率的历史数据进行分析,建立银行业盈利预测的ARIMA模型对我国行业经济进行分析。     

关于离子选择性电极分析中的等电位差－标准加入法的探讨

本文提出了一种新的离子选择性电极分析方法，即等电位差－标准加入法。本方法已用于氟的测定。进行了理论数据验证及误差分析，标准溶液的回收率为９６．６％－１０４．３％。本方法的影响因素少、准确度好、操作及计算简便。     

电感耦合等离子体原子发射光谱法及离子选择电极法测定荧光级氧化钇中痕量铈的研究

文章描述了荧光级氧化钇中痕量稀土铈的测定方法,在溴酸钾存在下,5摩尔/升HNO_3介质中,以P507萃取微量铈,然后有机相用硝酸、过氧化氢反萃取、再将水相浓缩定容,然后以电感耦合等离子体原子发射光谱法分析。同时用铈的离子选择电极以二次标准加入法作第二种手段分析。样品溶液以乙醇预去溶方式引入等离子体,测定下限为2微克/克,方法简单、快速、准确。离子选择电极法测定铈离子下限1×10～(-5)摩尔/升,回收率为94-101%,方法简单,结果满意、价格便宜。     

用有限元法分析多波导耦合系统本征模的模式特性

本文应用有限元法(FEM),计算和分析了多波导耦合系统的本征模(超模)的模式特性及其变化规律,得到了强度均匀分布的基超模,克服了微扰理论计算这类问题的局限性.