数值函数

Based on the fundamental solution of two perfectly bonded elastic halfspaces, the boundary integral equation method is used to reduce the problem to a hypersingular integral equation in which the unknown function is the crack opening displacem...

首先根据双材料空间的弹性力学基本解，使用边界积分方程方法，在有限部积分的意义下导出了以裂纹面位移间断为未知函数的超奇异积分方程，并为其建立了数值法。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道，基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差，并且作为形式简单且恢复函数为多项式的一种信息基算法，其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

A Primitive Function Description of Generalized Perron Integral;2. Expecially, when primitive function can t be found, the advantage lay definitely with it.

在数值分析中，常用复化梯形公式求∫baf dx的满足一定精度的近似值，特别是在 f的原函数找不到的情况下更显示出它的优越性。

In this paper, The numerical method is adopted to calculate the motions in time domain based on the simple Green function and perturbation expansion method put forward by Isaacson and Cheung.

本文应用简单格林函数和摄动展开的理论方法在时域内对锚泊系统进行了数值模拟。

The research results show as follows. As plastic deformation increases, the Young's modulus of material continuously changes. This variation law is able to be described using a piecewise linear function .Hardening model and whether the variation is considered or not make great effet on springback prediction. It is proved that the springback prediction result which adopts the elastic-plastic constitutive model based on INLK hardening model and the variation of Young's modulus is considered, is more close to experimental result. After the sheet metal undergoes multiple bending, the corner radius and bending height also affect springback greatly.But the effect trend is different. At the same time, the reliability of springback research using numerical simulation is proved.

研究结果表明：材料弹性模量随塑性变形的变化是不断变化的，该变化规律可用分段线性函数进行描述；强化模型及考虑弹性模量变化与否对回弹预测有很大的影响，基于INLK强化模型和考虑弹性模量变化的弹塑性本构模型对回弹的预测结果与试验最接近；多次弯曲中圆角半径与弯曲高度对板料变形后的回弹有较大影响，但影响趋势不同；证明了数值模拟方法对回弹研究的可靠性。

There are two ways to access the point spread function in general: numerical calculation and physical measurements.

显微镜系统的点扩展函数的获取通常有两种方式：数值计算和物理测量。

The precision of integration can be evidently improved by using smooth function transition, adaptive step size change method, implicit integration and predictor corrector method. Increasing the order of the LMM may not improve the precision in this case.

采用光滑函数过渡、自适应变步长技术及隐式和预测校正等方法，可以有效地提高数值计算精度，而提高方法的阶次不能有效提高精度。

Therefore,a series studies of ice-pier vibration are performed from different aspects in this paper.The main work of this his thesis is summarized as follows:(1) Ice response spectra is proposed based on the idea of a seismic response spectra analysis of str .. uctures.Firstly,ice response spectra on the basis of power spectra density function is established;Secondly,based on the assumption of quadratic parabolic interpolation method,the nonlinear interpolation analysis method of ice response spectra is studied from both theoretical and practical points of view,and the successive computation formulas including ice displacement,velocity and acceleration response spectrum are deduced by Duhamel integral.Furthermore,to analyze the effectivity and applicability of the method, the real temporal curves of ice pressure are used to be studied.The results show that the presented method is more convenient and accurate to study the structural response induced by ice force,also it can be effectively applied in the design of ice resistance.

鉴于此，本文针对冰激桥墩结构振动问题从不同方面展开了一系列与之相关的研究，主要研究内容如下：(1)根据结构抗震反应分析思想提出了冰振反应谱，首先建立了基于功率谱密度函数的冰振反应谱；其次借鉴地震反应谱内插法的思想从理论和实际观点出发，假定在等距离微小时间间隔内冰荷载按二次抛物线规律变化，由Duhamel积分推导出冰振位移、速度以及加速度反应谱的一系列连锁公式，建立了基于非线性内插法的冰振反应谱，并利用实际冰压力时程曲线进行了冰振反应谱数值分析，为以后冰激结构振动的研究提供一种方便、简捷、精确的分析方法，也能够将其有效地应用到结构的抗冰计算中。

Firstly, based on the method of pressure-velocity coupling introduced by SIMPLE algorithm and a revised method of solving the unsteady equation of stream function and vorticity on uniform grid, a special algorithm called primitive-variable-time-dependent approach is formed in the present study. In this algorithm the Navier-Stokes equation in primitive variable form is solved by using the time-dependent approach on non-uniform staggered grid system. The second-order accuracy finite difference is used for the first and second partial derivatives of all variables of the convective terms and diffusion terms.

首先，本文在SIMPLE算法系列处理速度与压力耦合问题的思路和均匀网格下改进的关于流函数涡量方程的数值求解方法的基础上，将非定常原始变量Navier-Stokes方程的求解推广至非等距交错网格剖分，形成了具有本文特色的原始变量时间推进方法，其中对流项和扩散项中各变量的各阶导数均采用二阶精度公式，包括温度在内的离散方程组采用ADI迭代方法求解。

This dissertation establishes numerical methods in structural analysis on the basic of variation principle, finite member element method, spline function, etc.

本文利用变分有限元法、样条函数等，提出了薄壁箱梁结构分析的数值理论和方法。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。