边界积分方程中近边界点几乎奇异积分的计算

该文针对边界元法存在近边界点力学量计算的困难,给出了一个通用性方法,将近边界点到边界单元的距离参数通过分部积分变换到积分式之外,从而计算出二维问题近边界点参量的几乎强奇异和超奇异积分.该法同样适用于板壳问题的边界元法,尤其是对于将超奇异边界积分方程正则化为强奇异边界积分方程的边界元法,求解近边界点参量更加有效.     

位势问题直接边界元法中的边界层效应

边界层效应的数值分析是边界元法的难点之一,其实质是几乎奇异积分的准确计算.在直接变量位势问题的边界元分析中,位势梯度边界积分方程会衍生出超奇异积分.因此,在求解近边界点处的位势梯度时会面临几乎强奇异和几乎超奇异积分的处理问题,特别是几乎超奇异积分的处理会更加困难.通过采用一类非线性变量替换法,来消除积分核的几乎奇异性,并将其应用于位势及其梯度边界积分方程的求解中.数值实验算例表明,该算法可非常准确地求得近边界点处的位势梯度,即使场点非常靠近边界,仍能避免产生边界层效应现象.     

热弹性力学边界元中二次元的几乎奇异积分计算

采用正则化积分算法,计算了二维热弹性力学边界元法中近边界点的几乎奇异积分。算法采用二次元划分边界,但对与内点邻近的二次单元,几何量采用线性插值,位移、面力等物理量仍采用二次插值。对此二次非等参单元上的积分采用正则化积分公式。算例证明了该文算法的有效性和精确性。     

二维弹性静力学的奇异杂交边界点法

杂交边界点法是一种边界型的无网格法，它以修正变分原理和移动最小二乘近似为基础，同时具有边界元法和无网格法的优良特性。本文在原有杂交边界点法的基础上，借鉴了边界元法处理奇异积分的方法，避免了正则杂交边界点法中计算结果对于标量因子的依赖性。数值结果表明，奇异杂交边界点法具有较高的精度和数值稳定性。     

用自然边界元法计算位势问题的近边界位势梯度

在二维位势问题中,位势导数场边界积分方程通常衍生出超奇异积分问题。通过新边界变量的替换消除了常规的位势导数边界积分方程中超奇异积分,推导出以位势梯度为边界量的自然边界积分方程。在常规的位势边界积分方程执行后,采用自然边界积分方程的边界元分析比常规边界元法得到更加准确的近边界位势梯度;算例显示了自然边界元法的有效性。     

位势问题边界元法中几乎奇异积分的完全解析算法

导出了一种完全解析积分算法，用这种算法计算了平面位势问题边界元法中近边界点的几乎奇异积分。当内点离某单元较远时，保持常规高斯积分模式；而当内点离某单元较近时，因常规高斯积分结果失效，用本文的完全解析积分取代常规高斯积分．该算法适用于线性插值计算，对二次元，可将近边界点附近的二次元分解为两个线性元，该算法同样有效。算例证明了本法的有效性和精确性。二次元计算结果比线性元计算结果更精确。     

三维声场问题边界元法中几乎奇异积分的正则化

针对三维声场边界元分析的几乎奇异积分问题,将基本解中三角函数进行Taylor级数展开,分离奇异部分和非奇异部分.采用一种半解析正则化算法,计算了近边界点几乎奇异面积分,非奇异部分仍然采用Gauss数值积分,从而克服奇异积分障碍.该算法适用于三角形线性等参元,对高次单元将其细分为几个三节点三角形单元即可应用该算法.对三维声场内问题和外问题算例,计算了近边界点的声压,数值结果证明了该算法的有效性和准确性.     

边界元法计算声辐射时几乎奇异积分的处理方法

针对边界元法中几乎奇异积分计算难题,本文提出一种基于6节点三角形等参数单元的三维高阶单元半解析算法.通过对三维声场基本解中的三角函数进行T a y l o r级数展开,分离出基本解中的奇异积分项.根据单元的几何特性,构造出与奇异积分核函数具有相同奇异性的近似奇异核函数,对奇异积分项应用扣除法,将奇异积分核函数分为规则核函数和近似奇异核函数两项.规则核函数积分无奇异性,应用常规G a u s s数值积分就能够准确计算;近似奇异核函数积分由导出的半解析公式计算,即在局部极坐标系ρθ下分离积分变量,导出对变量ρ积分的解析计算列式,应用常规G a u s s数值积分计算变量θ积分,从而建立一种三维声场边界元法几乎奇异积分的半解析算法.算例结果表明,本文高阶单元半解析算法比双线性元算法更加有效且算法稳定,能够有效、准确地计算距离单元非常近的近边界点处的声压.     

三维Helmholtz方程的边界点方法

将移动最小二乘近似和边界积分方程相结合,提出了求解三维Helmholtz方程内外边值问题的无网格边界点方法.该方法用单层位势理论将Helmholtz方程转化为间接边界积分方程,并用边界点法离散间接边界积分方程.由于边界积分方程中含有基本解的积分计算时会出现弱奇异,详细推导了弱奇异积分的计算方式.数值算例表明了间接边界点法求解三维Helmholtz方程的有效性.     

近坝基面渗流场的边界元法分析

针对几乎奇异积分阻碍了边界元法准确计算近坝基面基内点的渗流参量的问题,首先给出了多种正交各向异性介质渗流问题边界元法基本方程,然后引入一种正则化算法,化解了边界元法计算近坝基面基内点的渗流参量时遇到的几乎奇异积分障碍,获得了近坝基面基内点的渗透压力和水力梯度值.算例表明该方法较常规方法能计算距坝基面更近的内点的渗流参量.     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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