非线性电报方程解的存在性

讨论了非线性电报方程βut utt-uss p(x,ut) g(x,u)=h(t,x)周期Dirichlet问题弱解的存在性．     

非线性电报方程解的存在性

讨论了非线性电报方程βｕｉ＋ｕｔｔ－ｕｘｘ＋ｐ（ｘ，ｕｔ）＋ｇ（ｘ，ｕ）＝ｈ（ｔ，ｘ）周期Ｄｉｒｉｃｈｌｅｔ问题弱解的存在性。     

具有热储备和常规故障系统的非负弱解

本文讨论具有热储备和常规故障系统模型,且主要利用系统算子生成的正压缩C0-半群理论,来证明该系统非负弱解的存在唯一性.     

理想流体流动方程推导专题教学方法探讨

连续性方程和欧拉方程是动量传输的核心内容,其推导过程一直是教学中的重点和难点,以往教学中学生普遍反映难于理解。为了使学生更好的理解和掌握连续性方程及欧拉方程的推导过程,文章对此专题性教学方法进行探讨,采用易于学生理解和掌握的方法分别推导了流体流动的连续性方程及欧拉方程,并分享了连续性方程和欧拉方程推导专题教学中的一些认识与体会,为动量传输理论的教学提供一定的参考。     

变截面板簧偏心异形辊设计分析

建立了偏心圆曲线展开线的参数方程及其特性参数方程。用数学分析和计算机计算分析相结合的方法，进行了特性分析并绘出方程及特性方程曲线。为变截面板簧偏心异形辊的设计提供了依据。     

变截面板簧偏心导形辊设计分析

建立了偏心圆曲线展开线的参数方程及其特性参数方程，用数学分析和计算机计算分析相结合的方法，进行了特性分析并给出了方程及特性方程曲线，为变截面板簧偏心异形辊的设计提供了依据。     

一个非线性粘弹性粉末热压方程及其实验验证

本文运用一个非线性粘弹性流变力学模型,导出了下列粉末热压方程: 用电解铜粉和氧化镁粉的热压实验数据对上述方程的验证表明,该方程具有良好的精确性和广泛的适用性。此外,本文还提出了一个描述热压终点密度与热压压力之间关系的方程,运用最优化处理方法对方程的精确性进行了分析验证。     

一个通用粉末压制方程及其统计分析验证

在分析现有各种粉末压制方程特征的基础上,提出了一个通用粉末压制微分方程:
$\frac{{dD}}{{dp}}=\frac{{K(1-D){D^n}}}{{{p^m}}}$
统计分析结果表明,当n值在0~4之间时,由该方程导出的一系列粉末压制方程的线性相关系数均大于0.99。将由n=0导出的方程与Balshin方程、Heckel方程及川北公夫方程进行了定量比较,表明该方程不仅具有更高的精度,而且具有更广泛的适用性。     

钒渣生产V_2O_5尾渣全钒含量与相关工艺指标的函数关系

基于物料平衡原理,建立了尾渣全钒含量与焙烧熟料全钒含量、焙烧转化率及浸出率之间的函数方程,并结合某公司实际生产数据对方程的有效性进行了验证.在此基础上,系统研究了方程自变量间相互作用及对尾渣全钒含量的影响,进一步简化了原方程.结果表明:原方程和简化方程能够正确反映尾渣全钒含量和上述因素之间的内在作用规律,可为尾渣全钒含量的实际生产技术控制提供判断依据;而简化方程函数关系简单,更利于实际应用.     

中厚板轧制过程侧弯模型及控制策略

为建立中厚板侧弯模型并为制定侧弯控制策略提供理论依据,针对影响函数法局限性和P-H图的不足,在轧辊刚性及工作辊凸度二次抛物线分布假设的条件下,通过理论分析推导了辊缝刚性倾斜量方程、出口轧件楔形方程、轧件厚度分布方程、单位宽度轧制力分布方程、力平衡方程和力矩平衡方程,在此基础上建立了出口轧件侧弯及其控制数学模型。理论研究表明,只要轧件横向温度对称分布,无论侧弯源于何种因素,中厚板出口侧弯控制模型具有一致性。研究结果为侧弯缺陷的反馈控制奠定了理论基础。     

Study of Edge-Zone Equation of Mindlin-Reissner Plate Theory

Analytical solutions are obtained for the interior and edge-zone equations of Mindlin-Reissner plate theory in bending of composite circular sector plates laminated of transversely isotropic layers. Circular sector laminates, under various boundary conditions, are considered. It is shown that, depending on the boundary conditions of the laminate, the boundary-layer effect on the response quantities of the laminate will be strong, weak, or nonexistent.     

一类非主型方程定解问题的离散现象

应用奇型偏微分方程理论，对一类非主型的椭圆型方程的求解进行了讨论，并对此类方程的Ｄｉｒｉｃｈｌｅｔ问题和Ｎｅｕｍａｎｎ问题的解的存在性中的离散现象进行了初步的分析．     

带强迫项的二阶脉冲微分方程的振动性

文章给出引理解决了带强迫项的二阶脉冲微分方程的非振动解与其导数的符号关系,得到其振动性的判别准则,并举例说明准则的有效性。     

Bending Solutions of Axisymmetric Levinson Plates in Terms of Corresponding Kirchhoff Solutions

This paper presents exact axisymmetric bending solutions of circular and annular plates based on the higher-order plate theory of Levinson. The solutions are displayed in terms of the corresponding Kirchhoff (or classical thin) plate solutions. These Kirchhoff-Levinson bending relationships are derived using the mathematical similarity of the governing equations of the two plate theories and the basis of load equivalence. The relationships allow one to readily deduce the more accurate Levinson plate solutions that account for the effect of transverse shear deformation, without having to solve the more complicated Levinson plate equations.     

Determination of Length of a Horizontal Drain in Homogeneous Earth Dams

An earth dam can be prevented from a seepage failure due to softening of the downstream slope by providing a rock toe or horizontal drainage blanket. Analytical solutions are not available for determining the length of the filtered drainage blanket and downstream slope cover, though graphical solutions are available for them. Explicit equations have been obtained in the present work for calculating the downstream slope cover and the length of the downstream horizontal drain in homogeneous isotropic and anisotropic earth dams. Similar equations have also been obtained for maximum downstream slope cover and minimum and maximum effective length of the filtered drainage. These equations are nonlinear and representative graphs have been plotted for them covering all the practical ranges of the dam geometry. The numerical example demonstrates that the proposed equations are simple to use, hence the designers may find these equations as an additional check to their design by the conventional flownet method.     

Postbuckling of Beam Subjected to Intermediate Follower Force

This paper investigates the postbuckling behavior of a simple beam under an intermediate follower force acting in the tangential direction to the centroidal axis of the beam. One end of the beam is pinned, while the other end is attached to a roller support. Two approaches have been used in this study. The first approach is based on the elastica theory. The governing equations are derived and solved analytically for the exact closed form solutions that include the equilibrium configurations of the beam, equilibrium paths, and bending moment distribution of the beam. The exact solutions take the form of elliptic integrals of the first and second kinds. In the second approach, the shooting method is employed to solve a set of nonlinear differential equations with the boundary and intermediate conditions. The equations are integrated by using the Runge–Kutta algorithm. The error norms of the end and intermediate conditions are minimized to within a prescribed tolerance error. A comparison study between the analytical elliptic integral solutions and the numerical shooting method solutions show excellent agreement of results. Special features of the solutions are also highlighted.     

考虑固壁作用力的微可压缩流体纳微米圆管流动分析

针对流体在纳微米尺度下的流体流动规律不符合泊肃叶规律的理论依据不足的难题,研究了纳微米圆管中流体的流动,将流体的微可压缩和固壁对流体的作用同时考虑进来,并将固壁对流体的作用采用固壁作用力的形式引入到流体力学方程,采用涡函数流函数将方程解耦,并用正则摄动法求得一阶精度的压力和速度的解析解.结果发现:固壁作用力导致零阶径向压力的出现,一阶压力的增强和一阶速度的降低;量纲一的体积流量偏离了不可压缩流体的体积流量,偏离效应受流体的微可压缩性和固壁作用力的共同影响.体积流量在同尺度下偏离泊肃叶流动的流量大小随着可压缩系数和流体中和壁面产生作用的离子浓度增大而增大,随着纳微米圆管管径减小而增大,纳微米圆管管径低于某一尺寸时,流体将不能流动.通过研究表明:纳微米尺度下产生微尺度效应的原因是流体的微可压缩性和壁面力的共同影响.      

Theory of Plastic Sand Flow with Fluid Pressure Effect

Fundamental principles of elastic–plastic mechanics of soils and rocks are given on the base of the original publications. The solid friction and dilatancy effects are included in the nonstandard form of nonassociative rule of plastic flow. The resulting hyperbolic system of equations is represented for a plane case. The slip surfaces are assumed to be jump tangential discontinuities of a velocity field. The possibility of limit equilibrium at slip surfaces is accounted for. The attempts to account for grain rotations, permitting study of slip surface structure, are discussed. The Biot–Frenkel model of interpenetrating continua is developed for plastic flow of porous saturated matrix. In this case the solid matrix state is determined by the effective stresses and pore pressure diffusion happens in plastically flowing matrix. To illustrate the theory possibilities, solutions for failure and mass sand flow, driven by the pore pressure gradient, are selected. They are important especially for oil/gas reservoirs with a weak matrix, typical for offshore geology.     

Solution of Specific Energy and Specific Force Equations

Alternate depths and sequent depths are calculated by solving the specific energy and specific force equations, respectively. The specific energy and specific force equations result in fifth degree polynomial equations for trapezoidal cross sections. A methodology is developed for simultaneous determination of the alternate depths and/or sequent depths. The methodology uses solutions of quadratic and third-order polynomial equations to identify the two flow depths.     

Design of Minimum Seepage-Loss Nonpolygonal Canal Sections with Drainage Layer at Shallow Depth

Analytical solutions exist for the seepage discharge from polygonal and nonpolygonal canal sections underlain by a drainage layer at a hydraulically infinite depth. These solutions lead to underestimation of the seepage discharge if a drainage layer occurs at a shallow depth. This paper presents solutions for seepage discharge from circular and exponential sections overlying a shallow drainage layer. The discharge has been calculated by a finite-difference-based numerical solution of the differential governing the seepage flow. The phreatic boundaries of the flow domain were described in terms of two parameters that were estimated by a minimization process. Such seepage computations were performed for a large number of independent dimensionless variables of the section geometry. Subjecting the computed seepage to regression analyses, explicit equations for seepage discharge loss have been obtained. Using these seepage loss equations, the design variables for minimum seepage loss have been obtained. The use of the design equations has been illustrated by design examples.