弹性力学空间轴对称问题通解的研究

本文证明了横观各向同性弹性力学空间轴对称问题的通解是完备的.这里φ满足同时得到了轴对称问题一个新的完备通解这里φ满足     

弹性力学平面问题的位移型解答

本文证明了一个线性常系数偏微分方程的通解定理,利用这个通解定理导出了弹性力学平面问题的位移通解。     

Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的辛叠加解

研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性.     

弹性常曲率扁壳通解的完备性和不唯一性

导出了弹性常曲率扁壳的一种新的通解，证明了它的完备性和不唯一性，著名的符拉索夫（Ｖｌａｓｏｖ）解是它的特殊情形之一．论证了符拉索夫解不适用于球形扁壳，并给出了球形扁壳的新的通解     

弹性力学平面问题位移函数的研究

本文推导出各向同性弹性力学平面问题位移的完备通解，该位移通解的导出，使求解任何边界条件的平面问题成为现实     

矩形中厚板Hamilton正则方程的解析解

运用Fourier分析方法,建立了对边简支的矩形中厚板弯曲问题的完备的辛本征展开. 借助于Mathematica软件的帮助,得到了来源于矩形中厚板问题的Hamilton算子的本征函数. 接着证明了本征函数系的完备性,这为使用分离变量法求解相应问题提供了理论保证;进而运用完备性定理,得到了问题的解析解;一个数值算例验证了结果的正确性.     

Papkovich-Neuber(P-N)通解的互逆公式及其它

本文构造出了P-N解的互逆公式从而较简捷地证明了P-N解的完备性。利用互逆公式中自动包含的反映零位移场的任意调和函数,可以自然地引出“E-S 凸域定理”,此外,平面应变问题通解也是互逆公式的直接结果。     

斯托克斯阻力公式的简单推导

斯托克斯阻力公式的传统推导有些复杂.本文根据线性齐次微分方程所满足的叠加原理提出了一个简单的推导.由于斯托克斯方程是一个二阶线性偏微分方程,根据球表面的两个速度分量条件,方程应该有两个线性独立的和完备的解,这两个解应该构成方程的基本解组,它们的线性组合应该就是方程的通解.使用拉普拉斯方程的解以及量纲分析,找到了这两个解.这两个解的线性组合就是斯托克斯问题的解.     

A simple derivation of the Stokes formula of the drag

斯托克斯阻力公式的传统推导有些复杂.本文根据线性齐次微分方程所满足的叠加原理提出了一个简单的推导.由于斯托克斯方程是一个二阶线性偏微分方程,根据球表面的两个速度分量条件,方程应该有两个线性独立的和完备的解,这两个解应该构成方程的基本解组,它们的线性组合应该就是方程的通解.使用拉普拉斯方程的解以及量纲分析,找到了这两个解.这两个解的线性组合就是斯托克斯问题的解.     

饱和土中的任意形状孔洞对弹性波的散射

根据Biot波动理论建立了求解饱和土中任意形状孔洞对弹性波散射问题的复变函数方法.首先通过引入位移势函数把稳态条件下的Biot波动方程解耦为势函数所满足的Helmholtz方程.利用分离变量方法即得到Helmholtz方程完备的通解.根据所得位移势函数的通解,可得骨架位移、流体相对骨架的位移、应力和孔压的表达式.通过保角变换方法,把物理平面上的孔洞映射到像平面上单位圆.利用土骨架和流体的边界条件,即可确定波函数展开式中的未知系数.给出了一些数值结果.     

热点起爆理论的近似分枝点分析

本文用变分法对热点起爆理论进行了分枝点分析,并不是建立在热平衡条件的基础上,所以比较普遍。     

AGAIN DISCUSSING ABOUT SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATION CONTAINING TWO-PARAMETER

In this paper using the method of "The Two-Variable Expansion Procedure" we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than [1]. We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.     

弹性力学Hamilton方法广义解的适定性

首先引入了Hamilton体系中平面应力弹性力学问题正则方程的Galerkin变分方程,证明了Galerkin变分方程和目前文献中所用的Ritz变分方程的等价性,以及相应广义解的适定性,从而为目前的数值方法提供了理论基础。从证明过程中可以看到广义解实际上是Ritz变分泛函的一个鞍点。     

The axisymmetric problem with initial conditions for the equations of motion of an ideal incompressible fluid

The present paper presents a proof of the existence and uniqueness theorem for the solution of the axisymmetric problem with initial conditions for the Euler equations in the case of an incompressible fluid. We consider the case of the nonporous wall, and also the transpiration problem in the formulation given in [1]. Global unique solvability is proved for assumptions only on the smoothness of the conditions and for all values of the time t. The existence theorem for a small time segment in the case of a nonporous wall has been proved for the general three-dimensional problem in [2, 3]. For the proof we use a method analogous to that developed in [1] for planar flows. The a priori estimate of the vorticity which is used in the present study was obtained previously in [4],The author wishes to thank V. I. Yudovich for continued interest in the study and many valuable suggestions.     

A Remark on the Existence of 2-D Steady Navier–Stokes Flow in Bounded Symmetric Domain Under General Outflow Condition

Let Ω be a 2-dimensional bounded domain, symmetric with respect to the x₂-axis. The boundary has several connected components, intersecting the x₂-axis. The boundary value is symmetric with respect to the x₂-axis satisfying the general outflow condition. The existence of the symmetric solution to the steady Navier–Stokes equations was established by Amick [2] and Fujita [4]. Fujita [4] proved a key lemma concerning the solenoidal extension of the boundary value by virtual drain method. In this note, we give a different proof via elementary approach by means of the stream function.     

置于液体表面上的梁的塑性动力响应分析

本文讨论了置于液体表面上的梁在一般的非对称变形模式下的塑性动力响应问题。文中采用了复域内格林函数解法,将势函数的Herbert问题转化为对Cauchy型奇异积分方程的求解。并用此方法讨论了简支梁和悬臂梁的塑性动力响应问题。结果表明,这类问题的已有的解均为本文给出的一般变形模式下解的特例。     

A NECESSARY AND SUFFICIENT CONDITION FOR THEOSCILLATION OF SOLUTIONS OF LIENARD TYPE SYSTEM WITH MULTIPLE SINGULAR POINTS

I.IntroductionJ.R.Graer']andG.VillariI2]gavenecessar\JandsufficientconditionsfortheoscillationofsolutionofLienardsystemf~])~F(x),y~~glXJ(l.l)HanMaoanI3]gaveoscillatirytheoremsforLienardt}'pesystemt'.ithasingularpointi~h(.t/)~F(x),#~~g(x)(1.2)Whereas,aloto…     

横观各向同性板的分解理论

将分解理论从各向同性板推广至横观各向同性板,得到横观各向同性板的分解理论,即横观各向同性板 内应力状态可以分解成内应力状态、剪切应力状态和超越应力状态,并给出严格的数学证明.     

Bifurcation of periodic solution in a Predator–Prey type of systems with non-monotonic response function and periodic perturbation

A Predator–Prey type of dynamical systems with non-monotonic response function and time-periodic perturbation is considered in this paper. We present a proof for the number of equilibria in the unperturbed system at some parts of the parameter space. The perturbed system is a dynamical system defined by a periodic vector field. We present an alternative proof for a classical result on the period of the periodic solution. By using a numerical continuation method AUTO (Doedel et al., 1986 [9]), we present a bifurcation analysis for periodic solution of the perturbed system where we found fold, cusp and Swallowtail bifurcations.