关于带裂纹杆扭转问题中特征展开的一个改进

众所周知,在柱形杆的扭转问题中,可以通过应力函数Ψ(x,y)求解具体问题.在本文中,令其中 u(x,y)为新引入的函数.利用专著[2]中的式(2.40),(2.44a),(2.38)和(2.52a),不难 ...     

带裂纹角钢形截面杆抗扭附度和第三型应力强度因子的计算

本文是作者前一工作的继续,文中讨论了开裂角钢形截面抗扭刚度和第三型应力强度因子的计算方法.对于图1所示截面,若令扭转问题中的应力函数为φ(x,y)=-x~2 u(x,y) (1)不难导出对于函数u(x,y)的定解问题为((?)~2u/(?)x~2) ((?)~2u/(?)y~2)=0,u|L=x~2 (2)其中L 表示截面的周边.同时抗扭刚度为D=μJ J=2(?)(-x~2 u(x,y))dxdy (3)     

KANTOROVICH SOLUTION FOR THE PROBLEM OF BENDING OF A LADDER PLATE

ctangular plate in bending, this paper deals with the solutions for the ladder plate with various boundary conditions. The deflection of the plate is expressed in a first-order displacement function ω(x,y)=μ(x,y)υ(y) where the μ(x,y) in x direction is the generalized beam function. By making use of the principle of least potential energy, the variable coefficients differential equations for v(y) may be established. By solvingis, these differential euqations and making use of the boundary conditions, the accurate solutions of v(y) in y direction may be obtained. Then the displacement function w(x,y) is the solution for the problem of the bending of the ladder plate with a better degree of approximation.     

Singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations

In this paper,we study the singular perturbation of boundary value problem of systemsfor quasilinear ordinary differential equations:x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′ h(t,x,y,ε),x(0,ε)=A(ε),y(0,ε)=Bε,y(1,ε)=C(ε)where xf.y,h,A,B and C belong to R″and a is a diagonal matrix.Under the appropriateassumptions,using the technique of diagonalization and the theory of differentialinequalities we obtain the existence of solution and its componentwise uniformly validasymptotic estimation.     

Singular perturbation of the fourth order elliptic equation when the limit equation is elliptic-parabolic

3@1In this paper we cosider the singular perturbation of the fourth order elliptic equation-ε~2△~2u y~m(α~2u)/(αy~2) (α~2u)/(αx~2) α(x,y)-(αu)/(αy) b(x,y)(αu)/(αx) c(x,y)=0 when the limit equationis elliptic-parabolic,where εis a positive parameter,m is a positive real number,△isLaplacian operator,a.b.c are sufficiently smooth.Under appropriate condition we derivethe sufficient condition of solvability and prove the existence of solution and give auniformly valid asymptotic solution of arbitrary order.     

FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

Let X be a convex metric space with the property that every decreasing sequence ofnonempty closed subsets of X with diameters tending to(?)has nonempty intersection.This paper proved that if T is a mapping of a closed convex nonempty subset K of X intoitself satisfying the inequality:d(Tx,ty)≤ad(x.y) b{d(x,Tx) d(y,Ty} c{d(x,Ty) d(y,Tx)}for allλ.yin K,where0≤a<1,b≥0,c≥0,a c≠0 and a 2b 3c≤1,then T has auniquc fixed point in K.     

对于WKB近似解的一个简单物理解释

<正> Liouville 和 Green 在1837年同时考虑了如下的二阶线性常微分方程d~2y/dx~2+[λ~2q_1(x)+q_2(x)]y=0 (1)其中 q_1(x)在区间[a,b]中有二阶连续导数,且q_1(x)>0 (当 x∈[a,b]) (2)q_2(x)在[a,b]中连续,且     

Proper solutions and limit boundary value problems of nonlinear second-order systems of differential equations

For the system of differential equations x=r(t)y,y=-a(t)f(x)g(y) where a(t)>0, r(t)>0 for t≥t; f(x) >0 and is decreasing for x>0 g(y)>0, we give necessary and sufficient condition of the existence of a proper solution, a bounded proper solution or solutions of two kinds of boundary value problems on an infinite interval [c,∞] c≥t_g. Several examples are given to illustrate the conditions of these results.     

Extended airy function and differential equations with n-turning points

This paper studies a second order linear ordinary differential equation with n-turningpoints(d~2y)/(dx~2) [λ~2q_1(x) q_2(x)]y=0Where q_1(x)=(x-μ_1)(x-μ_2)...(x-μ_n)f(x),f(x)≠0 ,and λis a largeparameter.The formal uniformly valid asymptotic solution of the equation is obtained based onthe analysis of the three points by means of the matched method.By the work a method isdeveloped and the applicability of this method to the n-turning points is demonstrated.     

固定边矩形弹性薄板卡门大挠度与大振幅方程组的逼近解

1.大挠度问题图1所示的固定边矩形弹性薄板,其大挠度问题由下列卡门方程组定义:按文献考虑以下边界条件:当x=0及x=a 时:W=0(无挠度);((?)W)/((?)x)=0(无转角) (4)((?)~3φ)/((?)x~3) (2 μ)((?)~3φ)/((?)x(?)y~2)=0 (沿板边无法向位移) (5)((?)~2φ)/((?)x(?)y)=0 (没有阻止沿板边切向位移的力) (6)当y=0及y=b 时也有相同意义的边界条件如下:     

自伴微分方程特征值问题的子空间迭代法及其在结构振动分析中的应用

1.自伴微分方程特征值问题考虑特征值问题L_φ=λ_(ρφ) 在[a,b]上(1)其中λ为参数,ρ(x)为闭区间[a,b]上的连续函数,并且ρ(x)>0,L为n阶自伴微分算子其中P_j∈C~(n-j)在a≤x≤b上(j=0,1,…,n),P_j为x的实函数。L的定义域为满足与(1)相应的齐次边界条件并属于C~n的所有函数的线性集合,记作D,φ∈D。     

裂纹面受剪力作用的板的应力强度因子

考虑一个在ξ-η平面内一等厚度(厚度为h)的无限大板,在η=0,|ξ|≤a处有一条裂纹,如图1所示。在裂纹表面承受单位长度的剪力Q。为了方便,引入无量纲坐标,x=ξ/a,y=η/a。本文参照Wang解含裂纹板受扭的方法,采用了计及横向剪切变形影响的Reissner的薄板弯曲理论。根据该理论,需要求解挠曲函数w(x,y)的四阶偏微分方程(对于本题是双调和方程)和应力     

有任意径向单裂缝圆柱体的扭转

1.问题提法,保角映射和混合边值问题 本文讨论如图:半径为r,有一径向内裂缝的圆柱的线弹性扭转。直角坐标系z轴平行于圆柱轴。裂缝和正x轴上(a,b)段重合,b端较a端离圆周为近。坐标原点任取在圆内a端之左。若圆心c不在裂缝上,就取圆心为原点,问题大为简化。柱体各点翘曲w=(?)(x,y),其中(?)是扭率,(x,y)是翘曲     

On the boundary value problems for ordinary differential equations with turning points

In this paper,we consider the boundary value problems of the formsy″-f(x,ε)y′ g(x,ε)=0 (-a≤x≤b,0≤ε《1 )y(-a)=a,y(b)=βwhere f(x,0)has several and multiple zeros on the interval[-a,b].The conditions forexhibiting boundary and interior layers are given,and the corresponding asymptoticexpansions of solutions are constructed.     

广义平面应变问题

一般情况下平面应变问题归结为一个双调和方程、一个调和方程及轴向应变应满足平面坐标x、y 的线性函数条件下的求解.进一步分析证明,轴向载荷分布必须是x、y 的线性函数类问题都能按广义平面应变公式进行分析.     

变惯矩梁变形的函数解

<正> 一般说来,任何一个变惯矩梁(包括线性变惯矩梁和非线性变惯矩梁)的变形问题,都可以通过对梁的挠曲线微分方程y″=M(x)/EJ(x) (1)进行二次直接积分来求得其函数解.力学与实践     

Optimal control of parabolic variational inequalities with state constraint

1　IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr…     

Multiple reciprocity method with two series of sequences of high-order fundamental solution for thin plate bending

IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0　　(x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln｜x-y｜(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu…     

Singular perturbation of nonlinear vector boundary value problem

In this paper we study the perturbed boundary value problem of the form dx/dt=f(x,y,t;ε), εdy/dt=g(x,y,t;ε), a_1(ε)x(0,ε)+a_2(ε)y(0,ε)=a(ε) b_1(ε)x(1,ε)+εb_2(ε)y(1,ε)=β(ε)in whichx,f,β∈E~m, y,g,a∈E~n, 0<ε(?)1and a_1(ε), a_2(ε), b_2(ε)and b_2(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.     

HOPF BIFURCATION IN A THREE-DIMENSIONAL SYSTEM

In this paper,Liapunor-Schmidt reduction and singularity theory are employed todiscuss Hopf and degenerate Hopf bifurcations in global parametric region in a three-dimensional system x=-βx y,y=-x-βy(1-kz),z=β[α(1-z)-ky~2].Theconditions on existence and stability are given.