考虑横向剪切,周边弹性支承浅球壳的非线性静动力分析

1 基本方程在法向均布载荷q(t)作用下的浅球壳如图1所示.壳上任一点的坐标由中曲面的地理坐标((?),θ)及沿中曲面外法线方向的坐标z 确定.u,v,w 分别为沿(?),θ,z 方向的位移;ψ_1,ψ_2分别为球壳横截面在(?)-z 和θ-z 面内的转角;ρ_0为单位体积的质量,且ρ=     

实旋转体轴对称变形的一种有限元新模式

本文以节圆的环向应变 s_θ和轴向位移 W 为单元自由度在(r~2,z)平面上构造有限元的新模式,更符合实际的位移场并避免了应力在对称轴上存在的 l/r奇异项.采用本文提出的有限元新模式得到的计算结果较之文[1]、[2]在对称轴附近有明显的改善.     

Boundary and interior layer behavior for singularly perturbed vector problem

In this paper,we consider the vector nonlinear boundary value problem:εy~v=f(x,y,z,y′,ε),y(0)=A_1,y(1)=B_1εz~v=g(x,y,z,z′,ε),z(0)=A_2,z(1)=B_2whereε>0 is a small parameter,0≤x≤1 ,f and g are continuous functions in R~4,Under appropriate assumptions,by means of the differential inequalities,we demonstratethe existence and estimation,involving boundary and interior layers,of the solutions to theabove problem.     

锥壳固有振动的精确解

本文从锥壳的Mushtari-Donnell型位移微分方程组出发,通过引入一个位移函数U(s,θ,τ)(在极限情况下,它将退化成对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程。这个方程的解用级数形式给出。     

锥壳一般弯曲,稳定和振动问题的位移型统一方程及其应用

1.前言弹性锥壳的一般弯曲、稳定和振动问题,在实际工程中经常遇到,但对其研究基本上限于轴对称问题且都是以挠度函数和应力函数为基本未知量.我们认为,对于锥壳的特征值问题、弹性地基锥壳以及锥壳组合结构,则宜采用锥壳的位移解法.本文作者之一曾对锥壳一般弯曲问题的位移解法进行了系统的研究,以广义超几何函数给出了一般解.在应用文献[1]结果的基础上,本文通过引入一个广义载荷q_n(s,θ,t),得到了以位移函数U(s,θ,t)表示的弹性锥壳一般弯曲、稳定和振动(包括弹性地基影响)问题的统一型式的控制方程.文献[2]用级数给出了锥壳横向自由振动问题的解,但应指出,由于文献[2]中     

修正荷载的Wilson-θ法的稳定性与精度分析

Wilson-θ法求得的位移、速度与加速度不满足t时刻的动力平衡方程。提出修正荷载的Wilson-θ法:增加一个荷载δF(t),使得t时刻的动力平衡方程得以满足;将-θ′δF(t)作为荷载加入t+Δt时刻的计算中,当θ′=0时,修正荷载的Wilson-θ法退化为Wilson-θ法。对应于不同的θ′值,在无条件稳定的前提下,θ的取值范围也不同。定义了逐步积分法中的计算误差。计算结果表明:计算误差与θ值成正相关,当θ′=0.6,无条件稳定的θ为最小值1.24,因而θ′=0.6,θ=1.24时,计算误差最小,建议在计算中采用。保持Wilson-θ法无条件稳定、几乎不增加计算量的条件下,修正荷载的Wilson-θ法可以提高计算精度。     

水平刚性岩基上的弹性层表面受垂直集中力问题的积分方程解法

沿弹性空间z轴的[h,∞]和[-h,-∞]上与z=0平面对称地分布集度为X_1(c)=X_1(-c)的集中力,集度为X_2(c)=X_2(-c)的挤压中心,以及一对等值、反向、分别作用于z轴上的z=h和z=-h点的平行z轴的集中力,就能使具有刚性水平层的半空间表面受垂直集中力问题归结为两个联立的Fredbolm第一种积分方程。文中给出用DJS-21机进行数值计算的结果,根据这些结果给出位移的在Chebyshev意义下的最佳拟合的多项表达式。     

回转周期结构的离散富里叶级数解

一个结构如果在适当选定的圆柱坐标系中绕z 轴转过(2π)/n 角后能与原结构相重合(包括几何和物性两方面),则称为具有n 跨的回转周期结构.不难推断,如k 为任意整数,这样的结构绕z 轴转过(2kπ)/n 角后都能与原结构重合.用一系列通过z 轴的半曲面θ=α(z,r) (2kπ)/n,k=1,2,…,n,可把结构分割为完全相同的n 跨子结构,在每一跨中进行同样的有限元离散化,即得到一个离散的回转周期结构.作者在一篇文章中曾指出,如果通过适当的分割可使每一跨子结构具有左右对称的性质,则在引进离散富里叶变换后可以把整个结构的平衡问题化为n 个互不耦     

ON THE FREE ENERGY AND VARIATIONAL THEOREN OF ELASTIC PROBLEM IN THERMAL SHOCK

In some investigations on variational principle for cou-pled thermoelastic problems,the free energy φ(e_(ij),θ) ,Wherethe state variables are elastic strain e_(ij) and temperatureincrement θ,is expressed asφ(e_(ij),θ)=λ/2e_(kk)e(ij) μe_(ki)e_(kj)-γe_(kk)θ-c/2ρθ~2/T_o (0.1)This expression is employed only under the condition of|θ|≤T_o (absolute temperature of reference)But the value of temperature increment is great, evengreater than T_o in thermal shock. And the material pro-perties (λ,μ,γ,c,etc.) will not remain constant,theyvary with θ.The expression of free energy for this con-dition is derived in this paper. Equation (0.1) is itsspecial case.Euler’s equations Will be nonlinear While this expres-sion of free energy has been introduced into variationaltheorem. In order to linearise, the time interval of ther-mal shock is divided into a number of time elements △t_k(△t_k=t_k-t_(k-1),k=1,2,…,n),Which are so small that the tempera-ture increment θ_k within it is very small,too.Thus,t     

DISCUSSIONS ON“AN ASYMPTOTIC ELASTIC PLASTIC ANALYSIS IN PLANE STRAIN DEFORMATION NEAR A CRACK TIP”

I.In his paper,prof.D.W.Hsueh derived the following functionf(θ)=-[(1 2n)/(1 n)~2-k_1~2]A_1/k_1θ-[(1 2n)/(1 n)~2-k_2~2]A_2/k_2-cosk_2θ(1)In calculation of coefficients A_1,A_2 a mistake occurred.Making use of f′(π)=0 andf(0)=0,     

关于“非均匀各向同性介质弹性力学平面问题”

文献[1]讨论了指定位移的边界条件用应力函数表示的问题。阅读之后,感到有几个问题值得提出来讨论。 一、文献[1]导出的位移边界条件(3.1)有错误,现在重新简略推导如下: 在指定位移的边界S上,边界条件为: u(s)=(s),v(s)=(s), (1) 这里,分别代表边界线上的法向和切向指定位移(凡末加说明的符号均与文献[1]所     

拉伸时中心开裂有限板条裂纹端应力强度因子的计算方法

以Muskhelishvili关于平面弹性力学解析函数解法和Hilbert边值问题解法为基础,文中通过解析函数(?)(z)和ω(z),给出一种位移-合力-应力模式.这种模式适用     

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     

“论两种不同正交异性楔弹性接触”中应力奇异性

一般楔形体受面力作用时,其应力及位移有时会变为无限大。本文继续[1]的工作,分析均匀正交异性楔和两种不同正交异性复合楔的应力奇异性问题。由于假定了G_(rθ)=((E_rE_θ)/(1/2))/(2(1+(μ_(rθ)μ_(θr))/(1/2)),可用解析法得到应力奇异阶次为γ~(-s)型。对于均匀正交异性楔s只与材料弹性模量比值平方根kl=(E_θ/E_r)/(1/2)有关;对于正交异性复合楔,当k＇=k＇＇,s与复合楔中材料剪切模量比值e(=G_(rθ)~＇/G_(rθ)~＇＇)是无关的。     

薄壁箱梁剪力滞翘曲位移函数的改进与对比分析

基于能量变分原理,考虑箱梁横截面正应力轴向平衡条件和剪切变形的影响,构建了包含参数m的新剪力滞翘曲位移函数。以所得应力均方误差与挠度均方误差为精度标准,计算分析了不同m值(即不同幂次)抛物线下新构建剪力滞翘曲位移函数的适应性,得出了二次抛物线形式较为精确合理的结论。通过比较典型位置所得应力值,进一步分析了新构建剪力滞翘曲位移函数(m=2)的适应性和精确性。针对所得集中荷载作用下简支箱梁翼缘悬臂板最外端应力有较大偏差的情况,通过应力曲线拟合,得到了集中荷载作用下简支箱梁悬臂板的应力改进公式。将应力改进后新构建剪力滞翘曲位移函数与基本翘曲位移函数所得的应力与竖向挠度进行比较,论证了通过本文新构建的剪力滞翘曲位移函数推导计算所得的应力公式和应力改进公式的高精度。     

箱形梁剪力滞和剪切效应引起的附加挠度分析

将箱形梁腹板剪切变形纳入初等梁挠曲变形,在全截面上引入剪力滞翘曲修正系数,重新定义了剪力滞翘曲位移模式。选取剪力滞效应引起的附加挠度为广义位移,计算外力势能时考虑剪力滞广义位移的影响,应用能量变分法建立了反映剪力滞和剪切效应的控制微分方程,并导出了均布荷载作用下简支箱梁和两跨连续箱梁剪力滞和剪切效应附加挠度的解析解。数值算例表明,本文方法计算的总挠度值与有限元数值解吻合良好,从而验证了本文方法的合理性。算例箱梁剪切附加挠度明显大于剪力滞附加挠度;简支箱梁跨中截面的剪切和剪力滞附加挠度分别占初等梁挠度的2.50%和1.97%,两跨连续箱梁距中支点9l/16截面分别占27.45%和16.87%。     

The displacement solution of conical shell and its application

In this paper,the displacement solution method of the conical shell is presented.Fromthe differential equations in displacement form of conical shell and by introducing adisplacement function,U(s,θ),the differential equations are changed into an eight-ordersoluble partial differential equation about the displacement function U(s,θ)in which thecoefficients are variable.At the same time,the expressions of the displacement and internalforce components of the shell are also given by the displacement function.As special casesof this paper,the displacement function introduced by V.Z.Vlasov in circular cylindricalshell,the basic equation of the cylindrical shell and that of the circular plate are directlyderived.Under the arbitrary loads and boundary conditions,the general bending problem of theconical shell is reduced to finding the displacement function U(s,θ),and the generalsolution of the governing equation is obtained in generalized hypergeometric function,Forthe axisymmetric bending deformation of the     

圆形非均布动荷载下弹性半空间的表面位移

求解理想弹性半空间表面在分布动荷载下的位移场,在工程科学的许多领域内,都有意义。本文针对一类非均布的圆形直线分布动荷载,得到了半空间表面沿力方向的位移影响函数加权积分式以及受荷面的加权平均位移式(这可解释为半空间上刚性圆形基础的摇摆转角及扭转转角公式),依据这些公式实现了数值计算。将数值结果与用别的方法得到的已有解答比较可见,两种解答式数值结果吻合,说明本文的结果简便可靠,避免了处理广义积分。1. 圆形非均布的突加力半无限均匀、各向同性的弹性体位于半空间z≥0内,坐标原点取在表面(z=0)上,z轴的正向指向弹性体,在表面上给定应力边界条件     

用散光光弹性测量Ⅰ型应力强度因子

利用散光法确定Ⅰ型应力强度因子的可行性已在一根带边裂纹的梁承受纯弯曲的情况下得到证实。可以用光弹性条纹数据米获得裂缝尖端周围奇异区内的条纹梯度的表达式。Ⅰ型应力强度因子是通过把条纹梯度与奇异区内的局部应力联系起米,然后将这些结果外推到裂缝尖端而给予确定。实验结果和解析结果表示了良好的一致性,故建议将此法应用于三维断裂力学问题。 字符: σ_(xx),σ_(yy),σ_(zz)=笛卡尔坐标中的应力分量。 σ_0=远场应力在奇异区内的效应。 x,y,z=在图1中定义的笛卡尔坐标。 γ,θ=裂纹尖端处的极坐标。 K_Ⅰ=Ⅰ型应力强度因子。 K_(Ⅰth)=Ⅰ型应力强度因子的理论值。 f_σ=散光法应力条纹系数。 (dN)/(dx)=散光条纹梯度。     

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n < ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture.