Haug-Arora梯度投影法的改进

在Haug E. J. 和Arora J. S. 提出的梯度投影法中,所用的基本迭代表达式为{x}~(k+1)={x}~k-η~(k+1){δx_1}~(k+1)+{δx_2}~(k+1) (1)式中{δx_1}~(k+1)为第k+1次迭代使目标函数减小的向量,{δx_2}~(k+1)为修正第k次迭代所引起的约束误差的向量,η~(k+1)为第k+1次迭代的步长系数,它由下式确定     

各向异性平面变形及横观各向同性轴对称变形的塑性极限平衡方程

一、塑性条件 在各向同性情况下,普遍的塑性条件形式可写成(1.1)或1/2(σ_1-σ_3)sin2δ=f[1/2(σ_1+σ_3)-1/2(σ_1-σ_3)cos 2δ],(1.2)式中δ为滑移面与σ_1同的夹角,df/dσ_n=ctg2δ(图1)。由式(L2)易得     

Kelvin问题的一种解法

1.Kelvin问题所对应的定解问题在无界弹性体内,把集中力的作用点选为坐标系Ox_1x_2x_3的原点.设集中力的大小为P(常数),其方向沿单位矢量n,则此集中力可表示为Pδ(x)n,其中δ(x)为Dirac的δ函数,x为空间中一点的位置矢.弹性体内各点的位移矢量u是点的坐标的函数,表示为u=u(x).位移u在无界域中所应满足静     

大涡仿真:回顾和展望(续)

4.数值方法4.1 伪谱方法在本节,我们考虑在平面Poiseuille流动范围内适用于对方程(3.37)或(3.39)进行时间推进积分(仿真)的数值方法。[28,75]的大涡仿真采用有限差分方法,而[41]则在x_1和x_2方向采用谱方法(Fourier方法),但在垂直于边壁的x_3方向采用有限差分公式。[2]的直接谱仿真(没有小网格项)在边壁的同一方向采用Fourier方法,      

两类动点相对轨迹间的关系

在点的复合运动分析中,理论上可选择的动点有两类:一类是取在运动过程中始终为相关点(即连接点或接触点)的点为动点,我们称之为第一类动点,用M表示;另一类是只在运动的某一瞬时为相关点的点为动点,我们称之为第二类动点,用N表示。本文从普遍情况出发,阐述两类动点相对轨迹间的一般关系。在两个运动刚体上分别固连坐标系o_1x_(F_1)x_(F_2)x_(F_3)和o_2x_(T_1)x_(T_2)x_(T_3),它们将随刚体运动,因此都是动系,分别称为动系Ⅰ和动系Ⅱ。再取固定参考系ox_1x_2x_3(图1)。     

高分子合金UHMWPE/PTFE的微晶相结构与力学性能的关系

本文研究了超高分子量聚乙烯与聚四氟乙烯共混体系的磨损、抗拉强度,断裂仲长率与抗冲击强度等力学性能随体系组成变化的规律,並用偏光显微镜考察其微晶结构。结果表明,该高分子合金的聚结态结构与力学性能之间的关系也符合文献[1]中提出的关系式,即 x_1f_1/d_(1c)=0.40(x_1/d_1+x_2/d_2)。     

双底板散斑复位全场分析

对于具有刚体运动的变形体,如何消去刚体位移得到全场等位移线,我们进行了双底板散斑复位的实验研究。叙述如下: 1. 双底板复位全场分析公式的推导:采用单光束散斑照相光路设f (x_1,x_2)为变形前物体在底片1上所成象的复振幅。f(x_1+d_1-x_2a,x_2+d_2+x_1a)表示同时具有刚     

DISCONTINUOUS AND IMPULSIVE EXCITATION

In this paper,we study the solution of differential equation with Dirac function andHeaviside function.arising from discontinuous and impulsive excitation.Firstly,accordingto the theory of differential equation,we suggest x(t)=x_1(t) x_2(t)H(t-a);then wederive the equation of x_1(t)and x_2(t) by terms of property of distribution,and by solvingx_1(t)and x_2(t)we obtain x(t);finally,we make a thorough investigation about periodicimpulsive parametric excitation.     

A Mathematical Interpretation of Dirac δ Function

The two conditions(see[1]p.58)δ(x)=0,for x≠0 (1.1)∫_( ∞)_(-∞)δ(x)dx=1 (1.2)of the Diracδfunction are inconsistent in standard analysis.In this paper,the author began by studying the integral of the func-tions on tbe nucleon a(o),and then,making use of the point function ininfinitesimal analysis to define the Diracδfunctionδ(x)so that it satis-fies the condition(1.2)andδ(x)=0.for x∈R and x≠0Some various examples of Diracδfunctions have been presented andsome properties of theδfunction have been derived.     

Chaotic belt phenomena in nonlinear elastic beam

IntroductionThechaoticphenomenainsolidmechanicsfieldsbringmoreandmoreinterest.In 1 998,F .C .Moon[1]analyzedthechaoticbehaviorsofbeamsexperimentallyfirst.Thenhestudiedthedynamicsresponseoflinearelasticbeamsubjectedtransverseperiodicload .Thechaoticmotionsoflineardampingbeamshavebeenstudiedbymanyscholarsathomeandabroadinrecentyears[2 ,3].ThedynamicbehaviorsofnonlineardampingbeamssubjectedtotransverseloadP=δP0 (f+cosωt)sin(πx/l)arestudiedinthispaper.Thecriticconditionsthatchaosoccursinthes…     

高阶Schroedinger型方程的两层高精度恒稳差分格式

众所周知，高阶Schroedinger方程在量子力学、非线性光学及流体力学中都有广泛的应用。本文对高阶Schroedinger型方程δu/δt=i(-1)^mδ2m/δx^2m(其中i=√-1，m为正整数)，利用待定系数法，构造出一个两层高精度的隐式差分格式。其截断误差阶为O((△t)^2 (Δx)^6)，比同类格式精度高2～4阶，并用Fourier分析法证明了它是绝对稳定的。最后，数值例子表明本文格式比著名的Crank-Nicolson格式精度高10^-2～10^-7，这说明我们的格式是有效的，理论分析与实际计算相吻合。     

The boundedness and asymptotic behavior of solutions of differential system of second-order with variable coefficients

In this paper, the differential system of second-order withvariable coefficients is studied. and some criteria of theboundedness and asymptotic behavior for solutions are given.Consider a system of differential equationsdx_1/dt=p_(11)(t)x_1 p_(12)(t)x_2dx_2/dt=p_(21)(t)x_1 p_(22)(t)x_2Now we studg the boundedness and asymptotic behavior of its so-lutions. In the case of Pij(t)being periodic functions. it wasinvestigated by Burdina; in the case of Pij(t) being arbitraryfunctions. it has not been investigated yet. Besides. the me-thod used by Burdina is only oppropriate for the former but notfor the latter case. In this paper we shall give a method whichis appropriate for both cases.     

PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER SYSTEMS OF DIFFERENTIAL EQUATIONS

For the system of differential equations(?)=r(t)v_1 (?)=-a(t)f(x)g(v)where a(t)>0,r(t)>0 for t≥t_0;f(x)>0 and is decreasing forx>0,g(y)>0,we give necessary and sufficient condition of a propersolution.a bounded proper solution or sotutions of two kinds of boundary value problems onan infinite interval [c,∞),c≥t_0.Several examples are given to illustrate the conditionsof these results.     

过渡领域圆柱间Couette流动

圆柱间Couette流动问题是最简单的流动情况之一,当圆柱转速较大(M≈1)而间隙与半径之比[δ=(R_2-R_1)/R_1]不为小量时,却可用以检验求解过渡领域中非线性问题的各种方法。不久前,文献[1,2]在M≈1,δ=0.5条件下用电子束做了同心圆柱间氩气密度分布的测量,提供了一组比较流场结构的实验数据。在较早的稀薄气体Couette     

椭圆壳体的弹塑性失稳

在静水外压作用下理想圆柱薄壳丧失弹性稳定是个古典的力学问题。1884年兰范(M. Levy)首次给出了此问题的临界外压是P_(er)=2Ek~3/1-μ~2 (1)E为弹性模数,k=δ/D为尺寸因素,δ为壳体壁厚,D为壳体中面直径,μ为泊桑比。     

小参数广义Lienard型耗散方程周期及三角多项式定常解

本文沿文献[1]提出的,借待定系数法确定Fourier级数的途径,讨论了直接求出小参数广义Lienard型耗散方程定常振动的Fourier级数形式的周期解的可能性和力法.也讨论了非线性自由振动这一特殊情况.找到了求Fourier系数A_(2K-1),B_(2K+1)(K=1,2,…)及非线性角频率ω的公式及方法,这些公式将它们表为复合导数f_t~(K)(x_0),g_t~(K)(x_0)(K=0,1,…)的线性组合.于是,这两类方程的求解,便简化为求各阶复合导数问题.但由于求高阶复合导数的复杂性,本法只能用于求三角多项式近似解.     

是虚功原理的反例吗?

文[1]给出了平衡条件 Q_j=0(j=1、2,…s)的一个反例:约束在 y=x~2,x≥0上的质点 m,若选y 为广义坐标,则在平衡位置 y=0上,Q_y=δW/δy=-mg≠0;文[2]继续给出例证:约束为(?)或 y=x~3,若选 y 为广义坐标,在平衡位置 y=0上,同样有 Q_y≠0.文[3]指出:导致矛盾的原因很简单.即在平衡点附近的可能位移,如用广义坐标 y 表 ...     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

Lagrange equation of a class of nonholonomic systems

Making use of conclusions from[1]:(1)d-δoperations are commutative;(2)theAppell-Chetaev condition restricting virtual displacements is superfluous,the present paperderives the Lagrange equation without multipliers for a class of first-order nonlinearnonholonomic dynamical systems by means of variational principle.This kind of equationsis new.     

The mathematical principles of vibration reductor

In engineering and technology, it is often demanded that self-oscillation.be eliminated.so that the equipment or machinery may not be damaged In this paper, a mathematicalmodel for reducing vibration is given by the following equations:(?)_1+(?)((?)_1) +k_1(x_1-x_2) =0, (?)_2+c(?)_1+k_2(x_2-x_1) =0 (*)We have discussed how to choose suitable parameters c_1, k_1,k_2; of equations (*),so as to make the zero solution to be of global stability. Several theorems on the globalstability of the zero solution of equations (*) are also given.