“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。     

BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE

IntroductionConcerningtheelasticplaneprobleminaunitcircle ,ZhengShenzhouandZhengXueliangdevelopedaboundaryintegralformulaofthestressfunction[1]:Φ(r,θ) =-( 1 -r2 ) 24π ∫2π0ν( φ)1 -2rcos(θ-φ) r2 dφ　　 12π∫2π011 -2rcos(θ-ω) r2 dω∫2π0μ( φ)1 -cos(ω-φ) dφ　　 1 -r22π∫2π0μ( φ)1 -2rcos(θ -φ) r2 dφ　　 ( 0 ≤r <1 ) ,( 1 )whereμ(θ) =Φ(r,θ) ｜r=1,ν(θ) = Φ n r=1= Φ r r=1.Intheformula ( 1 )theseconditemisastrongsingularintegral,itshouldbeunderstoodasanintegra…     

空间轴对称问题的两类基本应力函数束及其应用

<正> 1.两类基本应力函数束众所周知,空间轴对称问题的基本应力函数(?)(r,(?))由双调和方程确定.本文采用变换(?)(r,z)=r~2f(r,z)或(?)(r,z)=(?)~2g(r,z)将方程(1)化为 f(r,z)或 g(r,z)的新方程,再利用[2]提出的变换-分离变量法求解此新方程,从而得到空间轴对称问题的两类基本应力函数.     

空间轴对称问题的两类基本应力函数束及其应用

1.两类基本应力函数束众所周知,空间轴对称问题的基本应力函数(?)(r,(?))由双调和方程确定.本文采用变换(?)(r,z)=r~2f(r,z)或(?)(r,z)=(?)~2g(r,z)将方程(1)化为 f(r,z)或 g(r,z)的新方程,再利用[2]提出的变换-分离变量法求解此新方程,从而得到空间轴对称问题的两类基本应力函数.     

有限变形下线弹性裂尖场的渐近分析

对有限变形下线弹性Ⅰ型裂纹场建立了无需分区的统一控制方程并进行了渐近分析, 利用“打靶法”得到位移场在物质描述与空间描述下的渐近阶次分别为3／4和1,Green应变、第二类P－K应力及Cauchy应力在物质描述与空间描述下的渐近阶次分数为－1／2和－2／3;对不同泊松比,裂尖有限变形线弹性场的位移均以UⅡ或u2为主导,裂纹张开角为π,现时构形中的大变形区为一垂直初始构形中裂纹表面的狭长带状区,应力则处于由σ22主导的单向拉伸状态,角分布函数U^-Ⅱ（0）及σ22^-(0)具有奇异性,但UL^-‘(Θ）／UⅡ^－‘(0)及σij^-(θ）/σ22^-(0)均趋于有限值。     

熔融渗硅法制备C/C-SiC复合材料的干态摩擦磨损行为及机制

本文以针刺炭纤维整体毡为预制体,采用化学气相渗透法和熔融渗硅法制得炭纤维增强双基体炭/碳化硅(C/C-SiC)摩擦材料;研究了C/C-SiC的干态摩擦磨损行为及机理.研究结果表明:C/C-SiC摩擦材料和30CrMoSiVA合金钢配对摩擦副制动性能稳定,当制动速度从5 000 r/min升至7 500 r/min,摩擦系数由0.33降至0.29,C/C-SiC线磨损率相应由2.01μm/次升至3.40μm/次;C/C-SiC与对偶件的摩擦是犁沟效应和黏着效应共同作用的结果,磨损是磨粒磨损、黏着磨损、氧化磨损和疲劳磨损相互作用的结果.     

关联噪声驱动非对称双稳系统的MFTP

考虑了由关联噪声驱动的非对称双稳系统的平均首次穿越时间(MFPT)问题,运用最速下降法求得平均首次穿越时间的表达式,并讨论了各个参数(包括p,q,r,λ)对两个方向的平均首次穿越时间的影响.结果表明:1)噪声关联时间λ对平均首次穿越时间T (x1→x2,λ,r)和T-(x2→x1,λ,r)的影响是不同的,T 随着λ的增加而增加,而T-却随着λ的增加而减小.2)平均首次穿越时间 T (x1→x2,λ,r)和T-(x2→x1,λ,r)都随加性噪声强度q的增加而减小;但乘性噪声P对T 和T-影响却是完全不同的,T-随着P的增加而减小,而T 随着P的增加曲线有一个极大值,即是一个共振峰.3)在不同的噪声关联强度的影响下,T /T-的曲线随着P的增加呈现不同的发展趋势,λ=0.1时,T /T-随着P的增加单调减小;而λ＝0.7时,T /T-随着P的增加先增加再减小,曲线出现了极值峰.     

General solution of A 2-D weak singular integral equation with constraint and its applications

Hertz'ssolutionTheProjectsupportedbytheNaturalScienceFoundationofGuangdongProvinceofChina[.IntroductionTheintegralequationsubjecttoconstraintp(s,te)=o,for(s,W)-(r,o)6Q={(r,O)lF(r,o)>c.}'(l.2)hasbeenstudiedin[l].Themultipleintegrationsimilartothelefthandsi…     

随机振动问题的广义坐标合成法

工程中的随机振动分析多采用完全二次型组合法(CQC)及其改进算法,如虚拟激励法(PEM)和谐波激励法(HEM)。广义坐标合成法(GCS)提出了一种计算随机响应的新思路,其基本原理是将物理空间的计算转移到自由度较小的振型空间进行,从而缩减了计算量和计算规模。对于较大规模结构体系的随机振动问题,GCS方法计算响应协方差矩阵的计算量只相当于PEM的2r/sT,其中s、r和T分别为激励功率谱矩阵的秩、振型总数和离散频率点数。此外,对于给定激励时程的问题,由于GCS方法直接求解广义坐标运动方程,因而可以方便得出响应时程。通过对几种方法的详细对比,说明对于大多数只需要求解响应方差的随机振动问题,GCS是最优的计算方法。PEM只有在s相似文献   

软件锁相环在惯性动量轮转速控制中的应用研究

研究了基于DSP和软件锁相环算法的惯性动量轮用高速(最高转速30000r／min)高精度转速控制系统。首先分析了组成软件锁相环的三个环节，设计了软件锁相环算法；然后与高精度反电势换相模块ML4425相结合，设计并实现了一种高精度无刷直流电机数字控制系统。该系统能在任意转速下进行稳速控制，且当转速高于3000r／min时，能实现1％％的转速控制精度。     

The analysis of thermal residual stresses near the apex in bonded dissimilar materials

By employing the complex variable method and constructing the particular solution sequences in the form of complex functions, all the cases of the thermal residual stress field near the apex in dissimilar materials bonded with two arbitrary angles are researched theoretically, and the corresponding classical solutions are obtained. Moreover, the primary paradox, the secondary paradox and even the triple paradox are discovered in the classical solutions and also resolved here, thereby it is confirmed that thermal residual stresses near the apex in bonded dissimilar materials probably possess the singularities of lnr (when the primary paradox occurs) , ln²r (when the secondary paradox occurs) and even ln³r (when the triple paradox occurs) . In addition, the systematic method to solve multiple paradox problems is put forward. © 1999 Elsevier Science Ltd. All rights reserved.     

The curved bar subjected to an arbitrarily distributed loading: Another paradox in the two-dimensional theory of elasticity

The problem of the curved bar subjected to an arbitrarily distributed loading on the surfacesr=a andr=b is solved by using the method of complex functions and expanding the boundary conditions atr=a andr=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bar is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 is equal to 2 and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox are obtained. Moreover, the modified classical solution which remains bounded as 2 approaches 2 is provided.     

受r^n分布载荷的楔：佯谬的解决

对表面受与ｒｎ（ｎ≥０）成正比的分布载荷的楔，当楔顶角２α与ｎ之间满足一定关系时，经典解为无穷大，这是一个佯谬．本文采用复变函数方法，研究了这个佯谬的所有情形，并发现存在二次佯谬，即对某些特定的（ｎ，α），佯谬解仍为无穷大，对此本文也予以解决     

Painlevé paradox during oblique impact with friction

In analyses using non-smooth dynamics, oblique impact of rough bodies in an unsymmetrical configuration can result in self-locking or “jam” at the sliding contact if the coefficient of friction is sufficiently large; this has been termed, Painlevé’s paradox. In the range of configurations and coefficients of friction where Painlevé’s paradox occurs, analyses based on rigid body dynamics give results indicating that either there are multiple solutions or the solution is nonexistent. This conundrum has been resolved by considering that the contact has small normal and tangential compliance which is representative of deformability in a local region around the contact point. An analysis using a hybrid model which includes local compliance of the contact region has calculated the time-dependent changes in relative motion of colliding bodies for a range of incident angles of obliquity, tan^?1[?V₁(0)/V₃(0)] where V₁(0)and V₃(0) are the incident tangential and normal relative velocities at the contact point, respectively. The paradox is shown to result from a negative relative acceleration of the contact points during an initial period of sliding – a negative acceleration that is inconsistent with the assumption of rigid-body contact.     

极坐标哈密顿体系约当型与弹性楔的佯谬解

讨论了极坐标弹性平面哈密顿体系的当型,并通过约当型的求解,直接给出了相关弹性楔体佯谬问题的解,从理论上阐明了经典弹性力学中某些佯谬问题的出现是由于其对应的是哈密顿体系中特殊的约当型解,同时也很自然地为该类问题提供了一个通用,有效的求解方法。     

Some passages to the limit in elasticity theory and “Sapondzhyan’s paradox”

We consider bending of thin plates with polygonal and curvilinear edges and indicate analogies and differences between the boundary conditions and boundary value problems arising in these two cases if the polygon is inscribed in the curvilinear contour and the number k of vertices of the polygon tends to infinity.We believe that the so-called Sapondzhyan paradox that arises when solving the boundary value problems for supported plates with a curvilinear contour and a k-gonal contour inscribed in it as k → ∞ can be called a paradox only by misunderstanding. Sapondzhyan’s paradox was studied in several papers briefly surveyed in the monograph [1]. Apparently, the interpretation of “paradoxes” and the results proposed in the present paper are published for the first time.Sapondzhyan’s paradox can be generalized to the case of bending of the so-called sliding-fixed plates (i.e., the generalized shear force and the rotation angle are zero on the plate contour) with a curvilinear contour and a k-gonal contour inscribed in it as k → ∞.In the case of three-dimensional elasticity problems, we present boundary conditions and boundary value problems similar to those listed above and consider the situations resulting in “paradoxes” similar to those arising in plate bending. We give the corresponding explanations and interpretations.     

The accuracy of some formulae for the interconversion of creep and stress-relaxation data

The accuracy of the approximation formulaeJ (t) ~ 1/G (t) andd lnJ (t)/d lnt ~ —d lnG (t)/d lnt, which interconnect stress-relaxation modulusG (t) and creep complianceJ (t) and their double logarithmic rates are investigated. For glassy polymers, the errors in the first formula are less than 1–2%, and in the second, they are generally in the order of a few percent, too. Similar estimates can also be found for the real parts of the analogous complex functionsJ ^* () andG ^* ().     

A new approach of predicting bifurcation points of elastic-plastic buckling of plates and shells

The paper proposes a new approach of predicting the bifurcation points of elastic-plastic buckling of plates and shells, which is obtained from the natural combination of the Lyaponov's dynamic criterion on stability and the modified adaptive Dynamic Relaxation (maDR) method developed recently by the authors. This new method can overcome the difficulties in the applications of the dynamic criterion. Numerical results show that the theoretically predicted bifurcation points are in very good agreement with the corresponding experimental ones. The paper also provides a new means for further research on the plastic buckling paradox of plates and shells.     

Solving Painlevé paradox: (P–R) sliding robot case

For a rigid body or a multibody system sliding on a rough surface, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. Painlevé paradox is the reason of a wide range of undesired bouncing motions which are observed during sliding. As Painlevé paradox is a practical problem in case of multibody systems, this research work has investigated that paradox. In this research work, the condition leading to Painlevé paradox has been determined for a general multibody system. Investigating the motion of a prismatic–revolute (P–R), sliding robot has been conducted. In order to solve the paradox and find the motion, a tangential impact is assumed at the contact point. The impact model has been developed and the paradox, consequently, has been solved. Consequently, the kinematics of the motion has been specified.     

Dissipation-induced instabilities and symmetry

The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox(1952),has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given(much earlier)by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.