无限均质弹性体中圆片裂纹受均布载荷时的超奇异积分方程封闭解

本文运用一种特殊技巧将一个受均布压力作用的圆片裂纹超奇异积分方程化为Ａｂｅｌ积分形式，从而可获得超奇异积分方程中未知位移间断的封闭解。再利用这个封闭解和应力强度因子的定义，得到了一个无限弹性体中受均布载荷分布时圆片裂纹前沿Ｉ型应力强度因子的精确表达式。所得到的结果与现有解完全相同。     

LOCAL BIFURCATION ANALYSIS OF STRONGLY NONLINEAR DUFFING SYSTEM

ＬＯＣＡＬＢＩＦＵＲＣＡＴＩＯＮＡＮＡＬＹＳＩＳＯＦＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＤＵＦＦＩＮＧＳＹＳＴＥＭＢｉＱｉｎｓｈｅｎｇ（毕勤胜）；ＣｈｅｎＹｕｓｈｕ（陈予恕）；ＷｕＺｈｉｑｉａｎｇ（吴志强）Ａｂｓｔｒａｃｔ：Ｂｙｕｓｉｎｇｃｏｏｒｄｉｎ...     

Analysis on Double Hopf Bifurcation Using Computer Algebra with the Aid of Multiple Scales

In this paper, a perturbation method based on multiple scales is used forcomputing the normal forms of nonlinear dynamical systems. The approach,without the application of center manifold theory, can be used to systematicallyfind the explicit normal form of a system described by a general n-dimensionaldifferential equation. The attention is focused on the dynamic behaviour ofa system near a critical point characterized by two pairs of purely imaginaryeigenvalues without resonance. The method can be easily formulated and implemented using a computer algebra system. Maple programs have been developedwhich can be `automatically' executed by a user without knowing computeralgebra. Examples chosen from mathematics, electrical circuits, mechanics andchemistry are presented to show the applicability of the technique and theconvenience of using computer algebra.     

多体动系统动力学方程在流形上的辛算法

多体系统动力学方程的数值方法一直是数学与力学家们的热门研 究课题.特别是多体系统动力学微分/代数方程组形式的数学模型，是所 谓的指标-3问题，它的求解是一个难题.目前流行的关于它的数值方法都 有不尽人意的地方，主要是对出现的所谓的违约问题和刚性问题未很好地 解决.多体系统动力学方程在流形上的辛算法是近几年出现的新的数值方 法，它将闭环型多体系统动力学的方程的约束部分和常微分方程部分利 用所谓的辛方法同时进行处理，其中的一些方法已证明是有效的，所以， 用它求解多体系统动力学方程前景看好.本文介绍了这些新的理论，并提 出了一些有待解决的问题.     

Shock reaction of hexane at 77, 193, and 273 K with special reference to shock pressure

Shock waves generated by projectile impacts were transmitted into hexane and the shocked hexane was analyzed by TCD-GC, FID-GC, GCMS, and FABMS for produced aliphatic hydrocarbons. The projectile length and its velocity were varied from 10 to 40 mm and from 220 to 1040 m/s, respectively. The initial temperature of the hexane was 77, 193 and 273 K. The major products detected throughout the reactions were hydrogen, light alkanes from C to C, and light alkenes from C to C. The minor products were heavy alkanes from C to C and soot-like materials. Experiments with varied projectile length revealed that the shock reaction occurred only while the shock wave was transmitted through hexane (about seconds). This short reaction time may be responsible for a lower yield of branched products in the shock reaction compared with yield produced by hexane pyrolysis in previous studies. In the shock reaction of hexane, the dehydrogenation was one of the important reactions and the recombination of hexyl radicals might play a role in the formation of -C. Experiments with varied initial temperature suggested that the molar yield of products depends not on the shock temperature but on the shock pressure, and that the reaction mechanisms for solid hexane and for liquid hexane are not identical. As the shock pressure increased, the relative yield of heavy products increased while that of light products decreased. This could be interpreted mainly by considering the activation volumes of the reaction involved. Received 12 September 1997 / Accepted 14 October 1997     

QUALITATIVE ANALYSIS OF SPHERICAL CAVITY NUCLEATION AND GROWTH FOR INCOMPRESSIBLE GENERALIZED VALANIS-LANDEL HYPERELASTIC MATERIALS

I. INTRODUCTION In practice, cavity formulation in materials is recognized as precursors to failure. Thus void nucleationand growth in solid materials have a great in?uence on failure mechanism. Gent and Lindley[1] have observed experimentally the phe…     

碳纤维板增强钢筋砼梁开裂性状试验研究

采用实验研究的方法，对碳纤维薄板增强钢筋混凝土三点弯曲缺口梁和无缺口梁的开裂性状及破坏规律进行探讨，分析其影响因子，研究结果表明：1)与无纤维板增强钢筋混凝土梁相比，碳纤维薄板增强钢筋混凝土三点弯曲梁的开裂性状和破坏模式更加复杂，开裂荷载和极限荷载提高，刚度增加；2)与无缺口梁相比，缺口梁的开裂性状大致相同，但开裂荷载和极限荷载都稍有下降，刚度增加；3)碳纤维薄板的粘贴长度对梁的开裂性状、开裂荷载、极限荷载和刚度有较大的影响；4)按照梁的不同的开裂性状，提出了相应的力学分析模型。     

三维含裂纹有限大体剪切型应力强度因子能量释放率方法的封闭解

本文利用能量释放率法,导出三维含裂纹有限大体剪切型应力强度因子的封闭解。这种方法非常节省机时,可获得大量K_Ⅱ和K_Ⅲ的有用结果,所得结果与现有少量结果基本吻合。     

跨地裂缝墙体开裂形态分析

应用非线性有限元法对跨地裂缝的墙体开裂形态进行了分析,确定出了具有三维活动性的地裂缝垂直穿越墙基时,墙体出现裂缝的位置、倾向、倾角和后期的发展状况,以及随沉降量与张开量比值变化的规律。结果表明:地裂缝垂直穿越围墙时,墙体上出现的裂缝一般有两种形式:一是位于地裂缝下盘的墙顶竖直裂缝,二是出现在地裂缝正上方墙体底部的斜裂缝;当地裂缝两盘的土体活动以水平拉张为主时,墙体底部出现的斜裂缝以高角度向上扩展,当地裂缝两盘的土体活动以差异沉降为主时,墙体底部出现的斜裂缝则以较缓的角度向上扩展,倾向与地裂缝相反;只要地裂缝的上下盘土体有微小的错动,一般2～3mm时,就会引起墙体的破裂,且墙体裂缝扩展迅速,几个毫米的错动量,就能使墙体裂缝扩展数十厘米,甚至贯通整个墙体;墙体斜裂缝在产生初期较为平直,随着裂缝的迅速扩展,端部稍向下弯曲,倾角减缓,整体呈弧弯状。     

Global dynamics of the cable under combined parametrical and external excitations

The chaotic dynamics and global bifurcations of the suspended elastic cable under combined parametric and external excitations are investigated. The non-linear equations of motion of the elastic cable to small vibration of one support are derived. The averaged equations are obtained by using the method of multiple scales. Based on the averaged equations, the theory of normal form and Maple program are used to obtain the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues. On the basis of the normal form, global bifurcation analysis of the parametrically and externally excited suspended elastic cable is given by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of the elastic cable is also found by numerical simulation.