弹性力学的杂交自然单元法

为了解决自然单元法无法直接求解节点应力以及应力解精度不高的问题, 将应力杂交的思想引入自然单元法中, 与弹性问题的Hellinger-Reissner变分原理结合, 提出了弹性问题的杂交自然单元法. 算例表明: 杂交自然单元法的计算结果与解析解吻合, 证明该方法是可行的; 在求解应力方面, 杂交自然单元法比自然单元法有着更高的计算精度, 而且可以直接求解出节点的应力.     

直接增强自然单元法计算应力强度因子

自然单元法是一种新兴的无网格数值计算方法,但应用于裂纹问题计算时,其近似函数并不能准确反映裂纹尖端渐进应力场的奇异性,为获得足够的计算精度,需要在缝尖附近增大结点的布置密度。针对裂纹问题提出一种增强的自然单元法,将缝尖渐近位移场函数嵌入到自然单元法近似函数中,给出了增强试函数的构造方法,推导了总体刚度矩阵和荷载列阵的相关列式。应力强度因子可以作为附加未知量直接算得,也可用J积分或相互作用能量积分方法进行计算,对增强区域的选择和影响进行了分析。算例结果表明,基于增强自然单元法采用围线积分方法计算应力强度因子具有很高的精度,但直接以附加结点自由度形式计算则精度有所降低。     

扩展有限元裂尖场精度研究

论述了扩展有限元方法和基本原理,研究了单元类型(四边形单元和三角形单元、线性单元和二次单元)、网格密度、J积分区域半径等因素对裂尖局部应力场(应力强度因子)计算精度的影响。研究发现,上述因素对裂尖应力强度因子计算的收敛速度与稳定性影响不大,证实了XFEM可以用较少的节点获得较高的裂尖场精度,并提出了通过固定裂尖附加区半径可以进一步改善XFEM的收敛速度。     

二节点变轴力平面梁柱单元

为了考虑平面梁柱构件在变化轴向荷载作用下的P-Δ效应,本文采用二节点平面梁柱单元,根据最小势能原理推导了单元的初应力刚度矩阵,并分别阐述了应用该单元求解结构临界荷载因子及迭代计算荷载-位移反应的方法。通过两个简单算例验证,该单元比常规的二节点常轴力梁柱单元更有效、精度更高。     

基于应力比值法的V形切口应力强度因子分析

本文基于有限元分析技术建立了一种应力比值方法,用于计算V形切口的应力强度因子。该方法不需要在V形切口尖端采用反映应力奇异性的奇异单元。求解时,首先给定参考问题的广义应力强度因子,然后利用待求问题的应力值与参考问题的应力值之间的比值来求解待求问题的广义应力强度因子。算例采用切口尖端应力方法分析了平板的V形切口问题。计算结果表明,该方法计算精度较高,能够方便地用于求解相关的工程问题。     

一种新的弹塑性杂交应力元法

本文基于一个改进的弹塑性的Hellinger/Reis■ner 混合变分原理构造了一种用于解弹塑性问题的四节点等参杂交应力元.新的模型中,在单元内增加了等效应力增量、塑性等效应变增量及不协调位移变量,从而使单元内的屈服准则及流动法则平均得到满足,不协调位移改进了单元应力精度.计算表明,新的模型可以提高弹塑性杂交法的精度和计算效率.     

弹性力学问题的一阶有限元解法

求解弹性力学问题的应力时,如果采用常规的位移有限元法,需要先求得单元的节点位移,再经过求导运算得到。为了解决这种求解方式引起的应力精度下降的问题,提出了弹性力学问题的一阶多变量形式,使得应力与位移精度同阶,并推导了弱形式。采用有限元方法,对弹性力学问题给出了一阶解法的二维、三维数值算例,并且将一阶解法的结果与常规位移有限元法的解进行了比较。数值计算结果表明,一阶解法有效提高了应力的精度,并且应力的误差和节点位移的误差具有相同的收敛阶,验证了本文方法的有效性,为提高有限元法的应力精度提供了新的思路。     

一种新的计算各向异性材料裂纹尖端应力强度因子杂交元法

利用有限元特征分析法研究了平面各向异性材料裂纹端部的奇性应力指数以及应力场和位移场的角分布函数,以此构造了一个新的裂纹尖端单元。文中利用该单元建立了研究裂纹尖端奇性场的杂交应力模型,并结合Hellinger-Reissner变分原理导出应力杂交元方程,建立了求解平面各向异性材料裂纹尖端问题的杂交元计算模型。与四节点单元相结合,由此提出了一种新的求解应力强度因子的杂交元法。最后给出了在平面应力和平面应变下求解裂纹尖端奇性场的算例。算例表明,本文所述方法不仅精度高,而且适应性强。     

复杂裂纹问题的多边形数值流形方法求解

数值流形方法是一种能统一处理连续和不连续问题的有效数值方法。该方法采用的数学覆盖系统可完全独立于物理域,能很好地求解各类裂纹问题,而n边形单元（n>4）则具有网格划分灵活,求解精度高等优点。本文基于数值流形方法,采用正六边形数学单元求解线弹性复杂裂纹问题。在导出相关方程的基础上对典型裂纹问题进行了分析,通过互能积分法得到了裂尖的应力强度因子,计算结果与参考解吻合得较好。除此之外,文中还对不同单元上的求解精度进行了比较,结果表明采用正六边形单元的求解精度较正四边形单元和正三角形单元上的精度均更高。     

悬索桥线形分析的悬链线单元法

从悬链线方程出发,以节点坐标和无应力索长作为未知量,推导了增量型索单元的刚度方程,提出了悬索桥在恒载作用下初始线形和无应力索长的计算公式及基于Newton-Raphson的求解方法.算例分析表明本文方法具有较高的精度.     

一种基于直接计算高阶奇异积分的断裂力学双边界积分方程分析法

相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.      

汶川地震诱发文家沟巨型滑坡 碎屑流基本特征及成因机制初步分析


2008年5月12日,汶川M80地震在四川省绵竹市清平乡文家沟内诱发一巨型滑坡。通过现场调查得知,滑坡前后缘高差455m,厚度20～30m,滑面为基岩层面,初始方量2750×107m3。滑体在运动中转化为碎屑流。滑坡-碎屑流总的水平运动距离为4022m,垂直运动距离为1443m,遗留的堆积物体积达5×107m3。滑坡距映秀—北川断裂仅36km,位于其下盘,地震烈度达XI度。滑坡导致文家沟中48人遇害,并形成一条完整的地震次生地质灾害链。初步分析表明滑坡启动速度快,滑坡向碎屑流转化过程明显、地点明确。碎屑流运动过程复杂,伴有强烈的“气垫效应”和“前缘气浪冲击效应”。作者认为,文家沟滑坡的高启动速度是长持时强烈地震动作用的结果,与山体的猛烈碰撞是导致滑体解体并转化为碎屑流的原因。     

Preface: Orbits around asteroid

One of the core issues in modern celestial mechanics is the orbital dynamics in the near-regime gravitational field of as- teroids, which provides deep insights into the mathematical nature of a class of nonlinear systems, and plays as a critical basis for in situ explorations of different science goals. Lots of efforts have been made to reveal the characteristics of orbital motion in the vicinity of asteroids, and to improve the skills of asteroid research in methodology.     

Effet de l'anisotropie élastique cristalline sur la distribution des facteurs de Schmid à la surface des polycristauxInfluence of crystalline elasticity anisotropy on Schmid factor distribution at the free surface of polycrystals

Experimental studies of the plasticity mechanisms of polycrystals are usually based on the Schmid factor distribution supposing crystalline elasticity isotropy. A numerical evaluation of the effect of crystalline elasticity anisotropy on the apparent Schmid factor distribution at the free surface of polycrystals is presented. Cubic elasticity is considered. Order II stresses (averaged on all grains with the same crystallographic orientation) as well as variations between averages computed on grains with the same crystallographic orientation but with different neighbour grains are computed. The Finite Element Method is used. Commonly studied metals presenting an increasing anisotropy degree are considered (aluminium, nickel, austenite, copper). Concerning order II stresses in strongly anisotropic metals, the apparent Schmid factor distribution is drifted towards small Schmid factor values (the maximum Schmid factor is equal to 0.43 instead of 0.5) and the slip activation order between characteristic orientations of the crystallographic standard triangle is modified. The computed square deviations of the stresses averaged on grains with the same crystallographic orientation but with different neighbour grains are a bit higher than the second order ones (inter-orientation scatter). Our numerical evaluations agree quantitatively with several observations and measures of the literature concerning stress and strain distribution in copper and austenite polycrystals submitted to low amplitude loadings. Hopefully, the given apparent Schmid factor distributions could help to better understand the observations of the plasticity mechanisms taking place at the free surface of polycrystals. To cite this article: M. Sauzay, C. R. Mecanique 334 (2006).     

Nonlinear behavior of matrix-inclusion composites under high confining pressure: application to concrete and mortar

This paper is devoted to a micromechanics-based simulation of the response of concrete to hydrostatic and oedometric compressions. Concrete is described as a composite made up of a cement matrix in which rigid inclusions are embedded. The focus is put on the role of the interface between matrix and inclusion which represent the interfacial transition zone (ITZ). A plastic behavior is considered for both the matrix and the interfaces. The effective response of the composite is derived from the modified secant method adapted to the situation of imperfect interfaces. To cite this article: T.H. Le et al., C. R. Mecanique 336 (2008).     

Dynamics and Breakup of Viscoelastic Liquids (A Review)

The phenomena of hydrodynamic breakup of liquid jets, drops, films, bridges, and filaments are reviewed for liquids with viscoelastic properties. The reasons for breakup are capillary instabilities, collisions with rigid obstacles, and other forms of dynamic action. The relationship between the properties of the liquids and the features of the breakup process is discussed.     

Flow stability analysis and excitation using pulsating jets

Classical flow stability applied to transition from laminar to turbulent flow may also describe the behavior of vorticity fluctuations created by a pulsating jet placed along a solid boundary. A numerical laminar flow experiment involving a pulsating jet placed along the surface of a duct with flow separation downstream, resulted in eliminating most part of the separated flow region. Applying the same approach to a turbulent flow, it was possible to develop a turbulent stability flow formulation and apply successfully turbulent pulsating jet flow separation control. To cite this article: D. Skamnakis, K. Papailiou, C. R. Mecanique 333 (2005).