有激发和衰减的有限长裂缝Ⅱ型破裂过程研究

本文考虑在Rayleigh阻尼作用时,沿裂缝长的边界上有剪应力作用,使裂缝一端失稳而产生快速扩展(即Ⅱ型破裂)问题.应用奇异摄动理论[1]及广义富氏级数,给出这个非线性断裂动力学问题的逐次逼近解.较之已有成果,本文考虑了非线性阻尼并给出各级近似解的显式.     

非线性双曲型守恒方程(组)的有限元分析

关于一阶线性双曲型方程有限元方法的计算格式及误差估计,G.A.Baker已在[1]中做过分析。本文将发展这个方法考察非线性守恒方程(双曲型)的初边值问题,得到了更一般的结论。这里对非线性项的处理类似于Axelsson在[2]中关于二阶拟线性抛物型方程混合问题所提出的方法。 对于非线性双曲型守恒方程组,在一定的条件下,也能得到这个结果,这样的条件在[3]或[4]中已讨论过。     

“超单元”法的误差估计

一、引言 关于平面弹性断裂问题,文献[1]指出采用普通的有限元方法。由于裂缝尖端处奇性的影响,其能量模误差只能得到h~(1/2)阶估计,不管采用多少次插值函数都不能改善其精度。因此用通常的有限元法计算弹性断裂问题,其精度是很差的,文献[2—3]通过在奇     

变系数迭代系统零解的稳定性

在文[1]中我们曾用分解理论研究了常系数线性迭代系统 (1) 零解的稳定性,这里,t_0≥0,k=0,1,2,…,对子系统所用的是二次型的函数。本文将研究变系数线性迭代系统 (2) 零解的稳定性问题,这里,τ∈I,我们仍用分解理论,但对子系统所作的函数为(|x|表示向量x的模)。当采用这种形式的函数时,运算可以大为简化,说明对处理线性迭代系统的稳定性问题时,用比用二次型的函     

线性V函数在变系数时滞系统中的应用

在文[7]的方法基础上，继续利用线性V函数研究时滞系统的稳定性．经过简洁的推导，给出了若干有效的充分性判据．     

不同材料拼接的半平面周期裂缝问题

在[1]中讨论了不同材料拼接平面裂缝中的数学问题,[2]中讨论了不同材料拼接的周期裂缝问题,在[3]中讨论了带周期裂缝的弹性长条基本问题。本文将讨论不同材料拼接的半平面周期裂缝问题,把问题化为某正则型的奇异积分方程,并采用分拆函数的方法,给出了周期直裂纹情况的封闭形式解,且导出了应力强度因子的公式。     

带裂缝的双周期平面弹性基本问题

求解带裂缝的双周期平面弹性基本问题,是路见可教授提出的。本文将路见可在[4]中讨论裂缝问题的第五章所采用的方法加以推广,把寻求复应力函数的问题归结为求解某种类型的奇异积分方程讨论了这种方程的可解性,从而解决了带双周期裂缝的无限弹性平面的第一和第二基本问题。我们限于讨论基本周期胞腔内仅含一条任意形状裂缝的情况。基本胞腔内含若干条裂缝时,复应力函数一般是多值的,可先把多值部份分出,完全类似地不难解决这种一般情况下的第一和第二基本问题。     

线性矩阵Hamilton系统振动性的区间判据

采用两种不同的方法,得到了线性矩阵Hamilton系统的振动性判据.这些振动性判据仅依赖于系数矩阵在[to,∞)的某些子区间上的性质,从而改进并推广了许多已知的Kamenev型振动准则.     

高烈度下双裂缝主控结构面危岩的断裂破坏机制分析

灰岩地区危岩具有典型类砌体结构特征,结构面发育复杂,其破坏本质是主控结构面在荷载作用下的断裂扩展失稳问题.基于地貌演化分析了灰岩地带陡崖复杂结构面形成与演化,获得了双裂缝主控结构面危岩的地质模型.构建了此类危岩的力学模型和断裂力学模型,按照最大周向应力准则,基于危岩自重、裂隙水压力及地震荷载作用,构建了双裂缝主控结构面危岩的断裂稳定系数表达式.通过案例分析验证了其合理性;各烈度对应的断裂稳定系数随贯通度增加而下降,基本地震烈度为Ⅷ度和Ⅸ度时,危岩处于不稳定状态;危岩稳定性受到主控结构面的裂隙贯通度与地震诱发的耦合作用影响,临界失稳贯通度随地震烈度的提高而降低;Ⅶ度地震的临界失稳贯通度理论值为25.8%,略小于贯通度实际值27.7%,略偏安全,其建立的断裂稳定系数表达式具有较好的适用性.研究结果可为推动此类危岩合理化防治提供重要的理论支撑.     

一类具有吸收边界条件的二阶非线性双曲方程的混合元法分析

1　引　　言关于二阶双曲型方程的有限元解的收敛性问题 ,目前已经有不少结果 .Dupont[1 ] 给出了一类线性双曲方程 Galerkin解的 L2 误差估计 ,Baker[2 ] 对此作了改进 ,用的是一种所谓“非标准的能量方法”.这一方法为 Cowsar,Dupont,Wheeler[3] 所采用 ,分析了一类具有吸收边界条件的线性双曲方程的混合元格式的 L2收敛性 .对于非线性双曲型问题 ,袁益让 ,王宏[4,5] 等给出了标准有限元方法的 H1 与 L2 误差估计 .本文试图把 [3]的工作更进一步研究 ,我们考虑如下非线性双曲问题 :φ(x) utt= mi,j=1 xi(aij(x) p(x,u) u xj) + mi=1…     

An investigation of the impact and penetration of solids of revolution into soft earth

The numerical method proposed earlier in [1] is developed to solve problems of the impact and penetration of rigid and deformable bodies of revolution into soft soil, which are described by Grigoryan's model [2]. The effect of the surface Coulomb friction, the bulk compressibility and the shear strength of soft soil on the forces of resistance and contact pressures in the contact zone is analysed. The results of numerical solutions of problems in a coherent formulation are compared with analytical relations and experimental data on the determination of the forces and coefficients of resistance to the penetration of impactors of different shapes into soft soil.     

An atomic interaction-based continuum model for computational multiscale contact mechanics

A computational multiscale contact mechanics model is presented which describes the interaction between deformable solids based on the interaction of individual atoms or molecules. The contact model is formulated in the framework of large deformation continuum mechanics and combines the approaches of molecular modelling [1] and continuum contact mechanics [2]. In the following a brief overview of the contact model is given. Further details can be found in [3], [4] and [5]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the computation of material forces in continuum‐atomistic modelling

Material forces govern the behavior and evolution of defects in solids. In elastic materials these forces which are associated with the Eshelby stress tensor are used to describe fracture sensitivities and can be employed to compute the J‐integral [2]. Since crack propagation begins with a variety of fundamental processes which occur within highly localized ultra–fine volume of material that constitute the fracture process zone surrounding a crack tip [3], the question of appropriate growth criteria, i.e. how far and in which direction a crack will glide under a certain loading condition is implied by the material force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

连续体力学中有限变形与转动的计算增量法

目前在非线性弹塑性力学计算中常用的经典非线性大变形理论由于内在的数学缺点,当变形量与转动很大时.往往误差达到不许可的程度.本文采用作者的有限变形力学理论表述了增量法.在作者与尚勇、谢和平联合研究的另二篇论文中,详细叙述这个新方法在工程中的应用,结果证明从微小变形过渡到大变形,计算结果总是可以满意地符合实验.     

Lur’e feedback systems with both unbounded control and observation: Well-posedness and stability using nonlinear semigroups

This paper is a complement of information to Grabowski and Callier (2006) [1]. A SISO Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static incremental sector type controller is considered. Well-posedness and a criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a novel nonlinear semigroup approach. A quadratic form Lyapunov functional is considered via a Lur’e type linear operator inequality. A sufficient strict circle criterion of solvability of the latter is found, using the solution of an operator Riccati equation by a novel self contained exposition, via reciprocal systems with bounded generating operators as recently studied and used by R.F. Curtain. The noncoercive case is finally considered using, in a novel way, LaSalle’s invariance principle.     

Fracture Mechanical Analysis of Cracks in Ice Shelves using the Finite Element Method and Configurational Forces

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

L p solutions of refinement equations

In the recent characterizations of the L_p solution of the refinement equation in terms of the “p-norm joint spectral radius,” there are problems in choosing the initial function for iteration [3, 23], or in addition, requiring stability of the refinable function [13, 17]. In this article we overcome these difficulties and give a more complete characterization of this nature. The criterion is constructive and can be implemented. It can be used to describe the regularity of the solution without assuming stability. This has significant advantages over the previous work. The corresponding results for vector refinement equations are also discussed.     

A numerical approach for the simulation of ductile fracture with embedded discontinuities

In the present study, a computational approach for the numerical simulation of ductile fracture within the framework of the finite element method is proposed. In the developed macroscopic formulation, the inelastic behavior in the bulk of the material is described by the finite elasto‐plastic material model proposed in [4]. The failure process is modeled by introducing discontinuities when a special local fracture criterion is satisfied. The discontinuities are incorporated via special triangular finite elements with embedded interfaces following the line of [2]. Finally, the numerical procedure is evaluated for a twodimensional representative test problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)