Some sufficient conditions for lower semicontinuity in SBD and applications to minimum problems

We provide some lower semicontinuity results in the space of special functions of bounded deformation for energies of the type and give some examples and applications to minimum problems, arising in Fracture Mechanics for linearly elastic materials. Copyright © 2011 John Wiley & Sons, Ltd.     

A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate

In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner’s principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given.     

页岩气藏压裂缝网扩展数值模拟

为探究页岩气藏水力压裂复杂裂缝网络的形成机理,开展了缝网扩展的数值模拟研究.考虑应力阴影和天然裂缝作用,建立了井筒和裂缝中流体流动模型,利用位移不连续方法求解应力与位移不连续量,然后构建了压力与裂缝宽度的迭代方程,并采用牛顿迭代法求解.通过比较数值解经典模型解析解,验证了模型和迭代解法的正确性.多簇裂缝同步扩展时裂缝间距越小,压裂液分配到各条裂缝越不均匀,靠近井筒跟部的裂缝的分流量越大,从而裂缝宽度越大;考虑天然裂缝作用时,逼近角越小或者应力各向异性越弱,水力裂缝越容易发生转向扩展,裂缝网络越复杂.      

绝热流Chaplygin气体的Riemann问题

本文研究了绝热流Chaplygin气体动力学方程组,利用特征分析方法,在得到所有基本波的基础上,构造出Riemann问题的所有解.Riemann解由前向疏散波(激波)、后向疏散波(激波)、接触间断以及δ波构成.     

On the Hochstadt–Lieberman Theorem for Discontinuous Boundary-valued Problems

In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.     

Numeric treatment of contact discontinuity with multi-gases

In this paper we work with a finite-volume-procedure for the computation of the one-dimensional Euler equations for the treatment of multi-gases and the problem of the correct treatment of the discontinuity was more nearly investigated. A suggested equation was embedded in the finite volumes context and implemented in our code accordingly and regarded as validated.     

一种守恒型间断跟踪法用于处理一维Euler方程组中的若干问题

1引言间断跟踪法(front-tracking)是数值求解双曲型守恒型方程(组)的一种重要的数值方法,其主要特点是把间断作为移动的内边界来处理,光滑区域中的数值解用计算光滑解有效的数值方法来求解,而间断的移动和间断两侧的数值解的修正要满足Rankine-Hugoniot条件．我们称这样的跟踪法为传统的间断跟踪法(见[3],[14])．本文的第二作者多年来研究设计了一种基于解的守恒性质的间断跟踪法(见[11],[12]),其最主要的特点是以解的守恒性作为跟踪的机制,而不是象传统的间断跟踪法那样利用     

A Theorem on Discrete,Torsion Free Subgroups of Isom H <Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Let H ⁿ be the hyperbolic n-space with n⩾ 2. Suppose that Γ H ⁿ is a discrete, torsion free subgroup and a is a point in the domain of discontinuity Ω (Γ). Let p be the projection map from H ⁿ to the quotient manifold M=H ⁿ/Γ. In this paper we prove that there exists an open neighborhood U of a in H ⁿ∪ Ω (Γ) such that p is an isometry on U∩ H ⁿ.Mathematics Subject Classification (2000). primary: 51M10; secondary: 22E40, 57M50.     

Bifurcation of Equilibria in a Class of Planar Piecewise Smooth Systems with 3 Parameters

The goal of this paper is to investigate the bifurcation properties of stationary points of a class of planar piecewise smooth systems with 3 parameters using the theory of differential inclusions. We especially study the existence of the stationary points on the line of discontinuity of this kind of planar piecewise smooth system.