A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead of the finite element method is used to perform lower bound limit and shakedown analysis of structures. The self-equilibrium stress fields are constructed by a linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains and obtained through elastic-plastic incremental analysis. The complex method is used to solve nonlinear programming and determine the maximal load amplifier. The limit analysis is treated as a special case of shakedown analysis in which only the proportional loading is considered. The numerical results show that SGBEM is efficient and accurate for solving limit and shakedown analysis problems. Project supported by the National Natural Science Foundation of China (No. 19902007), the National Foundation for Excellent Doctorial Dissertation of China (No. 200025) and the Basic Research Foundation of Tsinghua University.     

轴对称结构极限下限分析的自然单元法

作为一种基于自然邻近插值的新型无网格法,自然单元法克服了大多数无网格法难以施加本质边界条件的困难．将自然单元法与减缩基技术相结合,建立了一种轴对称结构极限下限分析的数值格式和求解算法．通过不断修正自平衡应力场,轴对称结构极限下限分析可转化为一系列的非线性数学规划子问题,并由复合形法求解．在每个非线性规划子问题中,自平衡应力场表示为一组带有待定系数的自平衡应力场基矢量的线性组合,并且这些自平衡应力场基矢量可由弹塑性增量分析的平衡迭代结果得到．算例结果表明,本文所提的轴对称结构极限下限分析方法行之有效．     

极限下限分析的正交基无单元Galerkin法

基于极限分析的下限定理，建立了用正交基无单元Galerkin法进行理想弹塑性结构极 限分析的整套求解算法．下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接 得到，所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模 拟．这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到．通过对自平衡应力场 子空间的不断修正，整个问题的求解将化为一系列非线性数学规划子问题，并通过复合形法 进行求解．算例表明该方法有效地克服了维数障碍问题，使计算效率得到了充分的提高，是 切实可行的．     

弹塑性结构安定下限分析的无网格局部

将基于Voronoi结构的无网格局部Petrov-Galerkin法与减缩基技术相结合,建立了一种安定下限分析的新方法．为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻近插值构造试函数.通过引入基准载荷域上载荷角点的概念,消除了安定下限分析中由时间参数所引起的求解困难．利用减缩基技术,将安定分析问题化为一系列未知变量较少的非线性规划子问题．在每个非线性规划子问题中,自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,而这些自平衡应力场基矢量可应用弹塑性增量分析中的平衡迭代结果得到．算例结果证明了提出的分析方法的有效性．      

结构安定分析的Galerkin边界元方法

基于Melan静力安定定理,利用Galerkin边界元方法建立了多组交变载荷作用下结构安定分析的下限计算格式.在给定载荷域的载荷角点所对应载荷作用下,采用Galerkin边界元法计算相应的虚拟弹性应力场,并且利用结构在Galerkin边界元弹塑性增量计算中同一增量步中不同迭代步之间的应力差作为自平衡应力场的基矢量,通过这些基矢量的线性组合构造了自平衡应力场,大大降低了所形成的数学规划问题的未知变量数.并通过复合形法对非线性规划问题直接进行求解,得到了结构在交变载荷作用下的下限安定乘子.计算结果表明,所采用的方法具有较高的精度和计算效率.     

Lower bound shakedown analysis by the symmetric Galerkin boundary element method

In this paper, the static shakedown theorem is reformulated making use of the symmetric Galerkin boundary element method (SGBEM) rather than of finite element method. Based on the classical Melan’s theorem, a numerical solution procedure is presented for shakedown analysis of structures made of elastic-perfectly plastic material. The self-equilibrium stress field is constructed by linear combination of several basis self-equilibrium stress fields with parameters to be determined. These basis self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains obtained through elastic–plastic incremental analysis. The lower bound of shakedown load is obtained via a non-linear mathematical programming problem solved by the Complex method. Numerical examples show that it is feasible and efficient to solve the problems of shakedown analysis by using the SGBEM.     

下限原理在岩土工程中的应用

采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合，把整个结构离散化，设定每个结点的应力，把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数，以结点应力为优化变量，以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题，得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场，解决了三维可静应力场的构造问题。算例分析表明，本文的方法是正确、可行的。     

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

In this paper, an adaptive boundary element method (BEM) is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method (FMM) and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element (RVE) for short fiber-reinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.The project supported by the National Natural Science Foundation of China (10472051).The English text was polished by Yunming Chen.     

Evolution of a 2-D disturbance in a supersonic boundary layer and the generation of shocklets

Through direct numerical simulation, the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated. At a chosen location, a small amplitude T-S wave was fed into the boundary layer to investigate its evolution. Characteristics of nonlinear evolution have been found. Two methods were applied for the detection of shocklets, and it was found that when the amplitude of the disturbance reached a certain value, shocklets would be generated, which should be taken into consideration when nonlinear theory of hydrodynamic stability for compressible flows is to be established.     

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media. The project supported by the Basic Research Foundation of Tsinghua University, the National Foundation for Excellent Doctoral Thesis (200025) and the National Natural Science Foundation of China (19902007). The English text was polished by Keren Wang.     

STREAMLINE-BASED MATHEMATICAL MODEL FOR CO2 MISCIBLE FLOODING

According to the research theory of improved black oil simulator, a practical mathematical model for C02 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening andmiscible oil field.reservoir dynamic management of the CO2 miscible oil field.     

基于正交基无单元Galerkin法和非线性规划的安定分析方法

基于安定分析的下限定理,用正交基无单元Galerkin法建立了交交载荷作用下理想弹塑性结构安定分析的下限计算格式.在给定载荷域的载荷角点所对应的载荷作用下,采用正交基无单元Galerkin法计算相应的虚拟弹性应力场.并且利用结构在正交基无单元Galerkin法弹塑性增量分析中平衡迭代结果计算得到自平衡应力场基矢量,然后由这些基矢量的线性组合模拟自平街应力场.安定分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题,通过复合形法求解.算例表明该方法的计算结果是令人满意的,并且对初始复合形顶点和用于构造自平衡应力场基矢量的载荷增量是非常不敏感的.     

Structure of nonnegative nontrivial and positive solutions of singularly perturbed p -laplace equations

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small. Foundation items: the National Key Basic Research Development Project Program of China (1999032801); the National Natural Science Foundation of China (10371095) Biography: ZHANG Zheng-ce (1976≈)     

极限分析的弹性补偿法及其应用

有限元法与数学规划法相结合，应用极限上、下限定理，将极限分析归结为求解最优化问题，是目前被普遍应用的极限分析方法，但是该方法受到计算能力的限制，难以应用到实际工程问题中。鉴于此，本文介绍一种基于线弹性分析基础上的简单的求解复杂结构极限栽荷下限、上限的方法——弹性补偿法，同时结合三维有限元分析，求解内压下三通结构的极限载荷。通过与弹塑性分析结果比较发现，简单的弹性补偿法能够很好的评估复杂三雏结构的塑性承载能力。     

BEM for simulation of a 2D elastic body with randomly distributed circular inclusions

Based on our 2D BEM software THBEM2 which can be applied to the simulation of an elastic body with randomly distributed identical circular holes, a scheme of BEM for the simulation of elastic bodies with randomly distributed circular inclusions is proposed. The numerical examples given show that the boundary element method is more accurate and more effective than the finite element method for such a problem. The scheme presented can also be successfully used to estimate the effective elastic properties of composite materials. Project supported by the National Natural Science Foundation of China (No. 19772025).     

A class of nonlinear boundary value problems for the second-order<Emphasis Type="Italic">E</Emphasis><Subscript>2</Subscript> class elliptic systems in general form

A class of nonlinear boundary value problems (BVP) for the second-order E₂ class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods. Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030, 01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014) Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−)     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)     

含缺陷结构的塑性极限分析

结合极限分析中的数学规划理论和有限元技术,提出了三维含结构极限分析的数学规划方法,并采用罚函数法引入塑性不可压条件,对于考虑多组独立变化载荷作用的情况,提出了加载路径射线辐射求解方案,并基于这种射线射状的加载路径,推导了多组载荷联合作用下结构塑性极限上限分析的数学规划格式,编制了相应的有限元程序,文中的数值了该方法的正确性与有效性。     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.