SINGULAR PERTURBATION OF NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we consider the boundary value problem where ε.μ are two positive parameters. Under f_y≤-k<0 and other suitable restrictions, there exists a solution and it satisfied where y_(0,0)(x) is solution of reduced problem while y_i-j,j(x)(j=0,1,...,i;i=1,2,...,m) can be obtained successively from certain linear equations.     

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper,a new analytical method of symplectic system.Hamiltonian system,is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain.In the system,the fundamental problem is reduced to all eigenvalue and eigensolution problem.The solution and boundary conditions call be expanded by eigensolutions using ad.ioint relationships of the symplectic ortho-normalization between the eigensolutions.A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space.The results show that fundamental flows can be described by zero eigenvalue eigensolutions,and local effects by nonzero eigenvalue eigensolutions.Numerical examples give various flows in a rectangular domain and show effectivenees of the method for solving a variety of problems.Meanwhile.the method can be used in solving other problems.     

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.     

NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES

The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.     

复合材料层板的抗贯穿机理与模拟研究

为了研究树脂基纤维增强复合材料层板的抗侵彻贯穿机理和动态力学行为与抗侵彻毁伤的关系, 通过球形破片模拟弹贯穿实验表征了复合材料层板抗高速侵彻的吸能特性;通过高速摄影技术分析了层板 贯穿过程的瞬态变形失效特点;采用CT扫描成像及SEM 电镜分析等手段研究了复合材料层板的抗贯穿破 坏耗能模式。实验结果显示,高速冲击下层板抗贯穿吸能与入射速度成正比;高速侵彻过程是复合材料层板 高应变率变形的动态过程,高应变率动态力学行为对复合层板抗贯穿吸能特性影响显著;冲击波在层板中的 传播特性决定了不同破坏模式阶段的划分以及损伤区域的范围。基于复合层板高速贯穿下的动力学瞬态分 析,建立了复合层板抗高速侵彻吸能的两阶段动态破坏模型,模型计算值与实验值符合良好。研究结果表明, 应变率效应与惯性效应在复合材料层板抗侵彻性能分析中是不可忽视的2个关键因素。     

复合材料层板边缘效应的准相似元解法

用准相似单元法研究了复合材料层板直边和孔边的自由边缘效应，得到了一些具有工程意义的结果。准相似单元法是相似单元法的推广，利用这一方法可以求解三维的应力集中问题，避免了求单刚时的重复计算。由于采用了按相似层求解的技术，应用准相似单元法求解应力集中问题时对计算机容量的要求大为降低     

基于对偶变量变分原理的完整约束系统保辛算法

基于对偶变量变分原理,选择积分区间两端位移为独立变量,构造了求解完整约束哈密顿动力系统的高阶保辛算法。首先,利用拉格朗日多项式对作用量中的位移、动量及拉格朗日乘子进行近似;然后,对作用量中不包含约束的积分项采用Gauss积分近似,对作用量中包含约束的积分项采用Lobatto积分近似,从而得到近似作用量;最后,在此近似作用量的基础上,利用对偶变量变分原理,将求解完整约束哈密顿动力系统问题转化为一组非线性方程组的求解。算法具有保辛性和高阶收敛性,能够在位移的插值点处高精度地满足完整约束。算法的收敛阶数及数值性质通过数值算例验证。     

基于对偶变量变分原理和两端位移独立变量的保辛方法

将广义位移和动量同时用拉格朗日多项式近似,并选择积分区间两端位移为独立变量,然后基于对偶变量变分原理导出了哈密顿系统的离散正则变换和对应的数值积分保辛算法。当位移和动量的拉格朗日多项式近似阶数满足一定条件时,可以自然导出保辛算法的不动点格式。通过数值算例分析了位移和动量采用不同阶次插值所需最少Gauss积分点个数,并讨论了位移插值阶数、动量插值阶数以及Gauss积分点个数对保辛算法精度的影响,说明了上述不动点格式恰好是一种最优格式。     

微裂纹损伤对复合材料层板分层的影响

本文将双标量损伤模型推广,考虑层内及层间微裂纹损伤相互作用,建立了层合复合材料的多标量损伤本构关系,并将该本构关系应用于含贯穿分层层板的后屈曲分析,采用准三维有限元法研究了分层尖端场与极限损伤区演变的特点,结果表明：损伤导致裂尖区层间应力奇异性消失,引起层间应力重新分布;损伤区的发展方向取决于分层上下表面层的铺设角,能量释放率不能反映损伤和分层扩展特征,因而有必要建立基于损伤演化的分层扩展准则。     

3-D numerical study on the bending of symmetric composite laminates

３－ＤＮＵＭＥＲＩＣＡＬＳＴＵＤＹＯＮＴＨＥＢＥＮＤＩＮＧＯＦＳＹＭＭＥＴＲＩＣＣＯＭＰＯＳＩＴＥＬＡＭＩＮＡＴＥＳＣｈｉｅｎＷｅｉ－ｚａｎｇ（钱伟长）;ＨｕａｎｇＱｉａｎ（黄默）;ＦｅｎｇＷｅｉ（冯伟）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｔｙｏｆＴｅｃ...     

Edge effect in a fibrous composite with near-surface fibers subjected to uniform loading

The decay rate of the edge effect in a material reinforced with fibers of square cross-section and subjected to transverse uniaxial deformation is studied. The case of uniform loading of near-surface fibers is considered. The edge effect is analyzed by numerically solving a boundary-value problem of elasticity for inhomogeneous bodies and applying a quantitative decay criterion for normal stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 15–23, November 2007.     

Influence of a thin isotropic coating on the edge effect zone in isotropic and transversely isotropic materials

The effect of a thin isotropic coating on the edge effect zone in a representative element of a coated material is examined. Isotropic and transversely isotropic materials are considered. The transversely isotropic material has the elastic properties of unidirectional glass-fiber-reinforced plastic. The decay of the edge effect in the directions perpendicular to the coating plane and to the plane of isotropy is studied. A boundary-value problem of elasticity for piecewise-homogeneouse orthotropic bodies and a quantitative edge effect decay criterion for normal stresses are used as a design model. The problem is solved using the finite-difference method and base schemes. The results of evaluation of the edge effect zone in homogeneous and inhomogeneous materials are presented. It is shown that the presence of a thin isotropic coating blocks the edge effect, that is, decreases the edge effect zone in both isotropic and transversely isotropic materials __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 61–67, December 2007.     

基于能量变分法的钢底板波形钢腹板组合箱梁畸变效应分析

为合理分析钢底板波形钢腹板梯形箱梁的畸变效应,按各板件面内外抗弯刚度不变的原则将全截面等效为钢材,利用圣维南原理考虑顶底板对波形钢腹板的约束作用,修正畸变扇性坐标分布模式,基于能量变分法建立畸变控制微分方程。与已有文献及有限元进行对比分析,并研究腹板俯角和波形钢腹板厚度变化对畸变翘曲正应力的影响。结果表明,本文解析解与文献解及ANSYS解均吻合较好;基于圣维南原理修正后的扇形坐标分布模式更合理;利用本文等效方法亦可分析传统波形钢腹板组合箱梁的畸变效应;腹板俯角的设置有利于减小畸变翘曲正应力;波形钢腹板厚度变化对腹板与底板交接处的畸变翘曲正应力影响显著。     

Influence of Young's Moduli of a Laminated Composite with a Periodic System of Cracks on Edge Effects

A problem on edge effects in a laminated composite with a periodic system of symmetric contact cracks is studied. Loading of the composite induces constant deformation in the reinforcement direction beyond the edge effect. The problem is solved in an exact formulation under the linear theory of elasticity for piecewise-homogeneous media. An approximate solution is found by the mesh approach using the concept of a base scheme. For stresses _ij , the shape and size of the edge effect zone are studied depending on the ratio of Young's moduli of the composite components, which varies over a wide range     

基于卷积非粘滞阻尼模型的超高层结构风效应分析

有限元方法中相对于对结构质量与刚度特性的描述,结构阻尼的描述仍具有较大的模糊性。随着新型建筑材料与复杂结构体系的发展,以及对计算机模拟要求的提高,阻尼作用的机理与相应阻尼模型的研究成为值得关注的问题。基于一种阻尼力与质点速度历程相关的卷积非粘滞阻尼模型,采用微分求积求解算法,对一个大型复杂超高层建筑结构的风振响应进行了分析,并与常用的比例粘滞阻尼模型进行了对比。对卷积非粘滞阻尼力模型系统的响应特征进行了分析,特别是该模型的松弛效应对结构响应的影响。另外,作为将这种新阻尼模型应用于实际工程的一次探索,本文采用微分求积算法,建立了一套可将该阻尼模型及其求解算法嵌入通用有限元软件的求解系统,可用于复杂结构的动力响应分析。     

Application of dual kriging to structural shape optimization based on the boundary contour method

Summary The paper presents an approach in which the coupling of dual kriging and the boundary contour method (BCM) is applied to structural shape optimization problems in mechanical engineering design. The problems consist of optimizing the shape of an elastic body, which requires minimizing an objective function subject to some given constraints, such as those of displacement, stress or manufacturing. The originality of the present work is involved with the use of two novel methods that are combined here to solve structural shape optimization problems. The first one, called dual kriging, is a general, versatile interpolation and geometric modeling tool. The second one is a new variant of the boundary element method (BEM), called the BCM, which achieves a further reduction in dimensionality of analysis problems. Based on the advantages of these two methods, the coupling approach presented here is expected to offer an effective as well as a straightforward manner for solving shape optimal design problems. Received 18 December 1997; accepted for publication 21 April 1998     

钢桁腹式混凝土组合箱梁的扭转效应分析

结合钢桁腹式混凝土组合箱梁的结构特点,基于薄壁箱梁扭转理论,推导出组合箱梁闭口断面的混凝土顶底板和换算钢腹板的扭转翘曲应力表达式,进而推导出组合箱梁约束扭转控制微分方程;利用初参数法求解微分方程,并分析出翘曲双力矩以及扭转翘曲正应力随梁跨的变化规律.通过有限元模拟分析,将有限元值和理论值进行比较,结果吻合良好.研究表明...     

Similarity solutions of vertical plane wall plume based on finite analytic method

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.     

Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures

The first-order shear deformation moderate rotation shell theory of Schmidt and Reddy [R. Schmidt and J. N. Reddy, J. Appl. Mech. 55, 611–617 (1988)] is used as a basis for the development of finite element models for the analysis of the static, geometrically non-linear response of anisotropic and laminated structures. The incremental, total Lagrangian formulation of the theory is developed, and numerical solutions are obtained by using the isoparametric Lagrangian 9-node and Serendipity 8-node shell finite elements. Various integration schemes (full, selective reduced, and uniformly reduced integration) are applied in order to detect and to overcome the effects of shear and membrane locking on the predicted structural response. A number of sample problems of isotropic, orthotropic, and multi-layered structures are presented to show the accuracy of the present theory. The von Kármán-type first-order shear deformation shell theory and continuum 2D theory are used for comparative analyses.     

惯导系统火箭撬试验数据处理方法

惯导系统火箭橇试验技术在国内还属于一门新兴的试验技术,刚处于起步探索阶段。惯导系统火箭橇试验是验证惯导系统在复合环境下的误差模型、评定制导系统误差模型精度以及分离大过载条件下惯导系统误差系数的有效手段。主要探讨了惯导系统的误差模型,提出了基于火箭橇试验的动态条件下的误差分离和数据处理方案,并对火箭橇试验中数据处理方法进行了分析。这些研究为在我国进一步开展惯性装置火箭橇试验研究提供理论基础。