阻尼介质中简支圆板在大挠度时的塑性动力响应

本文从理论上分析了受矩形脉冲荷载作用的阻尼介质中简支理想刚塑性圆板在大挠度时的塑性动力响应.文中给出了在中载和高载情况下各相的解析解.     

动态环板元的动刚度矩阵

本文对于环形薄板单元取包含贝塞尔函数的谐振变形作为形状函数,解决了关于特殊函数的复杂积分问题.从而精确推导了环形单元的动刚度矩阵,并用直接刚度法进行了校核.接着,又着重于将封闭形式的动刚度矩阵,按频率平方的升幂式展开,得到了简洁完备的结果,以此作为结构动力特性分析和响应计算的基础.     

作旋转流动时非线性流体的改进模型

在圆环结构中研究拟塑性流体作圆形的Couette流动.流体的粘度依赖于对守恒方程有直接影响的剪切率,守恒方程采用谱方法求解.可以证明所采用的拟塑性模型,可以被适当地表示为典型的非线性流动.在早期研究中,为了方便数值计算,粘度表达式中只考虑了剪切率的二次项,与此不同,这里考虑了二次幂项.圆形Couette流动中弯曲的流线,造成离心的不稳定性,引起环形的漩涡,称之为Taylor漩涡.进而发现,随着拟塑性影响的增加,临界Taylor数下降.与已有圆形Couette流动的实验相比较,两者有着良好的一致性.     

样条状态变量法分析弹性矩形板的动力响应

应用样条元与状态空间法分析矩形板的动力响应问题.对空间域采用样条元法,对时间域采用现代控制论中的状态空间法.建立了状态变量递推格式,可直接计算结构的动力响应量.文末给出了若干数值算例,计算结果表明,该方法的计算精度与效率是令人满意的.     

晶体塑性理论的极值原理

本文基于晶体塑性增量理论,讨论了给定应力率或给定应变率的情况下,滑移剪切率的确定方法;提出了相应的多变量函数的极值原理;把问题归结为二次凸规划问题. 对于晶体在外力作用下塑性响应问题,本文提出了两个新的与边值问题等价的极值原理.在这些极值原理中,滑移剪切率将作为独立宗量,通过变分方程求得.     

平台—群柱基础对浪流冲击的动力反应分析

本文研究平台-群柱基础系统对浪流冲击的动力反应分析.文中考虑了群柱基础与水流和地基土的动力相互作用,由解析法给出了系统对浪流力激励的动力响应分析,给出了算例的位移响应结果,并讨论了系统参数对动力特性的影响.     

粘塑性动力学问题的最优控制变分原理与有限元分析

本文运用最优控制变分理论,对Perzyna型粘塑性体,提出了粘塑性动力问题的参数变分原理,并给出了相应的动力有限元方程和参数二次解法.     

基于可靠性的工程结构动力响应优化设计

在考虑结构物理参数和作用荷栽同时具有随机性的情况下,建立了具有动应力、动位移可靠性约束和设计变量上下限约束的工程结构优化设计数学模型;分别对结构动力响应的数字特征和基于可靠性的结构动力响应的灵敏度进行了推导.利用内罚函数法求解.算例表明文中构建的优化模型和提出的求解方法是合理与可行的.     

常曲率大深宽比河湾拟序扰动结构与床面响应关系探讨

蜿蜒河流床面形态既是其复杂动力结构响应的结果,同时也是决定河流进一步演化方向的重要因素.以蜿蜒河流中一种典型的大深宽比河湾为背景,探索其动力结构与床面响应的关系,将黏性不可压缩流体方程、泥沙输移方程和床面变形方程耦合,通过摄动方法求解床面响应,分析床面形态变化特性.研究成果显示在水流二维扰动作用下,河道中浅滩深槽呈现规则响应.当弯曲度等于0时,床面响应形态围绕河道中轴线基本呈反对称分布;当弯曲度不等于0时,床面响应形态呈不对称分布,中轴线向凹岸偏移.该文给出了由Reynolds(雷诺)数、扰动波数、床面形态增减率等构成的床面响应发展趋势稳定关系的判别方法.     

Dynamic Responses Analysis of Bridges With Uncertain Parameters Under Moving Loads北大核心CSCD

针对具有不确定参数桥梁在移动荷载作用下的动力响应分析,首次建立了移动荷载作用下桥梁响应分析的多项式维数分解法.将结构的不确定参数视为独立的随机变量,构造了结构动力响应关于不确定参数的随机函数;进而采用一组变量数目逐次增加的成员函数实现结构动力响应的维数分解,并利用Fourier多项式展开推导成员函数的近似显式表达.通过降维积分方法降低概率空间内的积分维度,高效地实现了展开系数的计算.在数值算例中,进行了具有不确定参数桥梁在移动荷载作用下的响应估计,并与Monte-Carlo模拟进行对比,验证了该文方法的精确性和效率.     

An extended beam theory for smart materials applications part I: Extended beam models,duality theory,and finite element simulations

An extended theory for elastic and plastic beam problems is studied. By introducing new dependent and independent variables, the standard Timoshenko beam model is extended to take account of shear variation in the lateral direction. The dynamic governing equations are established via Hamilton's principle, and existence and uniqueness results for the solution of the static problem are proved. Using the theory of convex analysis, the duality theory for the extended beam model is developed. Moreover, the extended theory for rigid-perfectly plastic beams is also established. Based on the extended model, a finite-element method is proposed and numerical results are obtained indicating the usefulness of the extended theory in applications.The work of the first author was supported in part by National Science Foundation under Grant DMS9400565.     

A free boundary problem and stability for the circular plate

In the recent paper [6] we have answered the question of stability for the nonlinear beam which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. The basic idea that was first used in a numerical solution and subsequently in the mathematical analysis was to consider the free boundary problem in the interval in which the beam is not in contact with the obstacle. In this work we consider the analogous problem for the linear circular plate. Numerical computations are crucial here to establish conditions essential for the problem of stability and they also yield the critical parameter values, i.e., the secondary bifurcation points.     

2D frames optimization. Criterion: maximum stability

Structural analysis was one of the first disciplines to demand powerful computing tools. However, with current capacities of both calculus and manufacture and use of new materials, along with certain aesthetic conditions, it is possible to address problems such as the one presented in this article, whose aim is the optimal variation of any frame, so that few criteria are met, including stability. The problem is complex and must be solved numerically. This paper presents a formulation for solving the optimization problem, considering not only the buckling conditions but any other, such as allowable stress or limited displacement. The equilibrium of each beam in its deformed geometry is proposed under assumption of small displacements and deformations (Second Order Theory). The optimization problem is mathematically formulated to determine which values maximize the buckling load of the frame and numerically solved by sequential quadratic programming. Finally, for the optimal solution from the point of view of stability, the plastic collapse load is calculated. The plastic behavior is based on the bending moment and leads to sudden concentrated plastic hinges. Therefore, the structural stability is affected, which is checked during the loading process.     

Application of homotopy-Padé technique in limit analysis of circular plates under arbitrary rotational symmetric loading using von-Mises yield criterion

The upper and lower bound principals of limit analysis are employed to determine the critical loading on solid circular plate with simply supported boundary conditions and subjected to any distributed loading with rotational symmetry. In this study, material behavior follows a rigid perfectly plastic model and yielding obeys the von-Mises criterion. Homotopy analysis method is employed to achieve the analytical solution to the high nonlinear ordinary differential equations governing the problem. This analytic solution has been obtained in terms of convergent series with easily computable terms. The results are verified with the Tresca yield criterion and presented as plots to show the reliability and simplicity of the method.     

A modification of an approach to the solution of the Hilbert boundary-value problem for an analytic function in a multiconnected circular domain

We propose a modification of the approach proposed by us in Russian Mathematics (Iz. VUZ) 44 (2), 58–62 (2000) for the solution of the Hilbert boundary-value problem for an analytic function in a multiconnected circular domain. This approach implies the solution of the corresponding homogeneous problem including the determination of an analytic function from the known boundary values of its argument in a circular domain.     

The problem of the bending of a beam lying on an elastic base

The plane contact problem of the transmission of a normal force of specified strength onto an elastic anisotropic, wedge-shaped plate by an elastic beam of variable flexural stiffness is considered. The beam is coupled to one of the edges of the plate and its other edge is stress-free. The solution of the problem is obtained in closed form by reducing it to a Karleman boundary-value problem with shear for a strip. A conclusion is reached concerning the nature of the discontinuity of the normal contact stress at the vertex of the wedge.     

The growth of a circular hydrorupture crack in an elastic space when a plastic material is forced in

An axisymmetric problem of the growth of a circular hydrorupture crack whose cavity is filled with a non-standard plastic flowing material is considered. The cases of complete and incomplete penetration are analysed Prelimiting states of a crack of fixed dimensions are discussed.     

Buckling analysis of a ring under the action of internal pressure in a cylindrical shell

Buckling analysis of a thin cylindrical shell stiffened by rings with T-shaped cross section under the action of uniform internal pressure in the shell is performed. An annular plate stiffened over the outer edge by a circular beam is used as the ring model. The classical ring model, which is a beam with a T-shaped cross section, is inappropriate in this problem, since in the case of the loss of stability, buckling deformations are localized on the ring surface. The beam model does not allow one to find the critical pressure that corresponds to such a loss of stability. In the first approximation, the problem of the loss of stability of the annular plate connected with the shell is reduced to solving the boundary value problem for finding eigenvalues of the annular plate bending equation. Approximate formulas for determining critical pressure are obtained under the assumption that the plate width is much smaller than its inner radius. The results found using the Rayleigh method and the shooting method differ slightly from each other. It has been demonstrated that the critical pressure for rings with rectangular cross section is higher than that for rings with a T-shaped cross section.     

广义弹塑性梁理论及接触问题中的时偶变分不等式*

为研究摩擦接触问题,本文建立了一个具有二类独立交量的二维弹塑性梁模型。由此提出了一个新的非线性二次互补性问题。其中的外部互补性条件定义了自由边界;而内部互补性条件则控制了弹塑性分界面。文中证明了此二次互补性问题等价于一非线性变分不等式,并导出了其对偶变分不等式。本文结果显示对偶问题较原问题有更多的优越性。应用于塑性极限分析理论中,文中最后证明了一个简单的下限定理。     

On fractional powers of a pair of matrices and a plate-beam problem

In this paper we consider the transversal deflections of a dynamically-coupled Von Kármán system consisting of a plate which has a beam attached to its one edge. The problem is considered in the form of a non-linear evolution problem in a product space. We show the existence of a unique local solution by following a fractional powers approach to first construct a “weak” solution in a larger space. Regularity properties for this solution yield a unique local strong solution for the original boundary-value problem. This approach entails the introduction of fractional powers of a pair of matrices.