黏弹性结构蠕变屈曲特性的分析

分析了线黏弹性正交铺设层合板的蠕变失稳问题，由相空间的特征方程解出临界载荷，经Laplace数值反演得到屈曲载荷与时间的关系；然后，通过建立扰动模型和分析变形的有界与无界增长，讨论了黏弹性结构延迟失稳的特性，解释了临界载荷与失稳时间的具体含义．     

斜靠式拱桥结构侧倾失稳分析的Ritz法

采用Ritz法,首次推导了主拱肋拱脚铰接、稳定拱肋拱脚固接边界条件下,斜靠式拱桥的侧倾失稳临界荷载系数的计算公式,并通过有限元法验证了该计算公式的正确性.进一步分析了稳定拱肋弯曲变形能和扭转变形能、主拱肋与稳定拱肋间横撑切向和径向弯曲变形能及吊杆非保向力位势和桥面系侧向弯曲变形能对斜靠式拱桥侧倾失稳临界荷载系数λcr的影响.研究结果表明:稳定拱肋的侧向弯曲变形能对斜靠式拱桥侧倾失稳临界荷载系数λcr有一定的影响,而扭转变形对侧倾失稳临界荷载系数λcr影响甚微;若忽略横撑的所有变形能,侧倾失稳临界荷载系数λcr降低65％～83％,即横撑对斜靠式拱桥侧倾失稳临界荷载系数λcr的影响非常显著;随着稳定拱肋倾角的增加,侧倾失稳临界荷载系数λcr呈增大趋势,且增设稳定拱肋对提高斜靠式拱桥的侧向稳定性大有帮助.     

基于应变响应敏感性的单层球面网壳冗余度分析

冗余特性是结构鲁棒性的重要组成部分,也是复杂系统的安全性和传力路径可靠性的体现。如何对结构构件冗余度进行定量评价是目前结构工程界尚未定论的问题之一。本文借鉴P.C.Pandey方法,并将其推广应用到大跨空间网格结构,基于结构应变响应对构件单元截面面积的敏感性提出静力作用下的结构构件冗余度评价方法,从理论上以数值方式量化结构构件冗余度,并通过对三个球壳结构算例的冗余度分析说明该方法在空间结构体系中的有效应用。算例结果表明,结构构件冗余度能够反映构件在结构中的重要性,低冗余度构件是结构的关键构件。采取措施加固低冗余度构件可以有效提高结构整体刚度、结构稳定极限承载力,但在改善结构缺陷敏感性方面则视具体情况而定。     

半结构法在中心对称结构计算中的应用

半结构法是计算对称结构的一种简化分析方法,通常应用于轴对称结构.本文将探讨半结构法在中心对称结构计算中的应用问题,包括中心对称、反对称载荷作用下结构的对称性及其证明、等代结构形式及其应用等.算例表明,中心对称结构半结构法能够最大程度简化结构、提高结构计算效率,与其他方法联合应用的一题多解方法可丰富结构力学教学内容,有利于学生拓展其创新思维及分析解决复杂力学问题的能力.     

累积线性法在细长柔性悬臂梁结构分析中的应用

为了研究几何大位移悬臂梁的结构响应,在充分利用线性有限元原理与流程的基础上,本文提出"累积线性法" 来对这一问题进行结构建模与求解策略的探讨,数值计算过程表明：该方法在常规有限元软件平台上十分容易实现,并与常规的"一次线性法" 和"非线性求解" 进行了数值对比. 针对本文问题,不仅从理论上指出"累积线性法" 的合理与可行和"一次线性法" 存在的结果不可信等问题;同时,数值仿真也表明前两种方法得到的结果也是不同的, 前者更接近非线性求解的结果. 最后,给出4 点结论.     

微分求积单元法在结构工程中的应用

微分求积法（Differential Quadrature Method）是求鳃偏微分方程和积分-微分方程的一种数值方法,该法具有计算简便、精度较高和易于实现等优点。微分求积单元法（Differential Quadrature Element Method）是在微分求积法的基础上结合区域分割和集成规则而形成的一种新的数值计算方法,能通过自适应地选取微分求积网点数目正确模拟构件的刚度和荷载性质,其精度可通过细分单元或增加离散点数目加以提高。微分求积单元法是一种可供选择的、性能优越的数值计算方法。本文将详细论述这一数值方法的基本原理,并通过数值算例说明该方法的应用过程及其优越性,为这一方法在结构工程中的推广应用提供参考。     

残余力向量法在结构损伤识别中的应用研究进展

工程结构的损伤识别技术对于把握结构工作状态及评估结构的安全性与正常使用性能具有重要的意义。近年来基于残余力向量法的损伤识别技术受到了关注并取得了一定的研究成果。文章从基于残余力向量法的损伤识别技术、残余力向量法和灵敏度分析方法相结合、残余力向量法的改进、残余力向量法和人工神经网络技术的结合、残余力向量法和智能算法的融合等5个方面综述了目前国内外基于残余力向量法进行结构损伤识别研究的成果。并根据残余力向量法应用上存在的问题展望了应用残余力向量法进行结构损伤识别时在如何减小误差;如何克服测试信息不完备的影响;如何进行实际工程损伤识别的研究以及残余力向量法的改进以及残余力向量法和智能算法结合等方面的发展趋势。     

自由单元法及其在结构分析中的应用

通过吸收有限元与无网格法的优点,提出了一种新的数值方法------自由单元法.此方法在离散方面,采用有限元法中的等参单元,表征几何形状和进行物理量的插值;在算法方面,采用单元配点技术,逐点产生系统方程.主要特点是,在每个配置点只需要一个和周围自由选择的节点而形成的一个独立的等参单元,因而不需要考虑物理量在单元之间的相互连接关系与导数连续性问题. 本文介绍强形式与弱形式两种自由单元法,前者直接由控制方程和边界条件直接产生系统方程,后者通过在自由单元上建立控制方程的加权余量式产生弱形式积分式,并通过像传统有限元法中的积分过程建立系统方程组.本文提出的方法是一种单元配点法,对于域内点为了获得较高的导数精度,需要采用至少具有一个内部点的等参单元,为此除了可使用各阶次的拉格朗日四边形单元外, 还 给出了七节点三角形等参单元,用于模拟较为复杂的几何形状问题.      

力矩分配法在对称结构中的应用

以力矩分配法为基础，探索了对称结构的简化计算方法．为了克服对称结构计算时通常方法所产生的不便，提出了新的力矩分配概念，找出了新的分配系数和传递系数．应用改进的力矩分配法，对对称结构进行了计算，算例表明该方法简化了计算，加快了收敛速度．     

非线性结构动力学瞬态分析的摄动法

在用直接积分法求解非线性结构的动力响应时,常常需要做迭代运算。本文引入摄动方法后,加快了收敛速度,提高了计算效益。     

Improvements on the arc-length-type method

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods. The project supported by the Special Research Fund for Doctor Program of Universities (9424702)     

Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

Turbo-machineries, as key components, have wide applications in civil, aerospace, and mechanical engineering. By calculating natural frequencies and dynamical deformations, we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies. In this paper, the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed. The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations, including the centrifugal force and the aerodynamic force. In view of the first-order shear deformation theory and von-Kármán nonlinear geometric relationship, the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton's principle. The second-order ordinary differential equations are acquired by the Galerkin approach. With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance, the averaged equation is derived by the asymptotic perturbation methodology. Bifurcation diagrams, phase portraits, waveforms, and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.     

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is co…     

Bifurcation analysis of an electro-statically actuated micro-beam in the presence of centrifugal forces

In this paper, the influence of centrifugal forces on the stability of an electro-statically actuated clamped–clamped micro-beam has been investigated. The non-dimensional governing static and dynamic equations have been linearized using the step by step linearization method (SSLM), then, a Galerkin-based reduced order model has been used to solve the linearized equations. For constant value of a bias DC voltage and different values of angular velocity the equilibrium points of the corresponding autonomous system including stable center points, unstable saddle points and singular points have been obtained using the equivalent mass-spring model. Subsequently the bifurcation diagram has been depicted using the obtained fixed point. The static pull-in voltage value for different values of angular velocity and the static pull-in angular velocity for different values of bias voltage have been calculated. The obtained results are validated using results of previous studies and a good agreement has been observed. The effect of the centrifugal force on the fixed points has been studied using the phase portraits of the system for different initial conditions. Moreover, the effects of centrifugal forces on the dynamic pull-in behavior have been investigated using time histories and phase portraits for different angular velocities.     

多孔介质非线性渗流问题的摄动解

考虑变形多孔介质渗透参数(渗透率和孔隙度)与孔隙压力呈负指数变化的特点，建立了多孔介质渗流问题的数学模型，采用积分变换方法求出了一维非线性渗流问题的摄动解，并对常数渗透参数和指数渗透参数的渗流问题进行对比分析，计算结果表明：两者之间的差别较大，且渗透参数的变化对于流体渗流中后期过程有着重要的影响，但对渗流早期影响不大，这对于定量研究工程中非线性渗流问题模型参数的相对重要性提供了可靠的理论依据。     

Bifurcation and stability analysis of laminar flow in curved ducts

The development of viscous flow in a curved duct under variation of the axial pressure gradient q is studied. We confine ourselves to two‐dimensional solutions of the Dean problem. Bifurcation diagrams are calculated for rectangular and elliptic cross sections of the duct. We detect a new branch of asymmetric solutions for the case of a rectangular cross section. Furthermore we compute paths of quadratic turning points and symmetry breaking bifurcation points under variation of the aspect ratio γ (γ=0.8…1.5). The computed diagrams extend the results presented by other authors. We succeed in finding two origins of the Hopf bifurcation. Making use of the Cayley transformation, we determine the stability of stationary laminar solutions in the case of a quadratic cross section. All the calculations were performed on a parallel computer with 32×32 processors. Copyright © 2009 John Wiley & Sons, Ltd.     

Bifurcation Instability in Linear Elasticity with the Constraint of Local Injectivity

There are problems in linear elasticity theory whose corresponding deformations, usually associated with singular stress fields, are open to question because they are not one-to-one and predict self-intersection. Recently, a theory has been advanced to handle such situations, which consists in minimizing the quadratic energy functional of linear elasticity subject to the constraint of local injectivity. In particular, the Jacobian of the deformation gradient is required to be not less than an arbitrarily small positive quantity, and, thus, the local orientation is preserved. Here, this theory is applied to the classical Lekhnitskii problem of an elastic aelotropic circular disk which is loaded on its boundary by a uniform radial pressure. Without the injectivity constraint, this classical linear problem has a unique solution. This example, with the injectivity constraint, already has been considered in previous works, but radial symmetry was assumed in order to reduce the problem from 2D to 1D. Here, making use of an interior penalty formulation, a numerical scheme is implemented that solves a full 2D problem. Remarkably, it is shown that there are values of the material moduli for which the minimal potential energy solution is no longer symmetric, producing a strong azimuthal shear and nominally a 180° rotation of an internal central core of the disk. Although the elastic strain energy is quadratic and convex, the strongly nonlinear character of the constraint allows for bifurcation instabilities. We gratefully acknowledge the partial support of the Minnesota Supercomputing Institute and the Italian “Ministero per l’Università e la Ricerca Scientifica” under the program PRIN 2005 “Affidabilità di elementi in vetro strutturale: indagini teoriche e sperimentali sulla risposta termo-meccanica del materiale e di strutture trasparenti di tipo innovativo”. R.F. gratefully acknowledges the Department of Civil and Environmental Engineering at the Politecnico di Bari, Italy, for their kind hospitality and support during his visit of 2006. We appreciate the helpful comments and suggestions of Paolo Podio-Guidugli on an earlier draft of this work.     

Remarks on the Perturbation Methods in Solving the Second-Order Delay Differential Equations

The paper presents a study on the validity of perturbation methods, suchas the method of multiple scales, the Lindstedt–Poincaré method and soon, in seeking for the periodic motions of the delayed dynamic systemsthrough an example of a Duffing oscillator with delayed velocityfeedback. An important observation in the paper is that the method ofmultiple scales, which has been widely used in nonlinear dynamics, worksonly for the approximate solutions of the first two orders, and givesrise to a paradox for the third-order approximate solutions of delaydifferential equations. The same problem appears when theLindstedt–Poincaré method is implemented to find the third-orderapproximation of periodic solutions for delay differential equations,though it is effective in seeking for any order approximation ofperiodic solutions for nonlinear ordinary differential equations. Apossible explanation to the paradox is given by the results obtained byusing the method of harmonic balance. The paper also indicates thatthese perturbation methods, despite of some shortcomings, are stilleffective in analyzing the dynamics of a delayed dynamic system sincethe approximate solutions of the first two orders already enable one togain an insight into the primary dynamics of the system.