二维边坡稳定性分析的最小势能法新解

针对最小势能法研究的不足,通过条块虚位移方向的静力平衡方程确定滑面上剪应力的解析解,构建了一种新的剪切势能计算模型.同时,提出了一种多地层边坡稳定性分析方法.算例结果表明:剪切势能对边坡稳定性系数会产生影响,使得计算结果更为合理;运用文中方法计算得到边坡稳定性系数与极限平衡法的结果较为一致,表明文中的计算方法是可行且合理的;文中多地层边坡的计算模型,考虑了土层滑面长度以及法向力对边坡抗剪强度的贡献,且计算简便,易于工程人员使用.     

A compact finite difference method for solving Burgers' equation

In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD

在经典Padé逼近理论的基础上进行了相应推广,提出了广义Padé逼近方法,并针对强非线性自治振子同宿轨的求解问题,利用双曲函数构造了一种新的广义Padé逼近式. 首先,该广义Padé逼近式有着较简单的泰勒展开式,与现有的Padé逼近式相比,在计算同阶逼近时,计算量更少;其次,该方法在强非线性时,依然有着较高的精度;第三,该方法并不局限于某些特定的系统,而是有着较广的适用范围. 因此对于广义Padé逼近方法的研究具有一定的实际意义和理论价值.     

Elliptic averaging methods using the sum of Jacobian elliptic delta and zeta functions as the generating solution

The present paper describes an improved version of the elliptic averaging method that provides a highly accurate periodic solution of a non-linear system based on the single-degree-of-freedom Duffing oscillator with a snap-through spring. In the proposed method, the sum of the Jacobian elliptic delta and zeta functions is used as the generating solution of the averaging method. The proposed method can be used to obtain the non-odd-order solution, which includes both even- and odd-order harmonic components. The stability analysis for the approximate solution obtained by the present method is also discussed. The stability of the solution is determined from the characteristic multiplier based on Floquet’s theorem. The proposed method is applied to a fundamental oscillator in a non-linear system. The numerical results demonstrate that the proposed method is very effective for analyzing the periodic solution of half-swing mode for systems based on Duffing oscillators with a snap-through spring.     

New applications of variational iteration method using Adomian polynomials

In this paper, we discuss a new application of the variational iteration method considering Adomian’s polynomials on nonlinear physical equations. Two models of interest in physics are considered and solved by means of the variational iteration method. The behavior of the variational iteration method and the effects of different values of t are investigated. Comparisons are made among the standard Adomian decomposition method, exact solutions, and the proposed method. He’s variational iteration method is introduced to overcome the difficulty arising in calculating the Adomian polynomial in Adomian decomposition method. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems.     

基于虚拟材料的T-B梁拓扑优化ESO方法

自从Zhou和Rozvany于2001年以T-B梁(Tie-Beam)问题质疑渐进结构优化方法ESO(Evolutionary Structural Optimization)的算法收敛性以来,结构最优化领域的研究者提出了多种算法以求解决这一问题。T-B梁问题仍是当前结构拓扑优化领域的研究热点,因为现有的各种T-B梁解法或是存有不足或是无法获得满意解答。本文在传统ESO算法中,将虚拟材料引入待删除单元,用以检测结构传力路径是否受到破坏,进而确定单元删除的合理性。算例表明,本文算法可有效防止ESO方法求解T-B梁问题时的失效并获得最优解,且本文算法只需在ESO迭代中附加一次检测,不改变ESO方法的迭代进程和寻优能力。     

A self-optimizing inverse analysis method for estimation of cyclic elasto-plasticity model parameters

In this paper, a novel inverse analysis methodology call a Self-Optimizing Inverse Method (Self-OPTIM) has been presented, which inversely estimates cyclic elasto-plastic constitutive model parameters using global forces and displacement on the same partial boundaries and full-(or partial-) field displacement data. A novelty of the methodology is that it automatically self-estimates material parameters by updating “full-field” reference stresses and strains through two parallel nonlinear finite element simulations. Although a well-known classical cyclic plasticity model is chosen in this paper, it must be emphasized that the proposed Self-OPTIM method is a model-independent method, which means that any advanced model can be naturally integrated with the proposed methodology. Thus, using numerically generated test data of low-carbon steel specimens (AISI 1010), the proposed Self-OPTIM method has been verified showing its successful performance to estimate nonlinear isotropic and kinematic hardening parameters, yield stress, Young’s modulus and Poisson ratio. The effects of experimental noises from CCD camera and measurement errors of the boundary forces are also investigated for the Self-OPTIM method.     

Investigation of the stress field of a near-surface circular hole

By observing experimentally obtained photoelastic fringe patterns and applying classical solutions for an infinite plate containing a circular hole under remote tension and the modified Hertz contact theory, a replaced superposition method is proposed. In this paper we use this method to investigate the state of stress around a near-surface circular hole in a semi-infinite plate under a concentrated load. The well-matched conditions between the reconstructed and experimental photoelastic fringe patterns indicate the applicability of the proposed method. This paper was presented, in part, at a symposium honoring Dr. Christian P. Burger, Novel Applications of Experimental Methods in Mechanicsheld at the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2–4, 2003, Charlotte, North Carolina.     

Composite mechanics and energy method based stiffness prediction model for composite leaf springs

Predicting the stiffness of composite leaf spring accurately is the key to improve vehicles' performance. In this paper, a stiffness prediction model which is based on composite mechanics and energy method is proposed. Influence of un-coincident between neutral layer and middle of the thickness of each rectangular cross-section is considered. Calculation based on finite element method, existing theoretical method and bench test are carried out. Compared with these results, the model proposed in this paper can predict stiffness accurately. Besides, influences parameters are analyzed. The proposed model has a certain guiding significance for the lightweight of vehicles.

Communicated by Corina Sandu.     

薄壁结构多层级并发加筋拓扑优化研究

新一代航天装备的主承力薄壁舱段在追求极致轻量化的同时,还具有更高的刚度和抗屈曲等设计指标.传统结构形式和设计方法难以满足轻质高承载的设计要求.为此,本文提出了一种薄壁结构多层级并发加筋拓扑优化方法,通过构建主层级稀疏加筋和次层级密集点阵增强结构整体和局部力学性能,扩展结构设计空间,有效提升材料利用率.其中,主层级加筋布局通过变密度拓扑优化方法获得,次层级点阵构型通过基于改进的渐进均匀化方法提出的两种设计方法获得,并基于材料插值模型,建立了多层级并发加筋拓扑优化框架,实现在一次拓扑优化求解中同时获得主层级加筋布局和次层级单胞拓扑构型.基于上述方法,本文分别给出了考虑结构刚度和稳定性设计需求的优化算例,并与传统单层级加筋拓扑优化进行了对比.结果 表明,多层级并发加筋方法可以根据承载边界和设计目标寻找优化的结构形式,且在相同质量下,其优化构型相比传统单层级拓扑优化结果表现出更高的承载性能,证明了本方法在薄壁结构设计上的优势.     

基于尾流时程目标识别的流场参数选择研究

浸入流场中的固体壁面会形成高度复杂且具有一定特征的尾流流场, 利用尾流所包含的信息对物体的外形特征进行识别具有重要的应用价值. 然而, 在较高雷诺数情况下尾流流场形态及其时序特征复杂, 难以通过传统的数学物理方法对流场信号进行特征的识别与提取. 本文提出了基于尾流时程数据深度学习的流场特征提取与分析方法, 实现了基于一点的物理量时程进行流场中物体外形的识别; 同时, 对流场中不同物理参数时程的识别精度与识别结果进行分析与研究, 得到适用于目标识别的最优物理量参数. 通过对圆柱和方柱的尾流数据研究结果表明, 本文提出的基于卷积神经网络的模型具有好的训练收敛性和高的预测精度, 能够识别并提取得到时程数据中包含的流场特征, 采用流场横向速度时程作为物体外形识别信号的模型准确率高. 证明了本方法用于浸入流场中物体外形识别的可行性, 是一种目标识别的高精度方法.      

Constrained parameter-splitting perturbation method for the improved solutions to the nonlinear vibrations of Euler–Bernoulli cantilevers

In this paper, a new method named constrained parameter-splitting perturbation method for improving the solutions obtained from the parameter-splitting perturbation method is proposed for solving the problems in some extremal cases, such as the strongly nonlinear vibration of an Euler–Bernoulli cantilever. The proposed method takes the advantages of both the perturbation method and the harmonic balance method. The idea is that the solution obtained by the parameter-splitting perturbation method is substituted into the equation of motion and then the accumulative error of the equation is minimized for determining the unknown splitting parameters under the constraints constructed under the frame of harmonic balance method. The forced vibration of an oscillator with cubic geometric nonlinearity and inertia nonlinearity and the forced vibration of a planar microcantilever beam with a lumped tip mass are studied as examples to reveal the efficacy of the proposed method. The inspection of the steady-state response including its stability is conducted by means of comparing the frequency-response curves obtained by the proposed method with those obtained by the numerical continuation method and harmonic balance method, respectively, to show the efficacy and the advantages of the proposed method. Meanwhile, the nonlinear ordering effect on the solutions of the proposed method is also studied by comparing the results obtained by using different nonlinear orderings in the systems. In the last, we found through convergence examinations that it is necessary to have corrections to the erroneous solution which are obtained by harmonic balance method and Floquet theory in stability analysis.

     

Long-memory recursive prediction error method for identification of continuous-time fractional models

This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.

     

Determination of stress-intensity factors by the method of caustics in anisotropic materials

This paper studied the applicability of the method of caustics to anisotropic materials under Mode I and mixed-mode static-loading conditions and introduced the procedure to obtain stress-intensity factors (SIF) in anisotropic materials by the method of caustics.The mapping equations for initial and caustic curves in anisotropic materials were introduced and their computer graphical images were compared to the experimental ones to check the validity of the mapping equations proposed in this paper. The agreement between them was found to be satisfactory.Two kinds of equations to determine SIF in anisotropic materials by the method of caustics are proposed in this paper. Corroborative experiments carried out by using the orthotropic materials under various loading conditions are presented. In the case of Mode I loading condition, the SIF's obtained by this paper's methods were found to be close to the results by another method, i.e., boundary-element method (BEM). And in the case of mixed-loading condition, the SIF's by this paper and BEM show little differences, (2.2–24.4 percent) with respect to the slanted angle of crack.     

Decentralized control of uncertain nonlinear stochastic systems based on DSC

In this paper, the decentralized stabilization control approach based on the dynamic surface control (DSC) is proposed for a class of large-scale interconnected stochastic nonlinear systems. The proposed approach combined the existing dynamic surface control (DSC) with back-stepping technique. This approach can overcome the problem of “explosion of complexity” inherent in the back-stepping method. Thus, the proposed control approach is simpler than the traditional back-stepping control method for the large-scale interconnected stochastic nonlinear systems. The stability analysis shows that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Automatic generation of unstructured grids with Delaunay triangulation and its application

This paper is consisted of two parts. In the first part, a method is described which generates two-dimensional triangle mesh using the Delaunay triangulation criterion. An automatic algorithm was proposed which combines several advantages of the existing methods. Local mesh refinement can also be easily performed with this method. Examples of generated grids were presented for several convex, non-convex and multi-connected domains to demonstrate the effectiveness and feasibility of the proposed method. In the second part, the turbulent heat transfer in an annular space finned by wave-like longitudinal fins was numerical simulated. The proposed technique was adopted to generate the grid in the cross-section. The standard K-ɛ model in conjuction with wall function method was used to simulate the fluid flow and heat transfer in the complex geometry. The discretization of the governing equations was described. The computational results were compared with the authors' test data and the agreement was reasonably good. Received on 9 July 1998     

Sensor attack reconstruction for mobile robots via a switching Kalman fusion mechanism

Due to the poor security level in current industrial network, the control performance of robots may be severely affected by cyber attacks. This paper studies the sensor attack reconstruction problem of mobile robots, where a switching Kalman fusion mechanism is proposed to reconstruct the sensor attacks online. It is shown that the proposed mechanism is better than the existing extended state observer and event-triggered sensor attack reconstruction strategy. The experiment test demonstrates the effectiveness and superiority of the proposed method.

     

Online system identification using fractional-order Hammerstein model with noise cancellation

Slow convergence and low accuracy are two main drawbacks in nonlinear system identification methods. It becomes more complicated when time delay and noises are considered. In this paper, considering a fractional-order Hammerstein model, an online identification method is proposed. A combination of an evolutionary optimization method and recursive least square algorithm is used to estimate the system parameters and orders in the presence of unknown noises. Finally, simulation results are taken to prove the effectiveness of the proposed algorithm.

     

Secure communication based on chaotic synchronization via?interval?time-varying delay feedback control

In this paper, a synchronization method of Lur??e systems for chaotic secure communication systems with interval time-varying delay feedback control is proposed. To increase communication security, the transmitted message is encrypted with the techniques of N-shift cipher and public key. Based on Lyapunov method and linear matrix inequality (LMI) formulation, new delay-dependent synchronization criteria are established to not only guarantee stable synchronization of both transmitter and receiver systems but also recover the transmitted original signal at the receiver. Throughout a numerical example, the validity and superiority of the proposed method are shown.     

Power system transient stability analysis through a homotopy analysis method

As an important function of energy management systems, online contingency analysis plays an important role in providing power system security warnings of instability. At present, N-1 contingency analysis still relies on time-consuming numerical integration to assess transient stability. To reduce computational cost, this paper proposes a transient stability analysis method based on homotopy analysis. The proposed method analyzes power system transient stability by computing bifurcation points of nonlinear differential equations. These bifurcation points constitute transient stability region boundaries. The method judges if the post-fault system can survive a disturbance by analyzing whether the initial values following fault clearance locate within the boundaries. The proposed method provides an alternative approach to assessing power system transient stability instead of traditional numerical integration. A simple case is presented to demonstrate application of the proposed method; the analysis results of the proposed method are consistent with the results of numerical integration.