STUDY ON THE COMPLICATED DYNAMICAL BEHAVIORS OF NONLINEAR ECOSYSTEM (Ⅰ)

This series of papers is prepared to develop systematically the complicated dynamical behaviors of nonlinear ecosystem and its internal mechanism. In this paper, we state briefly the increasing importance of ecology, describe and comment on the situations and reasons why ecology theory is behind practice. Then, we point out a procedure which modern ecology research should obey, and discuss the four basic characteristics of ecosystem in detail: level, opening, nonlinear and far from equilibrium. At last, we discuss systematically equilibrium and nonequilibrium, stable and unstable, environmental stochasticity and dynamical stochasticity, and conclude that there exists a bridge between deterministic behaviors and stochastic behaviors, which will result in a new model for ecological prediction.Supported by Youth Fund of Chinese Academy of Science and Youth Fund of Lanzhou University.     

关于圆筒壳稳定性中的初始缺陷

本文综述了圆筒壳稳定性中初始几何缺陷的几个重要问题。讨论了初始几何缺陷对圆筒壳临界载荷的基本效应,它的随机性、测量以及相应的数据库的建立。最后介绍了失稳破坏占主要地位的壳体结构的交互设计的基本思想和方法,并对进一步的研究工作提出了看法。      

Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 140–146, March–April, 2007.     

Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory

Summary Since several years Lyapunov Characteristic Exponents are of interest in the study of dynamical systems in order to characterize quantitatively their stochasticity properties, related essentially to the exponential divergence of nearby orbits. One has thus the problem of the explicit computation of such exponents, which has been solved only for the maximal of them. Here we give a method for computing all of them, based on the computation of the exponents of order greater than one, which are related to the increase of volumes. To this end a theorem is given relating the exponents of order one to those of greater order. The numerical method and some applications will be given in a forthcoming paper.

---

Sommario Da diversi anni gli esponenti caratteristici di Lyapunov sono divenuti di notevole interesse nello studio dei sistemi dinamici al fine di caratterizzare quantitativamente le proprietà di stocasticità, legate essenzialmente alla divergenza esponenziale di orbite vicine. Si presenta dunque il problema del calcolo esplicito di tali esponenti, già risolto solo per il massimo di essi. Nel presente lavoro si dà un metodo per il calcolo di tutti tali esponenti, basato sul calcolo degli esponenti di ordine maggiore di uno, legati alla crescita di volumi. A tal fine si dà un teorema che mette in relazione gli esponenti di ordine uno con quelli di ordine superiore. Il metodo numerico e alcune applicazioni saranno date in un sucessivo articolo.

     

Estimation of stochastic nonlinear dynamic response of rock-fill dams with uncertain material parameters for non-stationary random seismic excitation

This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.     

线性随机结构在随机激励下动力响应分析

利用虚拟激励法对随机结构正交展开理论进行扩展,并在Ritz向量子空间中对扩阶系统方程进行动力聚缩,提出了一类可以快速高效地进行线性随机结构复合随机振动分析的计算方法．算例分析表明,该法可以方便地分析随机结构在平稳或非平稳随机激励下的复合随机振动问题,且分析结果与 Monte Carlo模拟分析结果符合良好;与均值参数确定性结构传统随机振动分析计算结果相比,随机结构在相同随机激励下响应自谱密度曲线具有峰值降低、谱宽增大的特点．     

Non-Filippov dynamics arising from the smoothing of nonsmooth systems,and its robustness to noise

Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires that piecewise-smooth and smooth dynamical systems have similar dynamics, but the conditions for such similarity are not well understood. Here we show that by smoothing out a piecewise-smooth system one may obtain dynamics that is inconsistent with the accepted wisdom — so-called Filippov dynamics — at a discontinuity, even in the piecewise-smooth limit. By subjecting the system to white noise, we show that these discrepancies can be understood in terms of potential wells that allow solutions to dwell at the discontinuity for long times. Moreover we show that spurious dynamics will revert to Filippov dynamics, with a small degree of stochasticity, when the noise magnitude is sufficiently large compared to the order of smoothing. We apply the results to a model of a dry-friction oscillator, where spurious dynamics (inconsistent with Filippov’s convention or with Coulomb’s model of friction) can account for different coefficients of static and kinetic friction, but under sufficient noise the system reverts to dynamics consistent with Filippov’s convention (and with Coulomb-like friction).     

Qualitative behaviors of the continuous-time chaotic dynamical systems describing the interaction of waves in plasma

In this paper, a new Lorenz-like chaotic system describing the interaction of three resonantly coupled waves in plasma is studied. Explicit ultimate boundedness and global attraction domain are derived according to stability theory of dynamical systems. The innovation of the paper is that this paper not only proves this chaotic system is globally bounded for the parameters of this system but also gives a family of mathematical expressions of global exponential attractive sets for this system with respect to the parameters of this system. Furthermore, the exponential rate of the trajectories is also obtained. Finally, numerical localization of attractor is presented.     

隧道峒口污染物扩散控制方案的研究

采用三维数值模拟的方法,对隧道峒口污染物的扩散情况进行了预测和分析,揭示了在不同风向条件下,隧道峒口废气的扩散特征,并根据计算结果提出了一种较为经济的控制污染物排放的方案,对工程设计具有一定的指导意义。     

On the representation of finite rotation in nonlinear field theory of continuum mechanics

One of the important basic theoretical problems in the development of continuum mechanics is the separation of finite strain and finite rotation at a point in the displacement field. Now it is certain that S-R decomposition theorem provides a rational theoretical solution for this problem. The purpose of this paper is to clarify some misleading basic concepts of finite rotation of deformed body in current literature, and to promote further progress.The detailed abstract of this paper was published in 1985 Shanghai International Conference of Nonlinear Mechanics. In the present paper some new results are included.     

张弦梁(桁架)结构的找形方法——分级卸载法

对张弦梁(桁架)结构的找形问题进行了深入研究,根据该类结构的受力特点,提出了分级卸载法。该方法无需假定结构零状态几何,而可以一次得到对应于初状态(即预应力态)几何的结构施工放样尺寸(即零状态几何),并通过分级加载对该方法的精度进行了检验。     

应用有限元法计算离心式叶轮内部流场

运用张量分析,采用半测地坐标系,导入了具有不变形式的流函数,推志了离心式叶轮内部准三元流动任意流面上函数所应满足的偏微分方程和定解条件,并运用伽辽金方法建立了相应的有限元方程。对离心式叶轮回转面上流动进行了计算,数值计算结果正确地揭示了离心式叶轮内部的流动规律。     

Kinematic analysis of a 5-R SP parallel mechanism with?centralized motion

The paper presents a kinematic analysis of a parallel mechanism, referred to here as a mechanism with centralized motion. The paper includes a proof, based on the geometry of the mechanism, that the platform exhibits centralized motion. An interesting feature of this parallel mechanism is that it is partially collapsible which may be beneficial in practical applications where storage space is limited. The platform is connected to a base, regarded as fixed in this paper, by five identical legs where each leg is a three-link chain connected by a revolute joint, a spherical joint, and a prismatic joint. The result is that the platform has a screw motion about an axis which is perpendicular to the base and passes through the centroids of the base and the platform, for all positions of the platform. The pitch of the instantaneous screw depends on the platform assembly configuration and is a function of the platform position and orientation. To complete the kinematic study, the paper includes closed-form solutions to the inverse and forward position and velocity problems. Finally, the paper includes several numerical examples to illustrate some of the key features of this novel parallel mechanism.     

Analysis of Wet Pressing of Paper: The Three-Phase Model. Part II: Compressible Air Case

In this study we consider a model of wet pressing of paper. We use the techniques and results from the first part of this paper, where a simplified model is studied in details. The model is, using suitable transformation, rewritten in the standard parabolic-hyperbolic form. Numerical solution for typical example is given and the effects of plastic deformations of paper are investigated. Finally, the model is employed to adres the problem of choosing an optimal pressing regime.     

An approximate method for determing the velocity profile in a laminar boundary-layer on flat plate

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄｔｈｅＳｅｌｅｃｔｉｏｎｏｆｔｈｅＴｒｉａｌＶｅｌｏｃｉｔｙＰｒｏｆｉｌｅＦｕｎｃｔｉｏｎＴｈｅｋｅｙｏｆｔｈｅｉｎｔｅｇｒａｔｉｏｎｍｅｔｈｏｄｏｆｔｈｅｌａｍｉｎａｒｂｏｕｎｄａｒｙ＿ｌａｙｅｒｏｎａｆｌａｔｐｌａ...     

圆盘状裂纹前缘塑性区尺寸及张开位移估计

将Ｄｕｇｄａｌｅ模型推广到三维裂纹问题计算了圆盘状裂纹前缘塑性区尺寸,并结合断裂力学中的Ｂａｒｅｎｂｌａｔｔ－Ｄｕｇｄａｌｅ裂纹模型和三维Ｊ－积分原理计算了圆盘状裂纹前缘张开位移,得到了Ｊ－积分与裂纹张开位移的关系,最后用非线性有限元方法对圆盘状裂纹的前缘塑性区尺寸作了数值分析,确定了公式中的未知常数,并对其正确性作了数值验证,本文的工作推广了Ｄｕｇｄａｌｅ模型的应用范围。     

The solution of large deflection problem of thin circular plate by the method of composite expansion

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky’s membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.     

同伦分析方法：一种不依赖于小参数的非线性分析方法

本文进一步一般化了作者所提出的一种新的非线性分析方法，称为“同伦分析方法”。“同伦分析方法”的最大优点，在于其不依赖小参数，从而可求解更多的非线性问题，甚至包括那些不含小参数的问题。本文给出了几个应用实例，以说明“同伦分析方法”的有效性及巨大的潜力。     

构造几何不敏感四边形膜元的广义协调方法

许多有限元模型在规则网格下具有很高的精度，但当网格畸变程度增大时，其计算精度也随之迅速下降．如何构造出对网格畸变不敏感的单元，长期以来是人们十分关注的课题．本文应用作者早期提出的广义协调方法，构造出具有平面内旋转自由度的任意四边形膜元．该单元不仅列式简洁，而且具有对网格畸变极不敏感的优异性能，为构造对网格畸变不敏感的优质单元提供了一个通用方法