改进Guyan～递推减缩技术

本文基于广义逆技术和逐级逼近思想，既建立了精度显著提高的改进Ｇｕｙａｎ减缩法，又提出了“物理型”近似减缩技术方面精度最好的准动态Ｋ级递推减缩公式，然而这些方法的执行时间却与其它“同一级”方法大抵相同，因此说，本方为工程界提供了至今综合效果最好的一类准动态模型减缩技术。     

改进Guyan～递推减缩技术

本文基于广义逆技术和逐级逼近思想,既建立了精度显著提高的改进Guyan减缩法,又提出了“物理型”近似减缩技术方面精度最好的准动态k级速推减缩公式,然而这些方法的执行时间却与其它“同一级”方法大抵相同．因此说,本方为工程界提供了至今综合效果最好的一类准动态模型减缩技术。     

GPSSA误差建模和对组合导航系统性能的影响

本文探讨了ＳＡ建模，即采用ＦＦＴ对ＴＡＮＳ－２接收机实测的ＧＰＳ静态定位误差样本作功率谱分析，并通过最小二乘拟合，获得ＳＡ的平稳线性模型；本文还用车载组合导航系统的仿真结果验证了近似模型的有效性。     

基于弹性动力学变分原理的模态综合法研究

视子结构为一包含许多内自由度的“大的元素”,子结构界面为“元素的边界”。本文基于弹性动力学的变分原理对界面的要求,选取模态集,导出了位移协调、位移杂交、应力平衡及应力杂交四种子结构模型;定义了有关模态贡献因子,给出模态减缩原则;并讨论了结果误差、提高精度的方法及问题的收敛性。     

弹塑性结构分析的减缩方法

1.引言通过对大量复杂结构作弹塑性计算发现:常用的弹塑性分析数值方法,如初载荷法和切线刚度法等,即使在目前的大型计算机上也仍需要大量的上机时间,因而十分昂贵。减缩方法通常是把当代有限元与经典的Rayleungh—Rite法结合起来的杂交方法。这种方法保留了有限元的模型通用性,同时通过,Rayleungh—Rite法近似大量地降低自由度,文献[3]对非线性问题的减缩方法进行了研究,但是,文献[3]利用摄动技术提出的减缩方法有如下缺陷:(1)误差较大;(2)减缩基本向量形成不便,需要计算高阶导     

力法分析的重分析及近似重分析技术

基于力法的矩阵平衡方法与变量无关的特性,本文提出了一种减缩基底的力法重分析及近似重分析技术。因为实际结构的静不定度一般都比较低,这些重分析技术显著提高了结构优化设计过程的计算效率。用几个桁架结构为例来说明所提出方法的原理与效用;重分析及近似重分析所用的时间仅分别为原分析时间的20～30％和8～15％。     

分析层状半空间对入射地震波响应的改进模型

采用层内位移线性近似的薄层元及基岩半空间刚度的Ｔａｙｌｏｒ级数展开技术，利用基岩地震动三分量反算入射波振幅，建立了层状半空间场地地震波响应分析的一种改进模型，分析了层状半空间对倾斜入射ＳＨ，ＳＶ和Ｐ波的动力响应．结果表明，本文模型不仅具有较高精度，而且非常便于数值处理和计算机编程     

减缩误差与减缩基矢量

对于线性或非线性系统振动方程，可采用自由度减缩降低其规模，再运用Ｎｅｗｍａｒｋ方法或Ｎｅｗｍａｒｋ－Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ方法求解其动态响应，关键在于如何挑选合适的减缩基矢量，并了解减缩的影响。对于一般线性减缩变换，本文通过比较变换前后分别得到的位移响应，给出了误差表达式。     

GPS／SINS组合导航系统的动基座快速初始对准方法

—本文首先建立了ＳＩＮＳ的误差模型，并对系统模型进行了可观测性分析，然后基于ＳＩＮＳ误差模型的特点，通过对所采用卡尔曼滤波器仿真结果的分析，提出了一种快速估计方位失准角Ｄ的方法，从而大大缩短了初始对准时间，提高了对准速度。最后计算机仿真结果表明了该方法的有效性。     

精化直接刚度法与不协调模式

基于不协调元的收敛条件，建立了精化直接刚度法（ＲＤＳＭ）所对应的不协调位移模式，从而使ＲＤＳＭ成为建立单变量不协调元的有实用性的一般方法。     

Holographic tomography by SART and it's application to reconstruction of 3D temperature distribution

Application of holographic tomography to reconstruction of 3D asymmetric temperature distribution is experimentally and numerically investigated. A new simultaneous algebraic reconstruction technique (SART) code for holographic tomography is presented. Important features of SART for reconstruction of temperature field were evaluated using numerical model functions. Data from diffuse-illumination holographic interferograms obtained at twenty different view directions and with 40° range of view angles were used to reconstruct a 3D thermal flow field by SART method. An average reconstruction error of about 5% is estimated. The ability to reconstruct the 3D field using a limited viewing range implies that SART is especially suitable for the holographic tomography of aerodynamic density field.

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Holografische Tomographie mit Simultaneous Algebraic Reconstruction Technik (SART) und ihre Anwendung zur Rekonstruktion von 3-dimensionalen Temperaturverteilungen

Zusammenfassung Die Anwendung der holografischen Tomographie zur Rekonstruktion von 3-dimensionalen asymetrischen Temperaturverteilungen wird experimentiell und numerisch untersucht. Eine neue simultane algebraische Rekonstruktionstechnik (SART) für holografische Tomographie wird beschrieben. Wichtige Eigenschaften der SART zur Rekonstruktion von Temperaturfeldern wurden unter Verwendung numerischer Modellfunktionen ausgewertet. Die numerische Analyse zeigt, daß die SART eine zuverlässigere, stabilere und wirksamere Methode zur holografischen Tomographie bietet.Die Daten von holografischen Interferogrammen mit diffuser Beleuchtung, die aus zwanzig verschiedenen Beobachtungsrichtungen und innerhalb eines Beobachtungswinkels von 40° erhalten wurden, dienten zur Rekonstruktion eines 3-dimensionalen Temperaturfeldes mit der SART-Methode. Der durchschnittliche Rekonstruktionsfehler wird mit 5% geschätzt. Die Fähigkeit 3-dimensionale Felder mit beschränkten Beobachtungswinkeln zu rekonstruieren weist die besondere Fähigkeit des SART für die holografische Tomographie von aerodynamischen Dichtefeldern nach.

     

Hopf bifurcations through delay in pilot reaction in a longitudinal flight

The paper is devoted to the study of pilot induced oscillations in the landing transition between the approach task and flare to touch-down. These oscillations are proved to appear in a longitudinal flight model when the delay in pilot’s reactions exceeds a certain threshold for which the stability of equilibria is lost and a Hopf bifurcation appears. The formulae needed to compute the Lyapunov coefficient and an approximation of the solution are developed for the delay differential equations that model the pilot–vehicle interaction in landing task. These are applied for a concrete model.     

On the Darcy–Brinkman–Boussinesq Flow in a Thin Channel with Irregularities

In this paper, we investigate the effects of a small boundary perturbation on the non-isothermal fluid flow through a thin channel filled with porous medium. Starting from the Darcy–Brinkman–Boussinesq system and employing asymptotic analysis, we derive a higher-order effective model given by the explicit formulae. To observe the effects of the boundary irregularities, we numerically visualize the asymptotic approximation for the temperature, whereas the justification and the order of accuracy of the model is provided by the theoretical error analysis.

     

On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound

An interface crack between two semi-infinite piezoelectric spaces under the action of remote mixed mode loading and electric flux is considered. The properties of the materials, loading and crack geometry admit to consider a two-dimensional problem in the plane perpendicular to the crack front. The crack is assumed to be free from mechanical loading and the limited permeable electric condition holds true. Assuming the electric flux is constant along the crack area, using the known presentations of all electromechanical fields via a piecewise holomorphic vector function, the problem is reduced to a vector Hilbert problem and solved in an analytical way. Clear analytical expressions for stresses and electric displacement as well as for stress and electric intensity factors are derived. As a particular case, a crack in a homogeneous piezoelectric material is considered and exact analytical formulae are presented for this case. The numerical analysis of the obtained formulae showed that for small values of the electric flux the model of a completely permeable crack can be used for any real crack permeability’s. The validity of such an approximation decreases with increase in the mechanical loading and especially of the electric flux.     

Reflection and refraction of plane quasi-P waves at a corrugated interface between distinct triclinic elastic half spaces

The reflection and refraction pattern of elastic waves at a corrugated interface between two triclinic half-spaces is discussed. The incident wave is taken to be the cause of the interface disturbance and the reflected and refracted waves are effects. This leads to the causality requirement that the reflected and refracted waves must propagate away from the interface. Closed form expressions of reflection and transmission coefficients are derived using Rayleigh’s method of approximation. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The analytical expressions of all the three phase velocities of qP, qSV and qSH waves have been derived. The variation of reflection and refraction coefficients with the angle of incidence and also with the corrugation parameter is shown. In this paper we have developed Graphical User Interface (GUI) Software in MATLAB which shows the variation of reflection and refraction coefficients with respect to incident angle and corrugation parameter. This software can be generalized to show the variation of reflection and refraction coefficients. Numerical computations are performed for a scientific model and the results obtained are shown graphically.     

弹性力学的一种边界无单元法

首先对移动最小二乘副近法进行了研究，针对其容易形成病态方程的缺点，提出了以带权的正交函数作为基函数的方法－改进的移动最小二乘副近法，改进的移动最小二乘逼近法比原方法计算量小，精度高，且不会形成病态方程组，然后，将弹性力学的边界积分方程方法与改进的移动最小二乘逼近法结合，提出了弹性力学的一种边界无单元法，这种边界无单元法法是边界积分方程的无网格方法，与原有的边界积分方程的无网格方法相比，该方法直接采用节点变量的真实解为基本未知量，是边界积分方程无网格方法的直接解法，更容易引入界条件，且具有更高的精度，最后给出了弹性力学的边界无单元法的数值算例，并与原有的边界积分方程的无网格方法进行了较为详细的比较和讨论。     

Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flow is governed by the prescribed pressure drop between pipe’s ends. Starting from the dimensionless Darcy–Brinkman–Boussinesq system, we formally derive a macroscopic model describing the effective flow at small Brinkman–Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model.     

Reduced numerical modeling of flows involving liquid-crystalline polymers

Kinetic theory models involving the Fokker–Planck equation can be accurately discretized using a mesh support (Finite Elements, Finite Differences, Finite Volumes, Spectral Techniques, …). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function has only local support and is related to a node that defines the associated degree of freedom. In the technique proposed here, a reduced approximation basis is constructed. The new shape functions have extended support and are defined in the whole domain in an appropriate manner (the most characteristic functions related to the model solution). Thus, the number of degrees of freedom involved in the solution of the Fokker–Planck equation is very significantly reduced. The construction of those new approximation functions is done with an ‘a priori’ approach, which combines a basis reduction (using the Karhunen–Loève decomposition) with a basis enrichment based on the use of some Krylov subspaces. This paper analyzes the application of model reduction to the simulation of non-linear kinetic theory models involving complex behaviors, such as those coming from stability analysis, complex geometries and coupled models. We apply our model reduction approach to the Doi's classical constitutive equation for viscoelasticity of liquid-crystalline polymer.     

ON THE FINITE DISPLACEMENT PROBLEM OF A HOLLOW SPHERE UNDER INTERNAL AND EXTERNAL PRESSURES

Taking advantage of successive approximations the present boundary-value problemis solved.We find the first-order and second-order solutions,and there fore we obtain theformulae in the second approximatior for the displacement,strain,and stress fields.     

Free damped vibrations of linear viscoelastic materials

Summary A mechanical system consisting of an inert component, attached to a linear viscoelastic spring, is studied theoretically. Basic assumptions about the viscoelastic material areBoltzmann's superposition principle and a positive discrete relaxation spectrum. The equation of motion and its formal solution for free damped vibrations are discussed.The theory focusses on the determination of the complex dynamic modulus, defined for undamped sinusoidal vibrations, by free damped vibrations. Simple approximation formulae to calculate the dynamic modulus from free vibration data, i. e. eigen frequency and logarithmic decrement, are given; upper limits for the approximation errors could be derived.Paper read at the Annual Meeting of the German Rheologists, Berlin-Dahlem June 7–10, 1966.