Fundamental solutions and numerical methods for flow problems

An approach for the numerical solution of flow problems based on the concept of fundamental solutions of differential equations is described. This approach uses the finite element methodology but does not rely on the concept of variational principle or that of residuals. The approach is shown to be well-suited for many types of flow problems. Various applications of this approach are discussed in this paper, with particular emphasis placed on the solution of potential flows and viscous flows containing appreciable regions of separation.     

Approximate Transformation Groups and Renormgroup Symmetries

An approach that makes use of approximate group symmetries forcalculating renormgroup symmetries for boundary-value problems inmathematical physics is discussed. A comparison of exact and approximatesolutions for the nonlinear Shrödinger equation and quasi-Chaplyginequations is presented that demonstrates promising features of thesuggested approach.     

Effective non-reflective boundary for Lamb waves: Theory,finite element implementation,and applications

This article presents a new approach to designing non-reflective boundary (NRB) for inhibiting Lamb wave reflections at structural boundaries. Our NRB approach can be effectively and conveniently implemented in commercial finite element (FE) codes. The paper starts with a review of the state of the art: (a) the absorbing layers by increasing damping (ALID) approach; and (b) the Lysmer–Kuhlemeyer absorbing boundary conditions (LK ABC) approach is briefly presented and its inadequacy for Lamb wave applications is explained. Hence, we propose a modified Lysmer–Kuhlemeyer approach to be used in the NRB design for Lamb wave problems; we call our approach MLK NRB. The implementation of this MLK NRB was realized using the spring–damper elements which are available in most commercial FE codes. Optimized implementation parameters are developed in order to achieve the best performance for Lamb wave absorption. Our MLK NRB approach is compared with the state of the art ALID and LK ABC methods. Our MLK NRB shows better performance than ALID and LK ABC for all Lamb modes in the thin-plate structures considered in our examples. Our MLK NRB approach is also advantageous at low frequencies and at cut-off frequencies, where extremely long wavelengths exist. A comprehensive study with various design parameters and plate thicknesses which illustrates the advantages and limitations of our MLK NRB approach is presented. MLK NRB applications for both transient analysis in time domain and harmonic analysis in frequency domain are illustrated. The article finishes with conclusions and suggestions for future work.     

Fracture and stability of materials and structural members with cracks: approaches and results

A new alternative approach to fracture problems for materials and structural elements with cracks is set out. It is based on the mechanism of local instability near defects. The approach is used to study the fracture of materials compressed along interacting cracks and the fracture of thin structural members with cracks under tension with allowance for local buckling.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 18–64, December 2004.     

Sigma transformation and ALE formulation for three‐dimensional free surface flows

In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian–Eulerian (ALE) approach. For that purpose we introduce the ALE‐sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd.     

Static and dynamic studies for coupling discrete and continuum media; Application to a simple railway track model

In this paper, we present a formulation for coupling discrete and continuum models for both dynamic and static analyses. This kind of formulation offers the possibility of carrying out better simulations of material properties than the discrete calculations, and with both larger length scales and longer times. Using only a discrete approach to simulate a large medium composed of many degrees of freedom seems very difficult in terms of calculation and implementation. Moreover, using only a continuum approach does not give an accurate solution in a zone where particular and localized phenomena can occur. A direct application of our coupling approach to the case of railway track models subjected to an external load, is proposed for its validation.     

Linear and nonlinear approaches and digital signal processing in aeroacoustics

The linear and nonlinear approaches to the calculation of small acoustic disturbance propagation and evolution in nonuniform flows are compared. In the conventional linear approach it is the linearized equations of time-dependent, ideal (inviscid and non-heat-conducting) or viscous gas flow that are integrated. In the nonlinear approach the original nonlinear equations governing the same time-dependent flow (Euler equations for an ideal gas) are integrated; these are the same equations that, together with time relaxation procedure, are used in the linear approach for calculating the stationary background. It is shown that the application of digital signal processing, widely used in acoustic experiments, makes it possible to isolate the harmonic acoustic waves from the results of integration of the nonlinear equations, though their intensity is smaller than that of the noise due to computational errors, including inadequate attainment of the stationary background.     

Structural-kinetic stochastic model of fracture and durability of brittle materials

structural-kinetic stochastic approach to the study of the brittle fracture of materials was developed. This approach was used to determine the conditions for passive (latent) and active development of brittle fracture. An asymptotic expression was obtained for the average durability of brittle materials at low stresses at which passive development of fracture occurs.     

Solution of electromagnetic scattering and radiation problems using a spectral domain appoach–a review

In this paper we present a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.     

Higher Conditional Symmetry and Reduction of Initial Value Problems

We give the exposition of a generalized symmetry approach toreduction of initial value problems for nonlinear evolutionequations in one spatial variable. Using this approach we classifythe initial value problems for third-order evolution equationsthat admit reduction to Cauchy problems for systems of twoordinary differential equations. These reductions are shown tocorrespond to higher conditional symmetries admitted by thecorresponding nonlinear evolution equations.     

Multiscale aspects of heat and mass transfer during drying

The macroscopic formulation of coupled heat and mass transfer has been widely used during the past two decades to model and simulate the drying of one single piece of product, including the case of internal vaporization. However, more often than expected, the macroscopic approach fails and several scales have to be considered at the same time. This paper is devoted to multiscale approaches to transfer in porous media, with particular attention to drying. The change of scale, namely homogenization, is presented first and used as a generic approach able to supply parameter values to the macroscopic formulation. The need for a real multiscale approach is then exemplified by some experimental observations. Such an approach is required as soon as thermodynamic equilibrium is not ensured at the microscopic scale. A stepwise presentation is proposed to formulate such situations.     

Driving Potentials of Heat and Mass Transport in Porous Building Materials: A Comparison Between General Linear,Thermodynamic and Micromechanical Derivation Schemes

In systems of coupled transport processes the question of the appropriate driving potentials is a point of discussion. In this article, three different approaches to derive models for transport currents are systematically compared. According to a general linear approach, an arbitrary full set of independent state variables and material properties is sufficient to describe any transport current. This approach is derived here from a symmetry principle. Thermodynamic and micromechanical approaches are more complex and even less general, but they allow additional statements about the transport coefficients and they reduce the number of transport processes. In the thermodynamic approach the additional information stems from the calculation of the entropy production rate; the micromechanical approach involves a microphysical model of the considered porous system. As a practical example, the three derivation schemes are applied to the often-encountered case of non-hysteretic heat and moisture transport in homogeneous building materials. It is shown, how the general state variables of a porous system are reduced to only two. Then from the general linear approach it can be seen, that all equations for the moisture transport current using a main driving potential (e.g. moisture content, vapour pressure, chemical potential) and an independent secondary driving potential (e.g. temperature, liquid pressure) are equivalent, without recurrence to the thermodynamic or micromechanical approach. However, the transport coefficients are arbitrary phenomenological functions depending on the two state variables. Based on a literature survey it is shown, which additional statements can be made in the thermodynamic and in the micromechanical approach. The latter yields the pressure-driven model (vapour and liquid pressure as the two driving potentials). Finally it is shown, what is to be expected, if in more complex systems the number of state variables increases.     

Simultaneous free-surface deformation and near-surface velocity measurements

 A newly developed non-intrusive approach has been devised for studying near-surface flows where it is important to be able to construct correlations between small-sloped free-surface deformations and near-surface velocities. This method combines digital particle image velocimetry (DPIV) and the reflective mode of the free-surface gradient detector (FSGD) technique into a single measurement system, providing us with an approach to be able to characterize correlations between elevation and kinematic properties, such as velocity and vorticity, which is essential in understanding near surface turbulence. Furthermore, as the free-surface elevation is directly proportional to the pressure for low Froude number flows, this method will allow for the measurement of pressure near the free surface. This will also be useful in calculating the pressure-velocity term in the turbulent kinetic energy equation for near-surface flows. The approach is explained and demonstrated by measuring these correlations for a vertical shear layer intersecting a free surface. Received: 2 August 1999/Accepted: 23 July 2000     

结合数码显微镜的数字散斑相关方法精度分析及应用

结合数字散斑相关方法和一种新型的显微镜数码显微镜,提出了一种测量多晶材料晶粒尺度面内变形的新方法,并通过零变形校准实验、重聚焦实验和平移实验等一系列验证实验分析了该方法的精度和实用性.作为应用实例,对一种镍基合金试件进行了单向拉伸和疲劳实验,得到了晶粒尺度下具有较大应变梯度的应变分布图像.结果表明,该方法能够得到精确的位移测量数据,是一种理想的测量晶粒尺度变形的光测方法.     

复合材料构件损伤类型识别的一种方法

复合材料构件在使用过程中会产生脱层、内部裂纹、裂缝等损伤，这些损伤会引起构件动态特性的变化。本文提出了通过测取构件的动态特性，结合波形分析和模式识别技术进行复合材料损伤检测和损伤类型识别的方法。在比较了飞机环境噪声信号和周期脉冲信号的优缺点的基础上，提出使用周期脉冲信号作为构件的激振信号，来进行构件动态特性的测量。本文的研究中制作了多种类型的损伤试件，进行了实验，已发现显著特征，能够对构件的多种类型损伤进行识别     

Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity

A triaxial constitutive law for concrete within the framework of isotropic damage combined with plasticity is proposed in this paper. It covers typical characteristics of concrete like non-linear uniaxial compression and tension, bi- and triaxial failure criteria and dilatancy with a unified strain-based approach. Thus, this model is quite simple and especially suitable for strain-driven methods like common finite elements. It is complemented with a regularization method based on the crack band approach. A further issue is discussed with procedures for the model parameter determination for a wide range of concrete grades. The application of the model is demonstrated with typical benchmark tests for plain concrete.     

Construction of approximate solutions of systems of differential equations with parameters and restrictions

We propose a new approach to the investigation of boundary-value problems for systems of differential equations with parameters and restrictions. This approach uses ideas of both iterative and projection methods. We develop and substantiate a new modification of the projection-iterative method for the construction of approximate solutions of boundary-value problems that has significant advantages over the existing versions of the method.     

基于傅里叶级数的汽轮机叶根轮槽结构设计

提出了一种基于傅里叶级数的枞树型叶根轮槽的优化设计方法。在叶根轮槽构型表征方面,采用傅里叶级数-直线法,与传统的圆弧-直线法相比,不但具有高保真度和完备性,还扩大了优化的搜索空间,减少了设计变量数目,有效降低计算代价。在优化设计方面,为避免以最小化峰值应力为目标函数引起的迭代震荡和不收敛现象,采用KS函数凝聚应力值,降低了优化问题的非线性程度,保证优化快速稳定收敛。以三齿枞树型叶根轮槽为实例,优化结果表明,傅里叶级数-直线法和KS凝聚法优化可有效降低汽轮机叶根轮槽的应力水平,提高汽轮机结构的可靠性。同时,提出的结构表征和优化设计方法具有较高的通用性和实际工程应用价值,可方便扩展至其他工程结构型线设计。     

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

IntroductionExtensive research works have been published for solving nonlinear mathematicprogramming problems.Nonetheless,it is still difficult to find an effective and universalapproach for general programming problems with multiple design variables and …