确定应力函数的一种简单方法

在归纳弹性力学平面问题各种选择应力函数方法的基础上,对于狭长矩形截面梁,提出了一种新的确定应力函数的方法. 该方法简单、实用,克服了选择应力函数的盲目性.在弹性力学教学中有一定参考价值.     

Applications of the finite volumes method for complex flows: From the theory to the practice

In this short paper, we recall some well-known results on hyperbolic systems of conservation laws. We introduce the Godunov finite volume scheme for their approximations. We then present two recent applications to multiphase flows: the computation of a wave breaking and the construction of entropic schemes for phase transition.     

A general method for the determination of appproximations to the spectral distributions from the dynamic response functions

Rheologica Acta - A method, based on the logarithmic differentiation of the dynamic response functions with respect to frequency, is presented which is more general than the Stieltjes transform...     

Gear tooth stress analysis by the complex potentials method

The complex potentials method of plane elasticity theory is applied to spur gear stress analysis. The concept is that the stress field in a gear tooth loaded by a point force can be obtained using the Boussinesq solution and a transformation function mapping a bell-shaped curve approximating the real tooth shape in the z-plane into the semi-infinite ζ-plane. The main features of an original computer code implementing this formulation are presented along with applications.

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Sommario Dopo un'illustrazione di come lo stato di sollectitazione in un dente di una ruota dentata a denti diritti puo' essere ottenuta mediane il metodo delle trasformazioni conformi e dei potenziali complessi della teoria dell'elasticita' piana, viene presentata la struttura di un codice di calcolo originale che implementa questo approccio ed alcune applicazioni.

     

A contour integral method for dynamic stress intensity factors

The contour integral method previously used to determine static stress intensity factors is applied to dynamic crack problems. The required derivatives of the traction in the reference problem are obtained numerically by the displacement discontinuity method. Stress intensity factors are determined by an integral around a contour which contains a crack tip. If the contour is chosen as the outer boundary of the body, the stress intensity factor is obtained from the boundary values of traction and displacement. The advantage of this path-independent integral is that it yields directly both the opening-mode and sliding-mode stress intensity factors for a straight crack. For dynamic problems, Laplace transforms are used and the dynamic stress intensity factors in the time domain are determined by Durbin's inversion method. An indirect boundary element method, incorporating both displacement discontinuity and fictitious load techniques, is used to determine the boundary or contour values of traction and displacement numerically.     

Applications of the dynamic mode decomposition

The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow.     

复杂链式结构动力分析中的直接迁移子结构方法

本文将频响函数和迁移矩阵引入子结构方法中，提出简单高效的直接迁移子结构方法。当子结构中内部自由度很大时，用这种方法进行链武结构的动力特性分析和求解谐和激励响应时依然能保持很高的计算效率和精度。而且有限元分析或试验得到的各子结构数据相互独立，因此对结构的不同组合进行分析只需改变相应连接条件；当结构有局部修改时也只需修正相应子结构的数据。这些特性对复杂链武结构动力优化和抗震设计问题十分有利。最后的数值算例说明了所提出方法的优越性及其在工程中的实用性。     

Scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout

Using the complex variable method and conformal mapping, scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied. The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique, the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations. As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular, elliptic cutout are graphically presented in sequence. The project supported by the National Natural Science Foundation of China     

Analysis of dynamic mixed mode stress fields in bimaterials by the method of caustics

The equations of caustics for dynamically extending curvilinear interface cracks are derived where optical isotropy and anisotropy of the material have been considered, respectively. The equations have been obtained by applying the method of generalized complex potentials. Moreover, an algorithm for the determination of stress intensity factors from experimentally obtained caustics is presented for the case of dynamic crack extension.     

THE CALCULATION OF THE MULTIPLY－CONNECTED ELASTIC PLANE PROBLEMS BY MEANS OF STRESS FUNCTIONS OF MULTIPLE COMPLEX VARIABLES

ＴＨＥＣＡＬＣＵＬＡＴＩＯＮＯＦＴＨＥＭＵＬＴＩＰＬＹ－ＣＯＮＮＥＣＴＥＤＥＬＡＳＴＩＣＰＬＡＮＥＰＲＯＢＬＥＭＳＢＹＭＥＡＮＳＯＦＳＴＲＥＳＳＦＵＮＣＴＩＯＮＳＯＦＭＵＬＴＩＰＬＥＣＯＭＰＬＥＸＶＡＲＩＡＢＬＥＳｗａｎｇＬｉｎｄｉａｎｇ（王林江）Ｌ...     

复杂加载下材料动态响应的数据反演技术

对梯度飞片撞击复杂路径加载实验中,具有冲击加载-斜波加载-斜波卸载的金属铝材料的波剖面信息进行了数据分析和处理,不同加载路径用不同力学响应关系式进行描述,以铝材料\氟化锂窗口界面处的速度剖面作为初始条件,用反积分方法向铝材料内部直至加载面进行了反向计算,所得计算结果与正向计算结果比较吻合较好。计算得到了材料内能、温度、声速及应变率在复杂路径加载中变化规律,并给出了材料的P-V参考线,所得结果可与正向积分计算结果相互校核。     

Applications of tensor functions to the formulation of yield criteria for anisotropic materials

Yielding of anisotropic materials can be characterized by yield criteria which are scalar-valued functions of the stress tensor and of material tensors, for instance, of rank two or four, characterizing the anisotropic properties of the material. Because of the requirement of invariance, a yield criterion can be expressed as a single-valued function of the integrity basis. In finding an integrity basis involving the stress tensor and material tensors, the constitutive equations are first formulated based on the tensor function theory. Since the plastic work characterizes the yield process, we read from this scalar expression the essential invariants to formulate a yield criterion. Some examples for practical use are discussed in detail.     

Elastic wave scattering and dynamic stress concentrations in exponential graded materials with two elliptic holes

Based on the elastodynamics, employing complex functions and conformal mapping methods, and local coordinates, the scattering of elastic waves and dynamic stress concentrations in infinite exponential graded materials with two holes are investigated. A general solution of the problem and expression satisfying the given boundary conditions are derived. The problem can be reduced to the solution of an infinite system of algebraic equations. As an example, numerical results of dynamic stress concentration factors for two elliptic holes in exponential graded materials are presented, and the influence of incident wave number and holes spacing on dynamic stress distributions is analyzed.     

Calculation of stresses in a multiply-connected anisotropic plate using stress functions of multiple complex variables

On the basis of anisotropic mathematical elasticity, using multiple conformal representations, the stress functions of multiple complex variables for an infinite multiply-connected anisotropic plate are derived. The functions are developed in Fourier series on unit circles, and the unknown coefficients of the functions are determined by undetermined coefficients method. Then the stresses in the plate can be calculated. A plate containing multiple elliptical holes or cracks is discussed, and the corresponding FORTRAN77 program is developed. Five examples are given. The results show that this method is very effective and convenient. The project supported by Aeronautical Science Foundation of China     

Extension of the line element-less method to dynamic problems

Meccanica - The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized...     

A general method for obtaining shear stress and normal stress functions from parallel disk rheometry data

The problems of converting the torque and normal force versus rim shear rate data generated by parallel disk rheometers into shear stress and normal stress difference as functions of shear rate are formulated as two independent integral equations of the first kind. Tikhonov regularization is used to obtain approximate solutions of these equations. This way of handling parallel disk rheometer data has the advantage that it is independent of the rheological constitutive equation and noise amplification is kept under control by the user-specified parameter in Tikhonov regularization. If the fluid under test exhibits a yield stress, Tikhonov regularization computation will simultaneously give an estimate of the yield stress. The performance of this method is demonstrated by applying it to a number of data sets taken from the published literature and to laboratory measurements conducted specifically for this investigation.     

Chebyshev analysis of stress concentrations

A specialized method of Chebyshev polynomial curve fitting is developed for stress-concentration analysis. The method is shown to be both economical and highly accurate.     

An approximation method to relate the linear viscoelastic functions

A method based on rational approximations is presented to interpolate the data from sinusoidal experiments in linear viscoelasticity. Bounds to the corresponding dynamical function and a discrete approximation to the spectrum are established. From this approximation the related viscoelastic functions can be computed. The method is checked by considering two theoretical models of physical interest and a satisfactory accuracy is achieved.     

Determination of stress intensity factors by the dynamic method of caustics for optically isotropic materials

Summary The method of caustics is an optical method for experimental determination of stress intensity factors at crack tips. The paper generalizes the method of caustics to dynamic situations and the dynamic stress intensity factor at the tip of a running crack in an optically isotropic material is determined. Higher order terms of the Westergaard type stress functions are included and their effect on the shape and extension of the highly constrained zone surrounding a crack tip is discussed. Analytical equations for the caustic are presented. For the singular solution it is found that dynamic K-values associated with larger shadow spots are lower than their static counterparts. Higher order terms induce a generalized evaluation formula for the stress intensity factor where powers of the order n + 5/2 (n = 0, ...) of the caustic diameter are present. The effect of superposition of dynamic and higher order term corrections on the K-value is discussed. The dynamic correction implies that the K(c)-characteristic (c ... crack velocity) is to be modified towards lower values of K. This correction is negligible for small and moderate crack velocities justifying the use of static equations for practical purposes. The K-values for crack branching, however, turn out to be smaller than assumed hitherto, a fact which is of particular interest in connection with SEN-type fracture test specimens.

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Übersicht Die schattenoptische Methode — auch Methode der Kaustik genannt — ist ein wichtiges Verfahren zur experimentellen Bestimmung des Spannungsintensitätsfaktors K an einer Rißspitze. Die vorliegende Arbeit verallgemeinert die schattenoptische Methode auf dynamische Rißausbreitungsvorgänge in optisch isotropen Materialien. Die Bestimmung des dynamischen Spannungsintensitätsfaktors an der Rißspitze schnellaufender Risse aus der Geometrie des Schattenflecks wird aufgezeigt und eine dynamische Korrekturfunktion angegeben.Glieder höherer Ordnung in den Westergaardschen Spannungsfunktionen werden beibehalten und deren Einfluß auf die Gestalt und Ausdehnung der Zone großer Verzerrungen um die Rißspitze sowie die Form und Größe der Kaustik werden untersucht. Bei Berücksichtigung des alleinigen singulären Anteiles des Spannungsfeldes um die Rißspitze zeigen die Rechnungen, daß die mit laufenden Rissen verbundenen K-Werte kleiner als die entsprechenden statischen sind, der Unterschied für praktische Zwecke jedoch erst bei Rißgeschwindigkeiten in der Umgebung der Verzweigungsgeschwindigkeit berücksichtigt werden muß.Die Glieder höherer Ordnung beeinflussen die Struktur der Beziehung zwischen Spannungsintensitätsfaktor und Kaustikdurchmesser. Die Auswerteformel, die im (statischen und dynamischen) singulären Fall eine D ^5/2- Abhängigkeit des Spannungsintensitätsfaktors vom Kaustikdurchmesser zeigt, weist bei Berücksichtigung höherer Terme Abhängigkeiten der höheren Ordnungen n + 5/2(n = 1, ...). auf. Die Korrekturfaktoren für die K-Werte, die im singulären Fall nur von der Rißgeschwindigkeit abhängig sind, werden explizite Funktionen des Kaustikdurchmessers. Das Zusammenwirken von dynamischen Effekten und Einflüssen zufolge des nichtsingulären Spannungsfeldanteiles kann bei bestimmten Arten der Probenbelastung und Probengeometrie zu einer erheblichen Korrektur des K-Wertes führen.Im experimentell gewonnenen Schaubild, das die Rißgeschwindigkeit in Abhängigkeit des Spannungsintensitätsfaktors darstellt, verursacht die dynamische Korrektur eine Verschiebung der Kurve zu etwas niedrigeren K-Werten. Dies bedeutet, daß der K-Wert bei der Rißverzweigung kleiner ist als bisher angenommen; eine Tatsache, die besonders in Verbindung mit der SEN-Bruchprobe von Interesse ist.