A closed form solution for falling cylinder viscometers

The paper presents a theory of the flow of a viscous fluid in a falling cylinder viscometer. The velocity profile for the flow in infinite tube and finite tube are obtained in finite form. That allows us to determine quite easily the influence of various parameters involved on the fluid flow and on the motion of the cylinder. Also a formula written in finite form is obtained for the determination of the viscosity coefficient. All these formulae contain a term that can describe the influence of a magnetic field on the motion of the falling cylinder. A comparison of the viscosities determined according to the present theory and with a cone-plate viscometers show a good agreement.     

A closed form solution for the static analysis of continuous skew-curved beams

Summary Based on the principle of superposition, the closed form solution for the static analysis of a continuous skew-curved beam in the most general case of response and loading is presented. Each differential element of the centroidal axis of the beam is given six degrees of freedom: three translations and three rotations. Three internal forces and three internal moments are assumed to act at each point of the centroidal axis of the beam. Finally, the correctness of the method is shown through an application to a special case of a continuous skew-curved beam.

---

Eine geschlossene statische Lösung für den räumlich gekrümmten Durchlaufträger

Zusammenfassung Mit Hilfe des Superpositionsprinzipes wird der allgemeinste Fall von Verformung und Belastung untersucht. Jedes Differentialelement der Schwerachse des Tragbalkens hat sechs Freiheitsgrade, drei Translationen und drei Rotationen. Es wird angenommen, daß drei innere Kräfte und drei innere Momente in jedem Punkt der Schwerachse des Balkens wirken. Die Richtigkeit dieser Methode wird durch Anwendung auf einen Sonderfall gezeigt.

---

---

With 3 Figures     

A closed form solution for the G/M/r machine interference model

This paper solves the machine interference problem in which N different machines are looked after by a team of r operatives. The run time of each machine is assumed to have a general distribution, different for each machine and the repair times are assumed to have a negative exponential distribution with different means for the different machines. An explicit expression for the probability that a particular group of machines is found running in the steady state is derived. From this other useful measures for the system can be obtained. It is shown that these depend on the run time distributions only through the means of those distributions.     

Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans

The purpose of this paper is to develop a process-targeting model for a product with two quality characteristics produced by two processes in series. The first quality characteristic is determined by the setting of the first process, whereas the second quality characteristic depends on the setting of the two processes. The quality of the product is controlled by a single sample inspection plan where inspection is assumed to be error free. The objective of the model is to determine the optimal target for both processes that maximises the profit. A realistic case study is used to demonstrate the utilisation of the model. The results of applying the model indicated that the plant could improve its profit by using optimal process setting and better inspection plans parameters. In addition, sensitivity analysis was performed to study the effect of different parameters on the expected profit and optimal processes means.     

A compound sampling scheme for acceptance testing of concrete

A sampling scheme which consists of the following two sampling rules is considered: (i) the sample mean value of the random samples should not be less than a times the specified standard and (ii) all individual test results should not be less thanb times the specified standard. By varying the constantsa andb and the sampling size, the sampling scheme generates a wide range of operating characteristics (OC) curves. An approximate closed-form solution is proposed for calculating the OC curve of the proposed scheme. Applications of the scheme are also discussed.

---

Resume On considère une procédure d’échantillonnage qui consiste à appliquer les deux règles suivantes: (i) la valeur moyenne d’échantillons pris au hasard ne devrait pas être inférieure àa fois la valeur spécifiée officielle: (ii) tous les résultats d’essai individuels ne devraient pas être inférieurs àb fois la valeur spécifiée officielle. La régle d’échantillonnage proposée présente trois paramètres: la taille de l’éprouvette,n, et les constantesa etb. En faisant varier ces trois paramètres, la procédure d’échantillonnage donne lieu à un vaste éventail de courbes de fonctionnement caractéristique. et permet d’établir une courbe OC acceptable pour le producteur et le consommateur. On peut l’utiliser aussi pour produire une nouvelle règle de réception qui donnera une courbe OC similaire à celle d’une procédure d’échantillonnage existante. On propose une solution approchée pour le calcul de la courbe OC de la procédure proposée. On discute aussi les applications de cette procédure.

     

A closed form solution for the limit moment in the plastic torsion of an elliptical cylinder

Summary A compact, closed form solution is obtained for the limiting torque of a perfectly plastic elliptical cylinder.     

基于土体连续性作用下挡土墙动力响应的显式闭合形式解

挡土墙-土动力相互作用是影响挡土墙地震响应的关键因素.基于连续介质模型分析挡土墙-土动力相互作用是当前主要的研究手段.但当前的连续介质模型无法获得挡土墙-土动力相互作用中各物理量的精确表达式,这对揭示挡土墙地震响应机理产生了阻碍.通过引入最小二乘响应面法改进了一种连续介质模型,并与现有方法进行对比,对地震作用下挡土墙动...     

A closed form solution for linear and nonlinear free vibrations of composite and fiber metal laminated rectangular plates

In this paper, the nonlinear equations of motion for laminated composite rectangular plates based on first order shear deformation theory, which include shear deformation and rotary inertia, have been derived. Then, through introducing a force function, these equations reduced to a set of coupled nonlinear partial differential equations and a compatibility equation. By using the Galerkin method, for the first time, a nonlinear ordinary differential equation is obtained, which includes nonlinear inertia and stiffness terms. By using the multiple time scales method, analytical relations for nonlinear frequency and transverse displacement have been obtained. Results are compared with the literature and good agreement is achieved for both linear and nonlinear frequencies. After proving the validity of our work for isotropic rectangular plates and laminated rectangular plates, linear and nonlinear free vibration of a Fiber Metal Laminate panel have been investigated. Also the effects of some system parameters on the nonlinear frequency have been investigated.     

On closed form solution for the elastic stress field around holes in orthotropic composite plates under in-plane stress conditions

The present paper presents analytical work performed care of the Aerospace Department of the University of Rome ‘La Sapienza’. Using the classical Airy's function solution method the expression of the stress-strain field, in a composite material, has been determined for different simple hole geometries in a closed form. The results have been compared with several extensive finite element calculations that confirm the accuracy of the theoretical solutions found.     

A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio

Various methods have been presented to obtain the effective damping of a symmetric laminated composite. In this paper, modified classical lamination theory based upon the elastic–viscoelastic correspondence principle was utilized by developing the basic damping of Poisson's ratio for accurately predicting the damping of laminated composite beams. The analysis involves an extension of the elastic–viscoelastic approach. Futhermore, Ni and Adams' theory was used for verifying the modified classical lamination theory. Six typical laminated composites with [±θ]_s,[0/θ]_s,[0/±θ/90]_s,[90/±θ/0]_s,[0/90/±θ]_s and [90/0/±θ]_s, stacking sequences were employed for this study. Numerical results have shown that damping values were in some difference among prediction methods over the particular range of fiber orientation.     

Convenient closed form stress intensity factors for common crack configurations

Linear elastic crack-tip solutions for twelve different shapes of cracked body of interest, are given. The purpose is to provide efficient closed formulations of data previously presented in a tabular or graphical manner. The formulae assist the user of fracture mechanics in that they carry out the interpolative step accurately and therefore may be usefully incorporated in other crack computational procedures, such as fatigue crack growth prediction, crack-tip plasticity corrections, etc. The method used to generate the formulae can be applied to other cracked body geometries.

---

Résumé On fournit les solutions linéaires élastiques correspondant aux extrémités de fissures dans le cas de 12 différentes formes de corps fissurés présentant un certain intérêt. Le but de cette étude est de procurer une formulation fermée efficace pour les données présentées antérieurement d'une manière tabulaire ou graphique. Les formules aident l'usager de la mécanique de rupture parce qu'elles effectuent les étapes d'interpolation d'une manière précise et, dès lors, elles peuvent être avantageusement incorporées dans d'autres procédures de calcul de fissure tel que la prédiction de la croissance de fissure de fatigue, les corrections de plasticité aux extrémités d'une fissure, etc... La méthode utilisée pour créer les formules peut être appliquée à d'autres géométries de corps fissuré.

     

Finite strain elastic closed form solutions for some axisymmetric problems

Summary In this paper, rate type constitutive equations using the Jaumann and 2nd Piola-Kirchhoff stress rate are used to develop axisymmetric finite strain, elastic, closed form solutions for a variety of loading conditions. We examined several cases comprizing compression-extension loading conditions, simple shear and cavity expansion conditions. Results from small strain analyses are used to indicate strain ranges for which such analyses will provide satisfactory solutions. For all the cases examined, except simple shear, the 2nd Piola-Kirchhoff stress rate does not appear to be a suitable stress rate to describe a material which follows a rate-type constitutive equation for strains greater than about 40%. The Jaumann stress rate solution shows oscillatory shear stress for axisymmetric simple shear similar to that found earlier by many other authors for rectangular (or cuboidal) condition. Negative excess pore water pressure (suction) at the cavity wall during the expansion of a cylindrical cavity was also observed in Jaumann stress rate solution.     

A closed form theory for calibrating a dual six-port networkanalyzer

The application of a general self-calibration procedure, the so-called TNA (through, network, attenuator) method, to a dual six-port network analyzer is presented for the first time. This innovation results from strictly separating the establishment of the complex measurement ability and the determination of the analyzers system error parameters. As will be seen, the well-known TRL (through, reflect, line) method is a special case of the general TNA technique     

A closed form solution of stress intensity factors for three dimensional finite bodies with unsymmetric cracks by energy release rate method

In this paper, a new semi-analytical, semi-engineering method of close form solution of stress intensity factors for three dimensional finite bodies with unsymmetric cracks is derived by means of the energy release rate method. This method is very time-saving. Hence a complete series of useful results of stress intensity factors can be obtained. The results provided by this method are in good agreement with that of the famous alternating method by which only special cases can be solved.     

A misuse of the EWMA-type statistic in acceptance sampling applications

We study a widely recommended acceptance sampling approach based on the use of an exponentially weighted moving average statistic. A correct mathematical assessment of the resulting sampling plans shows that the required statistical performance cannot be maintained over time. For this reason, these plans are flawed and thus should not be used.     

The economic effect of measurement error on variables acceptance sampling

Considerable attention to the economics of variables acceptance sampling has recently emphasized that the alpha-beta approach to sampling plan design may be far from optimal. Similarly, recent results conclusively show that measurement error manifested as bias (inaccuracy) and imprecision (variability) can have disastrous effects upon the OC curve of a variables sampling plan. This paper quantitatively combines economics and error and clearly illustrates the adverse monetary effects of imperfect measurement in situations where variables acceptance sampling is used     

A closed form solution of stress intensity factors for three-dimensional finite bodies with biaxial unsymmetric cracks by the energy release rate method

In this paper, a new semi-analytical, semi-engineering method of closed form solution for stress intensity factors for three-dimensional finite bodies with unsymrnetric cracks is derived by means of the energy release rate method. This method is very time-saving. Hence a complete series of useful results of stress intensity factors can be obtained. The results provided by this method are in good agreement with those of the famous alternating method by which only special cases can be solved.