Post-critical deformation of flexible laminar shells of revolution under combined loading

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 9, pp. 60–66, September, 1990.     

Experimental study of D16AT alloy deformation under periodic loading

An experimental procedure and results of an experimental study of the kinetics of the strained state of a material under periodic uniaxial loading are reported. Diagrams of the principal components of the total strain tensor for an asymmetric periodic “soft” regime of tension-compression of the samples are presented. Specific features of deformation revealed under periodic asymmetric loading of the samples can be used to formulate a criterion of fatigue fracture of materials and to identify the mechanism of strain hardening of pre-fracture zones in machine elements.     

Reynolds number dependence of two-dimensional laminar co-rotating vortex merging

The paper reports unsteady Navier–Stokes calculations of laminar two-dimensional co-rotating vortex merging for various Reynolds numbers. The unsteady, incompressible two-dimensional Navier–Stokes equations were solved with fourth-order Runge–Kutta temporal discretization and fourth-order symmetric compact schemes for spatial discretization. Calculations of the unsteady Taylor vortex benchmark showed that fourth-order accurate solutions for all primitive variables were indeed achieved. Calculations for a pair of equal-strength co-rotating vortices show good agreement with reported direct numerical simulation and experiments for the evolution of the separation distance and core radius. It is found that the time required for merging is inversely proportional to the square root of the Reynolds number. According to previous experimental research, it was also found that complete merging in laminar regime undergoes four stages with physical meaning. The physical mechanism responsible for the merging process is investigated and it is found that the antisymmetric vorticity dynamics plays an important role until full merging.     

爆炸下球壳变形空间周期分布的理论计算方法

早期研究提出了对振动叠加应变增长现象的解剖式分析方法,进而发现爆炸加载下带扰动源球壳上的弯曲波和壳体变形呈空间周期分布的规律。参考Timoshenko梁的弯曲理论,基于平截面假定和壳体发生较小的弯曲变形的假设,推导出球壳上弯曲波波速和波长的关系,计算得到最短弯曲波和与膜振动频率相近的弯曲波的波速,还结合早期研究提出的壳体变形分布周期与弯曲波波速的关系,计算得到了壳体变形空间分布的周期。结果表明：（1）理论计算结果与数值仿真结果基本吻合,其中弯曲波波速的计算结果与数值仿真结果相差在15%以内,壳体变形空间分布周期的计算结果与数值仿真结果相差在12%以内;（2）弯曲波波长越短,波速越快,当波长无限短时,波速趋于极限值,约为声速的0.574倍。本计算方法为解剖式分析方法提供了一定的理论依据。

     

Conjugated laminar forced convection in ducts with periodic variation of inlet temperature

Conjugated laminar forced convection with parabolic velocity is studied for flow inside both parallel-plate and circular ducts subjected to a periodically varying inlet temperature. The analysis of this classs of problems lead to a Sturm-Liouville type complex eigenvalue problem for which no known solution is available. In this work, a new methodology is presented for a direct solution of such complex eigenvalue problems in the complex domain using the shooting method along with the Runge-Kutta method. The methodology is applicable for solving both laminar and turbulent flow problems; here we consider only the laminar flow with a parabolic velocity profile. The results clearly show that the slug-flow assumption overestimates the phase lag and the Nusselt number. Some benchmark results are also presented for the eigenquantities in tabular form.     

Estimation of the losses in hydrodynamic cascades due to periodic flow unsteadiness

The losses in hydrodynamic cascades caused by periodic flow unsteadiness are theoretically estimated on the assumption that the losses are due to energy expenditure to the formation of unsteady trailing vortices shed from the profiles of the cascades. The trailing vortex intensity is determined within the framework of the inviscid fluid model, by solving the corresponding problems in the linear formulation. The work done on the trailing vortex formation is determined by the increment of the kinetic energy of the flow induced by the corresponding vortices. Examples of calculations are presented for the case of periodic unsteadiness of the flow due to the hydrodynamic interaction of the cascades. The calculated results are compared with the experimental data.     

Direct determination of periodic solutions of mechanical dynamical systems

Summary Methods for the direct determination of stationary and periodic solutions of systems whose behaviour is described by a set of ordinary differential equations, and the continuation of these solutions if a parameter is varied, are presented. The realization of these methods in a program for flexible multibody systems is discussed, which requires, besides the determination of the equations of motion, the determination of the linearized equations and the sensitivity of the equations with respect to parameter variations. The methods are applied to an elastic rotor with mass eccentricity and a slider-crank mechanism with a flexible connecting rod.

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Direkte Bestimmung periodischer Lösungen mechanischer dynamischer Systeme

Übersicht Verfahren zur direkten Bestimmung stationärer und periodischer Lösungen in Systemen, deren Verhalten durch ein System gewöhnlicher Differentialgleichungen beschrieben wird, und zur Fortsetzung dieser Lösungen wenn ein Parameter geändert wird, werden vorgelegt. Die Gestaltung dieser Verfahren in einem Programm für flexible Mehrkörpersysteme wird besprochen, was, nebst der Bestimmung der Bewegungsgleichungen, die Bestimmung der linearisierten Gleichungen und die Empfindlichkeit der Gleichungen gegen Parameteränderungen erfordert. Die Verfahren werden auf einen elastischen Rotor mit Massenunwucht und ein Kurbelgetriebe mit verformbarer Pleuelstange angewandt.

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Presented at theSecond U.S. National Congress on Computational Mechanics, August 16–18, 1993, in Washington, D.C.     

Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux

The laminar forced convection in a circular duct is investigated in the case of a sinusoidal axial variation of the wall heat flux. The axial heat conduction in the fluid is neglected, while the effect of viscous dissipation is taken into account. The heat transfer in the thermally developed region, where the temperature is the sum of a linear function and a periodic function of the axial coordinate, is analysed. Both the temperature field and the local Nusselt number are evaluated analytically. Comparisons with the solution in the absence of viscous heating are performed. It is shown that the effect of viscous dissipation on the temperature field may be relevant especially in the case of a sinusoidal wall heat flux distribution with a vanishing mean value. Received on 24 July 1998     

Reynolds number dependence of the drag coefficient for laminar flow through electrically-heated photoetched screens

Experiments are performed to measure the drag coefficient of electrically-heated screens. Square-pattern 80 mesh and 100 mesh screens of 50.8 m-wide wires photoetched from 50.8 m thick Inconel sheets are examined. Ambient air is passed through these screens at upstream velocities yielding wire-width Reynolds numbers from 2 to 35, and electrical current is passed through the screens to generate heat fluxes from o to 0.17 MW/m², based on the total screen area. The dependence of the drag coefficient on Reynolds number and heat flux is determined for these two screens by measuring pressure drops across the screens for a variety of conditions in these ranges. In all cases, heating is found to increase the drag coefficient above the unheated value. A correlation relating the heated drag coefficient to the unheated drag coefficient is developed based on the idea that the main effect of heating at these levels is to modify the Reynolds number through modifying the viscosity. This correlation is seen to reproduce the experimental results closely.List of Symbols A total screen cross sectional area - C fitting coefficient, near unity - c _D heated drag coefficient - c _{D, 0} unheated drag coefficient - C _p air specific heat at constant pressure - D photoetched wire width, sheet thickness - h _s stagnation point heat-transfer coefficient - k air thermal conductivity - M distance between adjacent wires - O open area fraction - p air pressure - p air pressure drop across screen - Pr Prandtl number for air, c _p/k - Q total electrical power to screen - R radius of curvature at stagnation point - Re _D wire width Reynolds number, UD/ - T air temperature - U air speed upstream of screen - air specific heat ratio - air density - air viscosity - exponent in temperature power law for viscosity - () quantity () evaluated at heated screen temperature The authors thank John Lewin and Bob Meyer for their assistance in the design and fabrication of the heated screen test facility and Tom Grasser for his help in performing the experiments. This work was performed at Sandia National laboratories, supported by the U.S. Department of Energy under contract number DE-AC04-94AL85000.     

Novel mechanical behavior of periodic structure with the pattern transformation

In periodic cellular structures, novel pattern transformations are triggered by a reversible elastic instability under the axial compression. Based on the deformation-triggered new pattern, periodic cellular structures can achieve special mechanical properties. In this paper, the designed architecture materials which include elastomer matrixes containing empty holes or filled holes with hydrogel material are modeled and simulated to investigate the mechanical property of the periodic materials. By analyzing the relationship between nominal stress and nominal strain of periodic material, and the corresponding deformed patterns, the influence of geometry and shapes of the holes on the mechanical property of architecture material is studied in more details. We hope this study can provide future perspectives for the deformation-triggered periodic structures.     

Reynolds number dependence of the drag coefficient for laminar flow through fine-scale photoetched screens

The laminar steady flow downstream of fine-mesh screens is studied. Instead of woven-wire screens, high-uniformity screens are fabricated by photoetching holes into 50.8 m thick Inconel sheets. The resulting screens have minimum wire widths of 50.8 m and inter-wire separations of 254 m and 318 m for the two screens examined. A flow facility has been constructed for experiments with these screens. Air is passed through the screens at upstream velocities yielding wire width Reynolds numbers from 2 to 35. To determine the drag coefficient, pressure drops across the screens are measured using pressure transducers and manometers. Threedimensional flow simulations are also performed. The computational drag coefficients consistently overpredict the experimental values. However, the computational results exhibit sensitivity to the assumed wire cross section, indicating that detailed knowledge of the wire cross section is essential for unambiguous interpretation of experiments using photoetched screens. Standard semi-empirical drag correlations for woven-wire screens do not predict the present experimental results with consistent accuracy.List of symbols A ₁, A ₂ screen aspect ratios - c _d screen drag coefficient - d woven-wire diameter - D photoetched minimum wire width (spanwise) - f woven-wire screen drag function - M distance between adjacent wires - N spectral-element order - o woven-wire open area fraction - O photoetched open area fraction - _p pressure drop across screen - Re _d woven-wire diameter Reynolds number - Re _D photoetched wire width Reynolds number - U fluid velocity upstream of screen - W photoetched sheet thickness (streamwise) - x, y, z spatial coordinates - fluid density - fluid viscosity     

Numerical analysis of bifurcation buckling for rotationally periodic structures under rotationally periodic loads

By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.