Time-Accurate CFD Predictions and Data Validation for Side Load Generation by Flow-Structure Coupling in Over-Expanded Rocket Nozzles

The present paper validates results from numerical simulations for side load generation in rocket nozzles against related data from analytical models that are presently used for rocket engine nozzle design activities.Time-accurate two- and three-dimensional turbulent Navier–Stokes (N–S) computations are performed for separated flow in deflected and ovalized nozzles as well as for nozzles under forced harmonic oscillations. Based on this comparison conclusions are drawn concerning the validity of the physical model assumptions that the analytical design methods are based on.Mathematics Subject Classification (2000) 74F10.     

Analysis of the anisotropic properties of honeycomb sandwich plates

A mathematical model has been described and an approach proposed to the diagnostics of the anisotropic properties of the relative elasticity constants of three-layer (sandwich) plates with a honeycomb filler. Compact analytical relationships between the anisotropy coefficients and the geometrical dimensions of the cells have been obtained. A practical approach has been proposed for the selection of rational parameters of the honeycomb structure, at which its anisotropic properties would be in the chosen region of the functional space. The conditions have been formulated at which the constructive anisotropy, inherent to honeycomb structures, degenerates to isotropy for some relative elastic constants.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 482–487, July–August, 1995.     

Modeling composites on graphs,with parameter optimization

Composites have been modeled by means of graph theory and the concept of a dynamic interfacial layer on both sides of the filler-matrix boundary. Certain assumptions were made in order to eliminate the indeterminacy created by the use of models. The magnitude of the dynamic interfacial layer has been estimated for the fillers and the epoxy matrix. The calculations have been compared with experimental data.Moscow State Open University, Center for Composite Materials, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 467–479, July–August, 1996.     

Integrating categorical variables in Data Envelopment Analysis models: A simple solution technique

This paper introduces a novel method to incorporate categorical non-discretionary variables in Data Envelopment Analysis (DEA) models. While solutions to this problem have been introduced before, they have rarely been employed in applied work. We surmise that existing solution concepts pose problems for applied researchers and develop a simple and straightforward alternative based on indicator variables. We thereby provide a flexible tool for models with categorical variables that–unlike the approaches mentioned above–can be solved with standard DEA software irrespective of scale assumptions even if no option for non-discretionary variables is available. Furthermore, there is no need to split the data and run multiple DEA, one for each data set generated. The model is extensible to categorical discretionary variables and in addition to non-hierarchical data.     

Buildup of failures in polymers on micro- and macrolevels

The buildup of damage in polymers has been studied by mechanical and structural—analytical methods. A method of programmed loading has been developed which makes it possible to make an estimate of damage buildup in macroscopic experiments. A comparison has been performed of kinetic curves of failure buildup on molecular and macroscopic levels. It is shown that the kinetic equations where the rate of failure is basically initiated by true stress qualitatively follow the experimental curves for failure buildup on micro- and macrolevels."Plastpolimer" Scientific-Manufacturing Association, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 263–268, March–April, 1976.     

Zero-moment laminated cylindrical shells with variable elasticity parameters obtained by the continuous winding method

Conclusions The general solution in the displacements of the problem of thermal-force loading of a zero-moment laminated cylindrical shell with variable elasticity parameters has been obtained in analytic form. Boundary-value problems for the practically important and often realized boundary conditions which arise in tests of samples, models, and natural structures have been discussed.Presented at the Fifth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1983).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 493–502, May–June, 1984.     

Transverse cracks in cross-ply laminates 2. Stiffness degradation

From the results of stress analysis between two transverse cracks in cross-ply laminate [1], a model for the stiffness reduction based on generalized plane strain assumptions has been developed. Simple analytical expressions are obtained for the longitudinal modulus and the Poisson's ratio as a function of the transverse crack density. Apart from the crack density, these expressions depend only on the elastic and geometrical properties of constituent laminae and the average crack opening displacement (ACOD) normalized in the proper way. Calculations of the ACOD are performed and analyzed with the FEM and analytical models used for the stress analysis in [1]. The predicting capabilities of approximate models are discussed in comparison with experimental data and FEM results. In order to predict the stiffness degradation for a wide variety of laminates, a simple procedure requiring only one FEM calculation for some average laminate with average crack spacing is proposed and has been proved effective.Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 211–233, March–April, 1998.     

Nonlinear moisture deformation of a composite with a densified reinforcement

Conclusion An analytical method is presented for estimation moisture deformation of densified in technological pressing wood-based composite material with nonlinear swelling properties. This includes modelling of the processing effects as well as interfacial bonding. By using the multilayer model supported on the laminate analogy the optimum particle alignment has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 314–320, May–June, 1994.     

A Numerical Method for Constructing a Self-Similar Isolated Wave Solution

An efficient numerical algorithm is developed for constructing self-similar isolated wave or switching wave solutions. The algorithm is developed for the well-known Kolmogorov–Petrovskii–Piskunov (KPP) problem, which has a switching-wave analytical solution, and is applied to construct an isolated traveling pulse in the four-component reaction–diffusion model.     

Energy capacity of rotating composite designs (review)

Conclusions Theoretical investigations that have been performed and experimental confirmation on models have conclusively confirmed the high efficiency of composite flywheels. The most promising design at the present time is the chorded flywheel, especially for pulse energy sources. It can be assumed that the flexibility of the chords makes it possible to achieve a balanced design more simply. Problems of balancing, as, in general, the dynamics of energy-storing rotating composite components, however, will be the subject of further independent research.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 65–78, January–February, 1986.     

Plastic deformation of models of a crystalline polymer with increased lattice defectivity

Conclusions 1. On the basis of two-dimensional models, the structure of a polymeric crystal containing more than one lattice defect has been determined on an electronic computer. The types of defects are: a) double vacancy, model I; b) two isolated vacancies, model II; c) a combination of isolated vacancies and double vacancies, model III. Plastic deformation curves have been calculated for all three models.2. It has been observed that increase in the degree of defectivity in a crystalline polymer significantly reduces the elastic limit and reduces the strength limit of the structure very little. The elastic limit falls particularly strongly with increase of the defectivity in a state of hydrostatic stress.3. Increase in the density of crystallographic defects causes significant mutual rearrangement of the coordination polygons of the crystal lattice, which occurs as the result of plastic deformation.Report presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 397–402, May–June, 1977.     

Shear creep of orthogonally reinforced spherofibrous composites

Our previous theory for the viscoelasticity of spheroplastics and two-phase structural models was used to construct stress creep and relaxation operators for shear of orthogonally reinforced spherofibrous composites. The operators were constructed using the Volterra principle, Rabotnov's fraction exponential kernels, and approximate analytical relationships for the integral composite characteristics. Operators were taken incorporating data on the rheonomic characteristics of the composite, components with hybrid, hollow, and other fiber types. Approximate formulas were obtained for operators convenient for studying stress creep and relaxation in elements of three-dimensional structures.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 770–779, November–December, 1996.     

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 646–659, September–October, 1995.     

Sandwich plates-free vibrations and damping analysis

A new analytical approach to the optimization analysis of stacking sequences of sandwich plate faces is presented. FRP faces are assumed to be constructed of 0₂°, 90₂°, and ±45° plies. A new set of design variables was succesfully used for the optimization analysis of natural flexural vibrations and modal loss factor of sandwich plates with FRP faces. In addition, the influence of the core thickness on optimization solutions was studied. Three variants of plate theories were considered, namely those of Love-Kirchhoff and first- and higher-order transverse shear deformation. To verify the results of the models proposed, the values of the natural vibrations were compared with the results obtained using the NISA II FEM package.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Institute of Mechanics and Machine Design, Cracow University of Technology, 31–155, Cracow, Poland. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 276–286, March–April, 1998.     

On the thermodynamic limit for Hartree–Fock type models

We continue here our study [10–13] of the thermodynamic limit for various models of Quantum Chemistry, this time focusing on the Hartree–Fock type models. For the reduced Hartree–Fock models, we prove the existence of the thermodynamic limit for the energy per unit volume. We also define a periodic problem associated to the Hartree–Fock model, and prove that it is well-posed.     

Limiting Connection between Discrete and Continuous Time Forward Interest Rate Curve Models

We study discrete time Heath–Jarrow–Morton (HJM) type of interest rate curve models, where the forward interest rates – in contrast to the classical HJM models – are driven by a random field. Our main aim is to investigate the relationship between the discrete time forward interest rate curve model and its continuous time counterpart. We derive a general result on the convergence of discrete time models and we give special focus on the nearly unit root spatial autoregression model.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

Some autoregressive moving average processes with generalized Poisson marginal distributions

Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987,J. Time Ser. Anal.,8, 261–275; 1988,Statist. Hefte,29, 281–300) and McKenzie (1988,Adv. in Appl. Probab.,20, 822–835). The models have the same autocorrelation structure as their counterparts of standard ARMA models. Various properties, such as joint distribution, time reversibility and regression behavior, for each model are investigated.     

Hygromechanics of composites with unsymmetric structure

Conclusions An analytical method is presented for estimation of midplane strains and curvatures of a 3D general composite. By using the multilayer model based on the laminate analogy, the effect of an unsymmetric distribution of moisture content and material structure on swelling and wrap as well as the stability in compression of a densified technological pressing wooden composite board has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 6, pp. 831–838, November–December, 1994.     

A new test for E-infinity fractal-spacetime theory

E-infinity theory is the analytical version of fractal-spacetime theory; the other is simulational fractal-spacetime theory. It is proposed that E-infinity theory can be used to calculate the size – and by implication the threshold energy for their formation – of microscopic black holes. This prospect is of great interest in the context of the Large–Hadron–Collider (LHC) experiment which may or may not produce miniblack holes at energies eight times higher than ever tried before.