On the activity of the S. P. Timoshenko institute of mechanics in 1991–2011

This paper, dedicated to the 20th anniversary of the independence of Ukraine (1991–2011), analyzes the activity of the S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, in 1991–2011. The major scientific achievements and their evaluation by the world’s scientific community are briefly reported. The scientific staff and training activity of the Institute are discussed. New books (m?n?graphs, textbooks) and publications in scientific journals are mentioned. It is shown that the scientists of the Institute participate in the establishment of the scientific information environment     

Discussion of “The asymmetry of stress in granular media”: [J.P. Bardet and I. Vardoulakis,Int. J. Solids Struct. 2001, Vol. 38, No. 2, pp. 353–367]

The discussion concerns a recently proposed definition of average stress for granular materials, one which can manifest asymmetry in the absence of surface couples, body couples, and contact couples. The average stress was derived from a new postulate that employs virtual work terminology. The discussion shows that the postulate leads to a non-unique average stress and to a non-unique stress asymmetry.     

A Brief Account of G.D.Birkhoff’s Problem in the Problem of Three Bodies

The present article gives a historical survery of G.D.Birkhoff’s seventh problem which is an inquiry about the topological structure of the set of definition of the reduced differential equations of motion.Recent advances in the problem and their meaning have been briefly indicated.The classical 3-body problem concerns how the three particles should move under their mutual Newtonian attraction.By a particle we mean a goometrical point endorsed with a constant positive number m which is called mass.Expressed mathematically,the problem appears as to solving of the following system of differential equations:     

Rheology of carbon black suspensions. IV. Effect of suspending media on the sol�Cgel transition behavior

Linear viscoelastic properties of carbon black (CB) suspensions with various CB concentrations (c_CB) in two suspending media, mixtures of a rosin-modified phenol resin-type varnish (Varnish-1)/an alkyd resin-type varnish (Varnish-2) and Varnish-1/petroleum solvent (AF) were investigated. The former medium has higher affinity and the latter has poorer affinity toward CB particles than Varnishi-1, although these two media have almost the same viscoelastic properties. Both CB/(Varnish-1/Varnish-2 = 60/40) and CB/(Varnish-1/AF = 80/20) suspensions exhibited a sol?Cgel transition on an increase in c_CB, as similar to the behavior of CB/Varnish-1 suspensions. But, for the CB/(Varnish-1/Varnish-2 = 60/40) suspensions the critical gel concentration (c_gel) was lower and the critical relaxation exponent (n) was higher than that of CB/Varnish-1 suspensions. In contrast, for the CB/(Varnish-1/AF = 80/20) suspensions c_gel and n, respectively, were almost the same value as those of CB/Varnish-1 suspensions. These results strongly suggest that c_gel and n are attributable to the medium affinity, but not to the medium viscosity, and the CB fractal structure changes from plane-like to straight-line structure with increasing medium affinity.     

Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion

Newton's second law is used to develop the nonlinear equations describing the extensional-flexural-flexural-torsional vibrations of slewing or rotating metallic and composite beams. Three consecutive Euler angles are used to relate the deformed and undeformed states. Because the twisting-related Euler angle is not an independent Lagrangian coordinate, twisting curvature is used to define the twist angle, and the resulting equations of motion are symmetric and independent of the rotation sequence of the Euler angles. The equations of motion are valid for extensional, inextensional, uniform and nonuniform, metallic and composite beams. The equations contain structural coupling terms and quadratic and cubic nonlinearities due to curvature and inertia. Some comparisons with other derivations are made, and the characteristics of the modeling are addressed. The second part of the paper will present a nonlinear analysis of a symmetric angle-ply graphite-epoxy beam exhibiting bending-twisting coupling and a two-to-one internal resonance.     

Handbook of Fluidization,Mooson Kwauk,Hongzhong Li （Eds.）.

Fluidization is an important process technology and is ubiquitously present in the process industry. The phenomena of fluidization also represent one of the most fascinating fluid-particle interactive behaviors in nature that are manifested by complex, intertwining science and engineering principles. Even though it is a centuries old practice, pursuit of the fundamental understanding of fluidization has its origins in the 1940s. Since the 1960s, fluidization has been a vibrant field for fluid mechanics, particle mechanics, as well as modeling and computation. From the historical perspective, Professor Mooson Kwauk and Professor Richard Wilhelm＇s 1948 article ＂Fluidization of Solid Particles,＂ is proved to be a pioneering work that sets a stage for subsequent fundamental studies in the characteristics of fluidization. As the field has evolved over the last six decades, Professor Kwauk has been a leader of fluidization research in China and the world,     

Measurement of thermal stresses in the S.S. “Boulder Victory”

A lack of comprehensive experimental measurements of thermal stresses induced in a ship's hull structure by diurnal temperature changes prompted this study. Its essential purpose was to provide reliable prototype measurements of thermal-stress patterns around a complete transverse section of a ship. These results are compared with stresses computed by the theory of simple beams under arbitrary temperature distributions across their section. Bridge-type SR-4 strain-gage assemblies were developed for attachment directly to the structure. A variety of temperature conditions were observed and corresponding strain measurements taken. The results are consistent and give a reliable picture of thermal-stress conditions in a ship. They also verify the prediction of thermal stresses afforded by the simple-beam theory.     

Reprint of “Size dependence and orientation dependence of elastic properties of ZnO nanofilms” [In. J. Solids Struct. 45 (2008) 1730–1753]

The elastic properties of ZnO nanofilms with different film thickness, surface orientations and loading directions are investigated by using molecular mechanics (MM) method. The size dependence of elastic properties is relevant to both the film surface crystallographic orientation and loading direction. Both atomic structure analysis and energy calculation are employed to identify the mechanisms of the size-dependent elastic properties, under different loading directions and surface orientations. Upon small axial deformation, the relationship between intralayer and interlayer bond length variation and film elastic stiffness is established; it is found that the atomic layers with larger bond length variation have higher elastic stiffness. The strain energies of atomic layers of ZnO nanofilm and bulk are decoupled, from which the stiffness of film surface, intralayers, and interlayers are derived and compared with their bulk counterparts. The surface stiffness is found to be much lower than that of the interior layers and bulk counterpart, and with the decrease of film thickness, the residual tension-stiffened interior atomic layers are the main contributions of the increased elastic modulus of ZnO nanofilms.     

In Memory of the Late Prof.Tang Zhao-qian

During his life time the Late Prof. Tang Zhao-qian was the Delegate of the SixthNational People’s Congress, Director of the Affiliated Institute of Engineering Mechanicsof Xi’an Jiaotong University and concurrently Editor-in-chief of“Journal of AppliedMechanics”and one of the members of the Editorial Board of “Applied Mathematics and     

Shock–Free Breakup of Droplets. Temporal Characteristics

In the present paper, we consider the shock–free breakup of droplets in their encounter with a layer (sheet) of a moving gas in the absence of pressure perturbations when the droplets are affected by a short U–shaped pulse of aerodynamic forces. Under a high pressure of the ambient gas medium p₀ = 20—80 bar, the droplets (ethanol or liquid oxygen) have a chance to break up after stay in a thing (2—5 mm thick) gas layer (jet) moving with a velocity of 1—10 m/sec. A distinctive feature of the process is that the characteristic time of droplet deformation and the period of natural oscillations coincide with the residence time for the droplets in the region of their interaction with the gas stream. Empirical formulas are proposed for determination of the total breakup time and the duration of the droplet disintegration stage in shock–free breakup.     

In Memory of the Late Dr.Chan Ho-cheung

One of the invited members of the Editorial Board of Applied Mathematics andMechanics,the Late Dr.Chan Ho-cheung,passed away on Oct.4,1984,in Hong Kong.Inrecognition of his concern and contribution to our periodical,we publish this brief     

The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy. I. Droplet Density

This is the first in a series of two papers in which we derive a Γ-expansion for a two-dimensional non-local Ginzburg–Landau energy with Coulomb repulsion, also known as the Ohta–Kawasaki model, in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small “droplets” of the minority phase in a “sea” of the majority phase. In this paper we show that an appropriate setting for Γ-convergence in the considered parameter regime is via weak convergence of the suitably normalized charge density in the sense of measures. We prove that, after a suitable rescaling, the Ohta–Kawasaki energy functional Γ-converges to a quadratic energy functional of the limit charge density generated by the screened Coulomb kernel. A consequence of our results is that minimizers (or almost minimizers) of the energy have droplets which are almost all asymptotically round, have the same radius and are uniformly distributed in the domain. The proof relies mainly on the analysis of the sharp interface version of the energy, with the connection to the original diffuse interface model obtained via matching upper and lower bounds for the energy. We thus also obtain an asymptotic characterization of the energy minimizers in the diffuse interface model.     

Design and fabrication of submerged cylindrical laminates—II. Effect of fiber pre-stress

This is the sequel to the first part of this paper (Dvorak et al., 1999, Int. J. Solids Structures 36, 3917–3943) , concerned with modeling and analysis of laminated composite cylinder fabrication procedures, such as filament winding or fiber placement, which involve fiber pre-stress for waviness reduction as well as overall or local heating to and cooling from matrix curing temperatures. The fiber pre-stress applied in individual plies is shown to cause a self-stress in the respective plies, and relaxation stresses in the already completed plies and in the supporting mandrel. The final residual stress state is reached after mandrel removal. Influence functions that relate the ply stresses to the applied pre-stress forces are derived. Direct problems are solved for ply stresses caused by prescribed constant or linearly or parabolically changing pre-stress magnitudes in the layers. A superposition of the constant and parabolic distributions is shown to lead to nearly uniform stresses through the cylinder wall. The magnitudes depend on the radial stiffness of the mandrel that supports the structure during fabrication. Inverse problems are formulated as nonlinear optimizations and solved by quadratic programming. The goal is to determine fiber pre-stress distributions through the wall thickness such that the total stresses due to external hydrostatic pressure and fiber pre-stress are as uniform as possible through the wall thickness and confined by the ply strength magnitudes.     

Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. I. Plane flow between two parallel plates

The Cercignani–Lampis scattering kernel of the gas-surface interaction was applied to numerical calculations of the plane Poiseuille flow, thermal creep, mechanocaloric flux and heat flux. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data the value of the accommodation coefficients can be calculated.     

The Braginskii model of the Rayleigh–Taylor instability. I. Effects of self-generated magnetic fields and thermal conduction in two dimensions

There exists a substantial disagreement between computer simulation results and high-energy density laboratory experiments of the Rayleigh–Taylor instability [1]. Motivated by the observed discrepancies in morphology and growth rates, we attempt to bring simulations and experiments into better agreement by extending the classic purely hydrodynamic model to include self-generation of magnetic fields and anisotropic thermal conduction.We adopt the Braginskii formulation for transport in hot, dense plasma, implement and verify the additional physics modules, and conduct a computational study of a single-mode RTI in two dimensions with various combinations of the newly implemented modules. We analyze physics effects on the RTI mixing and flow morphology, the effects of mutual physics interactions, and the evolution of magnetic fields.We find that magnetic fields reach levels on the order of 11 MG (plasma β ≈ 9.1 × 10^?2) in the absence of thermal conduction. These fields do not affect the growth of the mixed layer but substantially modify its internal structure on smaller scales. In particular, we observe denting of the RT spike tip and generation of additional higher order modes as a result of these fields. Contrary to interpretation presented in earlier work [2], the additional mode is not generated due to modified anisotropic heat transport effects but due to dynamical effect of self-generated magnetic fields. The overall flow morphology in self-magnetized, non-conducting models is qualitatively different from models with a pre-existing uniform field oriented perpendicular to the interface. This puts the usefulness of simple MHD models for interpreting the evolution of self-magnetizing HED systems with zero-field initial conditions into doubt.The main effects of thermal conduction are a reduction of the RT instability growth rate (by about 20% for conditions considered here) and inhibited mixing on small scales. In this case, the maximum self-generated magnetic fields are weaker (approximately 1.7 MG; plasma β ≈ 49). This is due to reduction of temperature and density gradients due to conduction. These self-generated magnetic fields are of very similar strength compared to magnetic fields observed recently in HED laboratory experiments [3].We find that thermal conduction plays the dominant role in the evolution of the model RTI system considered. It smears out small-scale structure and reduces the RTI growth rate. This may account for the relatively featureless RT spikes seen in experiments, but does not explain mass extensions observed in experiments.Resistivity, related heat source terms and the thermo-electric contribution to the heat flow were not included in the present work. We estimate their impact on RTI as modest and not affecting our main conclusions. These effects will be discussed in detail in the next paper in the series.     

Decomposition of the Deformations of a Thin Shell. Asymptotic Behavior of the Green-St Venant’s Strain Tensor

We investigate the behavior of the deformations of a thin shell, whose thickness δ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation v are estimated in terms of the L ²-norm of the distance from ∇ v to SO(3). This permits in particular to derive accurate nonlinear Korn’s inequalities for shells (or plates). Then we use this decomposition technique and estimates to give the asymptotic behavior of the Green-St Venant’s strain tensor when the “strain energy” is of order less than δ ^3/2.     

Exact Solution of the Wave‐Resistance Problem for a Submerged Cylinder. I. Linearized Theory

. We consider the problem of finding a holomorphic function in a strip with a cut ${\cal A}= \{(x,y) : \, x\in\RE,\,\,0 satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for $|x|\to\infty. We consider the problem of finding a holomorphic function in a strip with a cut satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for . A special solution can be selected by fixing the value of the circulation around the cut. The problem is obtained by linearization of the equations of the wave‐resistance problem for a “slender” cylinder submerged in a heavy fluid and moving at uniform speed in the direction orthogonal to its generators. The results obtained, besides their own interest, are a crucial step for the resolution of the non‐linear problem. (Accepted October 14, 1998)