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Repozytoria RCIN
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INSTYTUT ARCHEOLOGII I ETNOLOGII POLSKIEJ AKADEMII NAUK
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INSTYTUT BADAŃ LITERACKICH POLSKIEJ AKADEMII NAUK
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INSTYTUT BADAWCZY LEŚNICTWA
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INSTYTUT BIOLOGII DOŚWIADCZALNEJ IM. MARCELEGO NENCKIEGO POLSKIEJ AKADEMII NAUK
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INSTYTUT BIOLOGII SSAKÓW POLSKIEJ AKADEMII NAUK
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INSTYTUT CHEMII FIZYCZNEJ PAN
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INSTYTUT CHEMII ORGANICZNEJ PAN
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INSTYTUT FILOZOFII I SOCJOLOGII PAN
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INSTYTUT GEOGRAFII I PRZESTRZENNEGO ZAGOSPODAROWANIA PAN
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INSTYTUT HISTORII im. TADEUSZA MANTEUFFLA POLSKIEJ AKADEMII NAUK
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INSTYTUT JĘZYKA POLSKIEGO POLSKIEJ AKADEMII NAUK
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INSTYTUT MATEMATYCZNY PAN
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INSTYTUT MEDYCYNY DOŚWIADCZALNEJ I KLINICZNEJ IM.MIROSŁAWA MOSSAKOWSKIEGO POLSKIEJ AKADEMII NAUK
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INSTYTUT PODSTAWOWYCH PROBLEMÓW TECHNIKI PAN
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INSTYTUT SLAWISTYKI PAN
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SIEĆ BADAWCZA ŁUKASIEWICZ - INSTYTUT TECHNOLOGII MATERIAŁÓW ELEKTRONICZNYCH
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MUZEUM I INSTYTUT ZOOLOGII POLSKIEJ AKADEMII NAUK
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INSTYTUT BADAŃ SYSTEMOWYCH PAN
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INSTYTUT BOTANIKI IM. WŁADYSŁAWA SZAFERA POLSKIEJ AKADEMII NAUK
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- A constitutive theory is discussed for materials which undergo microstructural changes, and thus have different micromechanisms for the generation of stress in different regimes of response. Of particular interest is a two-network theory of polymer response in which, at some state of deformation, molecular cross-links are broken and then reformed in a new reference state. The mechanical response then depends on the deformation of both the remaining portion of the original material and the newly formed one. A particular constitutive equation is introduced in order to develop the methodology for performing calculations, and to study material behavior. The original and newly formed material are both treated as incompressible isotropic nonlinear neo-Hookean elastic materials, but with different reference configurations. Several homogeneous deformations are analyzed, and permanent set on release of load is calculated. Nonhomogeneous deformations are studied by means of the problem of the combined extension and torsion of a circular cylinder. Unloading and loading response is determined, as well as permanent set on release of load.
- A discrete kinetic model is proposed which has some properties typical for retrograde gases. The characteristic feature of the model is that the probabilities of direct and inverse collisions are not symmetric. The Euler and Navier-Stokes equations corresponding to the proposed model are derived. The plane shock wave is studied by means of these three types of equations. It is found that in some cases the number density must decrease in order for the shock to be stable. The transition line is shown to be the same for the Boltzmann and Navier-Stokes model equations and, in the case of weak shocks, it coincides with that found from the Euler model equations.
- A finite element method is used for solving the nonlinear transient heat transfer problem of the axisymmetric flash welding. The variational derivation of the finite element matrices and the algorithm for solving the resulting system of nonlinear equations are discussed. Numerical illustrations prove the effectiveness of the approach.
- A new computational delamination method using Damage Mechanics of composite laminates is proposed. A laminate is modeled as a stacking sequence of homogeneous layers and interlaminar interface. Both components are subject to damage. Deterioration such as fiber rupture, matrix and interface degradation are introduced at an intermediate level, which is called the meso-level. Damage is assumed to be uniform throughout the ply thickness. This makes it possible to avoid the main computational difficulties such as mesh dependency. For delamination analysis around a hole, an efficient numerical treatment is proposed to solve nonlinear (constitutive law) three-dimensional (edge effects) problems at a reasonable cost. Simulations are given.
- A new method is considered for the solution of the finite-part singular integro-differential equations, applied in many problems of mathematical physics and especially in elasticity and aerodynamic problems. This is obtained by reduction to a system of linear equations, by applying the singular integro-differential equation at properly selected collocation points. An application is given to the determination and solution of the generalized airfoil equation, which presents the pressure acting on a planar airfoil undergoing simple amplitude oscillations about the central plane of a two-dimensional ventilated wind tunnel.
- A Rayleigh-type surface stress wave propagation is considered in a “weakly anisotropic” semispace of “small nonhomogeneity”; two elastic shear moduli are assumed to be monotone functions of depth, the ratio of Young’s moduli is limited to the first two terms of a power series expansion. Waves of such type are described in part I by the solution of an ordinary, fourth order differential equation with variable coefficients satisfying the corresponding boundary conditions (see [1], Sec. 4). In this particular case of variability of the elastic moduli, the problem has a closed-form solution expressed in terms of Bessel functions. Analysis of the dispersion equation proves the Rayleigh wave speed to depend on the wave- length and on the anisotropy and nonhomogeneity parameters. Using the asymptotic expansions of Bessel functions, the dispersion equation is written in an approximate form enabling a numerical analysis of the influence of the anisotropy and nonhomogeneity parameters upon the surface wave speed.
- A simpler proof is given for Rychlewski's theorem that clarifies the ideal of extending a g-invariant function into a function which is invariant under a larger group. For an anisotropic solid, the theorem ensures the possibility of transforming the problem of representation of an anisotropic constitutive function into a representation of an isotropic function through some tensors characterizing the symmetry group. The structural tensors for all 32 crystal groups are presented. The structural tensors for all the orthogonal subgroups of non-crystal symmetries are also investigated.
- A system of infinite equations of a transversely isotropic plate of arbitrary thickness is proposed. Solution of the system expressed in terms of displacements satisfies the local equilibrium conditions, normal loading conditions in integral form, and modified boundary conditions across the thickness of the plate. Solutions in the form of infinite series are found for three practical cases and finite formulae for the model problems (loads having the form of eigenfunctions of the Laplace operator are given). In strongly anisotropic plates of large thickness- to-span ratio (of about 1/5) normal stress distributions considerably differ from the linear ones, stress maxima are higher then those predicted by the simplified theory, and the corresponding deflections are substantially different. The differences increase with increasing rigidity of the supports. Limits of applicability of the simplified “engineering” theory are estimated.
- The AIM of the paper is to propose and discuss a mathematical model of the interlaminae debonding process in layered composites. The proposed method of modelling leads to the time-dependent quasi-variational inequality for the displacement rates. The results obtained can be applied to composites made of elastic as well as elastic/viscoplastic materials subject to small strains.
- The aim of this study is to determine the elastoplastic properties of metallic polycrystals at large strains using the statistical methods developed by E. Kr ner [e.g.: Graded and perfect disorder in random medium elasticity. J. Eng. Mech. Div., ASCE 106, 889-914 (1980)]. The large number of microfields describing the internal structure evolution is taken into account. The evolution laws for these parameters are recalled or proposed. A few numerical results are finally presented which illustrate the evolution of the internal structure. Special attention is focussed on internal stresses and on stored energy linked with these second-order residual stresses and their influence on the overall behaviour of the polycrystal.
- An approximate solution is presented for the flow of blood through an intented tube. It is assumed that blood flowing in the tube is a suspension of red cells in plasma and the red cells are spherical in shape. Theoretical results obtained in this analysis are given for the axial velocity, wall shear stress and the pressure gradient. The numerical solutions of these results are explained graphically for better understanding of the problem.
- An example of a uni-axial state of stress is used to present an attempt to a dynamic description of failure of rocks, concretes and similar materials. A model is proposed of an elastic/viscoplastic body with softening in the range of inelastic deformations. The material is assumed to behave as a viscoplastic body of the range of stresses exceeding the elastic limit. During unloading the process follows the statical unloading curve and disturbances are propagated at infinite velocities.
- The author considers a system formed by a rigid profile carrying an elastic rod, moving in an inviscid incompressible fluid in irrotational motion, the forces exerted by the fluid on the rod being negligible. The elastic rod is suspended on a rigid horizontal string, this constraint being frictionless. In the first part of the paper, there are written the equations of motion by means of the theorems of momentum and of the moment of momentum and Hamilton-Ostrogradski’s principle; the first integrals are obtained. In the second part, the author studies the existence and the stability of motions of horizontal uniform translation of the profile with relative equilibrium of the rod in the undeformed state, the rod being directed vertically. The problem of stability is reduced to the problem of the minimum of a convenient functional; the author gives sufficient conditions of stability.
- Axisymmetric problem of plane wave propagation along the elastic rod of circular cross-section embedded in elastic space is considered. Approximation of plane uniformly deformed cross-section is employed for the rod. Shear stress continuity condition at the interface is replaced by the weaker integral condition of the axial momentum balance for the rod. Solutions for the elastic fields in the surrounding medium are constructed, Hankel functions of complex variable being used. The dynamic field obtained can be considered as the superposition of two elastic periodic waves emitted by the rod at strictly defined angles with respect to the rod axis. For certain sets of parameter values the characteristic equation has been numerically solved, the dispersive relations being obtained for the longitudinal wave in the rod. Relations describing the propagation angles and amplitude decay decrement changes versus the wave frequency have been also found.
- Basing on the ideas of a previous paper (Piechor, 1988), constructions of discrete velocity models (DVM) are presented for mixtures of noble gases and of those with binary chemical reactions. The first step in the constructions is to postulate the form of the space of collisional invariants. Owing to this, this space is determined for previously existing models. It is shown that DVM, in their present form, cannot be applied to models of gases with chemical reactions unless the principle of detailed balance is satisfied.
- The calculation procedure of centrifugal compressor internal flow and losses based on the quasi-three-dimensional turbulent model is considered. The procedure includes the prediction of hub-to-shroud and blade-to-blade flows with tip-clearance flow, surface curvature, rotation and secondary flows being taken into account. A comparison of calculated results with experimental data is presented. Satisfactory agreement of local and energy parameters is achieved.
- The computation of high Reynolds number laminar viscous inviscid interaction phenomena has been one of the central issues in fluid mechanics over the past two decades. An important contribution to the understanding of such flows has been provided by asymptotic theories. In particular these theories show that a locally interacting laminar boundary layer develops a multilayer structure. Viscous effects are of importance only inside a thin region adjacent to the wall where the flow is governed by the boundary layer equations, the pressure being coupled to the displacement thickness. Owing to the complicated general form of the pressure-displacement relationship most studies of local interaction processes deal with the case of two-dimensional flow. Three-dimensional interaction effects can be investigated more easily, however, if it is possible to exploit symmetry properties as in the case of axisymmetric flow.
- Cylindrical wave solutions for the Korteweg-de Vries equation are obtained within a reasonable approximation. They are shown to be representable as infinite sums of cylindrical solitons.
- Decay of the initial discontinuity is interpreted as a mechanism of passage from a regular to an irregular phase in the problem of nonstationary reflection of a shock wave from a surface. Modification of the Mach triple point theory resulting from the hypothesis presented is considered.
- The definition of the anisotropy degree of tensors, functions and functionals with respect to some given operation group is presented. The anisotropy degree of four-order tensors is investigated in details. Numerical examples are given for cubic, transversely-isotropic and orthoropic linear elastic materials.
- The dynamic in-plane problem of determining the stress and displacement due to three co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement around three co-planar Griffith cracks in an infinite isotropic elastic medium has also been considered. In both the cases, employing Fourier integral transform, the problems have been reduced to solving a set of four integral equations. These integral equations have been solved using finite Hilbert transform technique and Cook's result [16] to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.
- The equations of magnetohydrodynamics describing a motion of an ideal incompressible and infinite conductive fluid are considered. These equations are replaced by two kinds of equations: a system of symmetric hyperbolic equations and a Poisson equation. Using the results about the existence of solutions of symmetric hyperbolic equations, the existence of local solutions to the problems is proved by the method of successive approximations. These solutions belong to such spaces that equations of MHD are satisfied classically.
- Equations of magnetohydrodynamics which describe the motion of an ideal incompressible fluid with infinite conductivity in a bounded domain are considered. Vanishing of normal components of velocity and magnetic induction on the boundary are assumed as boundary conditions. Existence and uniqueness of classical solutions (local in time) are proved.
- The evolution of hydrodynamic instabilities in the convective flow of a fluid layer heated from below is considered, reviewing the results of recent theoretical investigations. Steady convection rolls and their instabilities, three-dimensional solutions in the form of knot convection, and traveling-wave convection are discussed, and results from numerical simulations are presented in graphs. It is shown that the instabilities of rolls offer a typical picture of several mechanisms involved in turbulent convection, and that turbulent convection, even at high Rayleigh and Reynolds numbers, still exhibits well defined structures and characteristic wavelengths. Such phenomena have been noted in satellite images of stratocumulus clouds or in observations of solar-surface granulation and supergranulation.
- The evolution of internal variables, mobile and immobile dislocation densities during plastic deformation is studied within the framework of continuum mechanics utilizing the assumption of minimization of potential of the two types of dislocations. A pair of partial differential equations is derived and various simplified forms are solved for dislocation densities in space with increasing time. These equations yield a periodic oscillation of the dislocation densities in agreement with the dislocation patterning in uniaxial deformation.
- The existence and uniqueness of local-in-time solutions of the motion of a drop of a viscous incompressible fluid bounded by a free surface in an ideal incompressible fluid are demonstrated. It is shown that the equations are satisfied classically in such Sobolev spaces. The density of the viscous fluid are assumed to be much larger than the density of the ideal fluid.
- Existence and uniqueness of solutions of boundary value problems with general boundary data for two-velocity models of the Boltzmann equation are investigated. Explicit examples of the nonunique positive solutions are given and their bifurcation from the unique solutions is discussed. Stability properties of the solutions are studied numerically.
- Flow-visualization motion pictures of side, top and span views in a plane confined mixing layer were obtained. The formation of vortical coherent structures and their further evolution were observed and filmed for several values of the characteristic parameters lambda = U2/U1 and Delta(U) = U1-U2. The influence of these two parameters on the appearance of the vortices and their subsequent evolution was investigated. A statistical analysis of digitized flow pictures has made it possible to determine the mean position of the birth of the vortices and to follow their evolution thoroughly.
- The geometric structure of the stress and strain tensors arising in continuum mechanics is investigated. All tensors are classified into two families, each consists of two subgroups regarded as physically equivalent since they are isometric. Special attention is focussed on the Cauchy stress tensor and it is proved that, corresponding to it, no dual strain measure exists. Some new stress tensors are formulated and the physical meaning of the stress tensor dual to the Almansi strain tensor is made apparent by employing a new decomposition of the Cauchy stress tensor with respect to a Lagrangian basis. It is shown that push- forward/pull-back under the deformation gradient applied to two work conjugate stress and strain tensors do not result in further dual tensors. The rotation field is incorporated as an independent variable by considering simple materials as constrained Cosserat continua. By the geometric structure of the involved tensors, it is claimed that only the Lie derivative with respect to the flow generated by the rotation group (Green-Naghdi objective rate) can be considered as occurring naturally in solid mechanics and preserving the physical equivalence in rate form.
- Homogeneous solutions for a linear anisotropic infinite elastic strip are given when the axis of anisotropy of the strip is not parallel to the boundary line. The solutions are then used to obtain the Airy stress function for a rectangular anisotropic disc subject to tension.
- In the framework of the linearized theory we study the plane-parallel uniform flow of an incompressible, ponderable, inviscid fluid in the presence of a submerged thin hydrofoil. We represent the complex velocity potential by a continuous distribution of sources and vortices potentials. From the boundary conditions we derive a singular integral equation for γ (the vortex circulation). A numerical method is used in order to solve the integral equation and to calculate the lift, drag and moment coefficients. Numerical results are given in the case of an oblique flat plate of small inclination.
- In this paper the thermo-elastic-plastic model for determination of stresses in a solidifying casting is proposed. The temperature fields, solidification rates, stresses and strains have been determined for a solidifying axially-symmetrical casting. The effect of plastic strains on the instant of generation and size of shrinkage gap has been discussed. The problems have been solved numerically by means of the finite element method.
- Incorporation of algebraic eddy viscosity models in numerical schemes is considered, and problems arising from typical mixing length models are discussed. An explicit model for two-dimensional duct flow is derived, and the model is compared with existing models. The computed velocity profiles for fully developed flow correspond favourably with experimental results.
- The initial value problem of surface waves generated by a harmonically oscillating vertical wave-maker immersed in an infinite incompressible fluid of finite constant depth is presented. The resulting motion is investigated using the method of generalized function, and an asymptotic analysis for large times and distances is given for the free surface elevation.
- It is shown that an application of the method of virtual power to a simple mulipolar rod model, with the force-system space representing force and couple distributions, leads to the correct equations of motions and, in the case of elastic rods, to a torsion-dependent strain-energy function - results that had eluded previous attempts to represent three- dimensionally deforming rods by simple body models.
- The localization of deformation in the form of shear bands is understood as an instability in the macroscopic description of inelastic deformation. The effects of thermomechanical couplings in the development of these shear bands are analyzed. Conditions for the onset of localization when these couplings are taken into account are given both inside a body and at its boundary. These conditions are illustrated by a particular set of constitutive equations. Destabilizing effects due to couplings are underlined.
- Nonlinear dynamical models of a rigid body working under oscillatory conditions with damping, and fastened at a fixed point, e g., centre of mass, are discussed. Special stress is laid on isotropic models, invariant under so-called hyperrotations, i.e. rotations of the rotation vector. For the damping-free (purely oscillatory) case completely degenerate potentials are determined, and general solutions of equations of motion are discussed. These results can be helpful in designing instruments sensitive to inertial forces and their moments, e.g., sensors of angular acceleration in automatic control systems and navigation.
- The objective of the present paper is the formulation of the general frame of an internal variable theory of high strain rate deformations in metals. Such deformation are characterized by nucleation, growth and coalescence of various microdefects like shear bands, cracks and voids. Localized deformations in the vicinity of these microdefects as well as disloaction motion in the remaining parts of the body contribute to the inelastic strain rate. After identification of appropriate internal variables through an approximate homogenization procedure, evolution laws and flow rules are introduced and investigated with respect to their consistency with thermodynamics. The Clausius-Duhem inequality is utilized as a measure of irreversibility. Introducing a polynomial representation of specific free enthalpy, thermodynamically consistent evolution laws are derived. Finally, the theory is applied to the problem of propagation of uniaxial acceleration waves into an unstressed homogeneous medium.
- The paper deals with recent developments of the space-time element method in vibration analysis. Discrete methods applied to date in structural dynamics make use of spatial discretization independently of the time integration procedure. It limits applications of such an approach. The full space-time approximation can be considered as an extension of the finite element method over the time domain and it allows to treat spatial variables in the same way as the time variable. Nonstationary discretization, adaptive techniques, directly obtained joint-by-joint procedure are not the only positive features of the space time finite element approach. Although the additional time variable in the shape functions is considered and the resulting element matrices are greater than static stiffness and mass matrices, the cost of the solution algorithm is comparable with other numerical methods. Some testing examples prove the efficiency of the method.
- Phenomenological relativistic hydrodynamics (RH) is fifty years old. Up to now it was regarded as an interesting although a bit academic topic. This has changed recently due to growing interest in astrophysical and high energy physics applications. This paper does not pretend to be a complete review of the present state to research in the field of relativistic hydrodynamics. RH is viewed from the physical point of view, and those points which are quite confused in the literature are discussed. In particular the role of the observer, the problem of physically motivated choice of the hydrodynamical variables, and the invariance of the constitutive relations are discussed. Most of those problems will be put into a proper perspective by the careful analysis of the relativistic kinetic Boltzmann equation.
- The plane laminar boundary layer in the case of an incompressible viscoelastic (simple) fluid in a stagnation point flow is considered in great detail. The scaling procedure characterizing the “elastic-type” boundary layer and the constitutive equations valid for thin-layer flows with dominating extensions (FDE) are applied. It is shown that the layer thickness as well as the velocity profiles essentially depend on the Weissenberg number and the extensional viscosity function.
- The present state of mathematical investigations on the Boltzmann equation is briefly outlined. In particular problems of existence and asymptotics, concerning space homogeneous and global solutions with different boundary conditions, are discussed. The existence of local solutions with external forces and the application of mollifiers are also briefly discussed. The asymptotic expansions resulting from the Boltzmann equation and concerning the bulk and the initial layer solutions are considered. Some of the many still open problems are mentioned.
- The problem of the homogenization of Cosserat continuum with a periodic structure is studied by means of the energy method. Homogenized quantities are derived and correctors are introduced. An example of the determination of homogenized quantities for the one-dimensional case is also presented.
- Problems connected with the theoretical description of plastic flow of polycrystalline sheet metals are discussed and commented. Sheet metals display distinct anisotropic properties in the plastic range of deformation. It is observed that these properties may be different depending on the plastic deformation histories in the course of the manufacturing process. Much attention has been devoted to the experimental tests of plastic anisotropy of sheet metals and to the comparison of test results with various theoretical descriptions.
- The propagation of coupled modes in a viscous incompressible dusty fluid confined between two perturbed parallel plates is considered. The treatment is confined to first-order perturbation theory in order to simplify the algebra. The multiple scales approach yields information on the transition curve separating passbands from stopbands as well as the interaction equations which govern the amplitudes and phases of the coupled modes.
- The purpose of the present paper is to compare some consquences of the classical flow-rule of plasticity due to Levy and Mises with those of the flow equation recently proposed by R. N. Dubey and S. Bedi [1]. The kinematics of a thin plate in large simple shear deformation is used for the purpose of comparison. The prescribed continued deformation is used to calculate the finite values of distortion and rotation, and to extract information about (Eulerian) strain-rate and spins of the various axes defined in the body.
- Rajagopal and Wineman [1] have recently established several new exact solutions to boundary-value problems in nonlinear elasticity. They have shown, for example, that a nonlinearly elastic slab can exhibit nonuniform uniaxial extension solutions, in addition to the classical uniform uniaxial extension solution. In this paper, a slab consisting of a mixture of a nonlinearly elastic solid and an ideal fluid is modelled in the context of mixture theory. The problem of uniaxial extension of this slab mixture is considered, and the possibility of an infinity of exact solutions is demonstrated.
- Regularity of nonlinear nonholonomic mechanical systems is discussed. A lumped mechanical system is called here the regular one, if the dynamic space of the system, i.e., the space plaited of the solution curves, equals the whole configuration space of the system - the space defined by the constraints imposed on accessible positions and velocities of the system, and the system has a well defined dynamic equation. Shrinkage of the configuration space can be easily observed among the electrical networks where one can find simple constructions of nonregular systems. However, except the lumped mechanical systems which exhibit some kind of discontinuous modes, the well-posed mechanical systems which are of practical interest are the regular systems. Thus, the conditions ensuring regularity and proved here for a broad class of mechanical systems are of special importance. It has been also shown that holonomic systems are regular, and hence, the examples of nonregular mechanical systems are among the nonholonomic systems. Hence, much attention has been paid to nonholonomic systems. A general procedure for finding the space of motion and the dynamic equation of a nonregular mechanical system is proposed. The description presented is the extension of the theory initiated in the area of electrical networks.
- The results concerning the moments of stochastic linear differential equations with the multiplicative parameter in the form of a stochastic telegraph process (Shapiro-Loginov formula) are generalized to the case of Hilbert-space-valued evolution equations. The obtained results are then applied to the investigation of the moment stability of some string equation with stochastic parametric excitation. The results obtained for exact and modal approaches are compared showing the possibility of the simplified analysis as well as differences. Additionally, the system with the appropriate white-noise excitation is considered, and, with the aid of an “equivalent” white-noise process the conditions of an approximation of the telegraphic stochastic process are studied.
- Shear banding is related with large plastic deformations produced by mechanisms of crystallographic slip and/or twinning and micro-shear. Physical foundations and motivations to formulate simplified phenomenological model are considered. Plane deformations of elastoplastic material accounting for micro-shear bands are studied. The derived relations show that micro-shear bands produce the non-coaxiality between principal directions of stress and rate of plastic deformations. It transpires that, depending on the contribution of the mechanisms involved in plastic flow, a fully active range, separated from the elastic range by a truly nonlinear zone called the partially active range, may exist. In case of continued plastic flow with the deviations from proportional loading contained within the fully active range the incremental plastic response is linear, whereas the constitutive relations derived for the partially active range appear thoroughly nonlinear. Relations to known nonlinear flow laws in rates of deformation and stress are discussed.
- The spectral decomposition of the fourth-rank compliance tensor of an elastic solid with an axis of symmetry of infinite order was given, and the characteristic values (eigenvalues) of the same tensor were calculated in terms of its Cartesian components. Energy-orthogonal stress states for the transversely isotropic solid were explicitly calculated and the elastic energy associated with these stress tensors was given a special identification with dilatational or distortional strain energy density. Bounds on the values of Poisson’s ratios of the transversely isotropic solid were established by imposing the eigenvalues of the compliance tensor to be strictly positive.
- The stability of the motion of a spherical drop is analyzed in the presence of Marangoni effect generated by heterogeneity of a temperature field. The solution of the linearized Navier-Stokes equations, describing the motion of a drop is found. Using the classical approach of the linear theory of stability, the equation determining the values of frequencies of disturbances is obtained. The given numerical example indicates the existence of disturbances growing in time, what means the instability of the investigated motion.
- Stationary shock wave profiles are investigated for the hexagonal discrete velocity model with binary and all triple collisions. The singular points corresponding to equilibrium limit states are studied analytically in the phase space of the relevant dynamical systems. The influence of triple collisions on various macroscopic quantities which characterize the shock profiles is investigated. The infinite Mach number case is treated as well as the shock profiles with general equilibrium distributions, for various directions of the shock propagation on the plane. Local density and entropy profiles in the shock transition zone are studied. The influence of a class of higher order, quadruple collisions is also discussed
- Stereophotometry makes it possible to measure and to average a large ensemble of instaneous velocity fields of hundreds or thousands of tracing particles. This allows the effective use of stereometry of tracing particles for experimental investigations of statistically stationary as well as statistically nonstationary developed turbulent flows. The labor involved in counting large amounts of stereometric data is well known. Using large and precise IMK 10/13 x 18, and 'Steco' stereometric correlators it was possible to reduce the counting and perforation time of stereometric data on the motion of 1000-1500 tracing particles to 15-20 hours. The use of stereometric data is also effective for the investigation of visual three-dimensional structures of developed turbulent flows.
- The stochastic stability problem is solved for rectangular plates with elastically supported edges. The plate is compressed by in-plane wide- band Gaussian forces. It is assumed that resistances to rotation of plate edges increase linearly as the mean values of in-plane forces increase. Results are graphically presented for cylindrical bending of a plate which is simply supported and the support stiffens under compression.
- The subject-matter of this paper is a method for calculation of frequencies and modes of free vibration of thin elastic, segmented shells of revolution reinforced with internal or external circumferential rings. The shape of the meridian and the change of thickness of the shell in the meridional direction may be arbitrary. Material and structural orthotropy of the shell have also been taken into account. The problem is posed in a variational form. The functional associated with Hamilton’s principle has been expanded into trigonometric series in the circumferential direction and finite-difference method has been applied along the meridian. In consequence, the problem has been converted into a generalized eigenvalue problem. Numerical examples, calculated with the program DYSAR based on an algorithm presented here, expose the possibilities of the method and the program itself. Analysis and comparison of these numerical results with the experimental data published in the literature confirm their correctness and accuracy, which turn out to be quite sufficient for practical applications even in the case of relatively small number of nodes of the finite difference net.
- The thermomechanical behaviour of fluid-saturated capillary-porous materials exposed to a drying process is examined in the paper. Basing on the balance equations of mass, momentum, energy and entropy and on the restrictions imposed on these equations by the thermodynamics of irreversible processes, one develops the differential equations describing the evolution of the drying body deformations, and the temperature and moisture concentration fields. Several periods of the drying process are distinguished and for these periods the respective models are proposed. The presented theory concerns an arbitrary technology of drying, but examples of boundary conditions are given for the convective means of drying, which is mostly employed in technology.
- This paper concerns the inelastic stability of a thin plate under in-plane loading. In Love-Kirchhoffs approximation, using Hencky's relations and the Von Mises criterion, yield the particular stress distribution across the plate thickness for elastic and elastic-plastic prestress fields. The principle of virtual work is used to study the equilibrium of the bifurcated solution. This leads to the energy relations where explicit dependence between the stability equation coefficients and the solution is carried out. In the equilibrium equation, two nonquadratic additional terms are obtained which are neglected in the classical equation. Some applications are made using Ramberg-Osgood's formula to show the importance of the additional terms.
- This paper describes experimental research on the acoustical aspects of an axially-symmetrical radial diffuser. Tests were made at high subsonic and supersonic speeds at the diffuser entry, using compressed air. The results are analyzed from the point of view of the internal flow and Lighthill's theory of sound generated aerodynamically. The outstanding features of this diffuser are a high efficiency in subsonic and supersonic ranges and extreme shortness and powerful sound attenuating capacity. The noise level of a supersonic nozzle at Mach 4.0 was reduced from about 110 dB to 80 dB.
- This paper is concerned with a uniqueness theorem for the mixed problem within the framework of a linearized theory of materials with memory predicting finite speeds of propagation.
