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INSTYTUT ARCHEOLOGII I ETNOLOGII POLSKIEJ AKADEMII NAUK
INSTYTUT BADAŃ LITERACKICH POLSKIEJ AKADEMII NAUK
INSTYTUT BADAWCZY LEŚNICTWA
INSTYTUT BIOLOGII DOŚWIADCZALNEJ IM. MARCELEGO NENCKIEGO POLSKIEJ AKADEMII NAUK
INSTYTUT BIOLOGII SSAKÓW POLSKIEJ AKADEMII NAUK
INSTYTUT CHEMII FIZYCZNEJ PAN
INSTYTUT CHEMII ORGANICZNEJ PAN
INSTYTUT FILOZOFII I SOCJOLOGII PAN
INSTYTUT GEOGRAFII I PRZESTRZENNEGO ZAGOSPODAROWANIA PAN
INSTYTUT HISTORII im. TADEUSZA MANTEUFFLA POLSKIEJ AKADEMII NAUK
INSTYTUT JĘZYKA POLSKIEGO POLSKIEJ AKADEMII NAUK
INSTYTUT MATEMATYCZNY PAN
INSTYTUT MEDYCYNY DOŚWIADCZALNEJ I KLINICZNEJ IM.MIROSŁAWA MOSSAKOWSKIEGO POLSKIEJ AKADEMII NAUK
INSTYTUT PODSTAWOWYCH PROBLEMÓW TECHNIKI PAN
INSTYTUT SLAWISTYKI PAN
SIEĆ BADAWCZA ŁUKASIEWICZ - INSTYTUT TECHNOLOGII MATERIAŁÓW ELEKTRONICZNYCH
MUZEUM I INSTYTUT ZOOLOGII POLSKIEJ AKADEMII NAUK
INSTYTUT BADAŃ SYSTEMOWYCH PAN
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.
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