Instytut Podstawowych Problemów Techniki

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This paper describes some insights on applicability of a Selective Laser Melting and Direct Metal Laser Sintering technology-manufactured turbine blade models for aerodynamic tests in a wind tunnel. The principal idea behind this research was to assess the possibilities of using ‘raw’ DLMS printed turbine blade models for gas-flow experiments. The actual blade, manufactured using the DLMS technology, is assessed in terms of surface quality (roughness), geometrical shape and size (outline), quality of counterbores and quality of small diameter holes. The results are evaluated for the experimental aerodynamics standpoint. This field of application imposes requirements that have not yet been described in the literature. The experimental outcomes prove the surface quality does not suffice to conduct quantitative experiments. The holes that are necessary for pressure measurements in wind tunnel experiments cannot be reduced below 1 mm in diameter. The dimensional discrepancies are on the level beyond acceptable. Additionally, the problem of ‘reversed tolerance’, with the material building up and distorting the design, is visible in elements printed with the DLMS technology. The results indicate the necessity of post-machining of the printed elements prior their experimental usage, as their features in the ‘as fabricated’ state significantly disturb the flow conditions.

Słowa kluczowe:

additive manufacturing,compressor blade,Direct Metal Laser Sintering (DLMS) technology,experimental aerodynamics,rapid prototyping,Selective Laser Melting SLM

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Upper and lower estimates of Stieltjes function by N-point Padé approximants can be obtained using the new general inequality reported by Tokarzewski et al. (Arch. Mech. 54 (2002) 141–153) and rigorously proved in the present paper. In addition, we prove that the multipoint Padé approximants to Stieltjes function are symmetric with respect to the order of choice of the considered points.

Słowa kluczowe:

N-point Padé approximants, Stieltjes functions

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The aim of this paper is to describe the effects of wear particles, generated during articulation of the bearing surfaces of the total joint prosthesis on bone-implant interface. Submicron particles migrate into effective joint space and stimulate cells present in the fibrous tissue to release molecular signal. Cytokines activate the osteoclasts and in consequence bone loss may result. It weakens the bone-implant fixation and may cause aseptic loosening of the prosthesis.

Słowa kluczowe:

wear debris, bone–implant interface, total joint replacemtnt

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The paper is a review of modern mathematical methods for the analysis of continuous problems of nonlinear mechanics and magnetism. The bibliography contains 175 items. The second part of the paper deals with mechanical problems described by nonconvex density energy functions and with numerical methods to solve such problems.

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A Stieltjes function is expanded in mixed T- and S-continued fraction. The relations between approximants of this continued fraction and two-point Padé approximants are established. The method used by Gilewicz and Magnus (J. Comput. Appl. Math. 49 (1993) 79; Integral Transforms Special Functions 1 (1993) 9) has been adapted to obtain the exact relations between the errors of the contiguous two-point Padé approximants in the whole cut complex plane.

Słowa kluczowe:

Two-point Padé approximation, Stieltjes functions

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The aim of this paper is to analyze different contributions and differents points of view concerning the meaning of the piezoelectric effect in the bone. It is now obvious that this effect is overhelming in dry bone. In wet bone more important are streaming potentials.

Słowa kluczowe:

bone, piezoelectricity

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The present paper is the second part of the contribution by Rojek and Telega (2001). An alternative adhesion law was used to the study of bone-implant interface. Numerical scheme was developed and applied to the knee joint after arthroplasty. Influence of wear debris on this interface and currently used wear models were investigated.

Słowa kluczowe:

unilateral contact, adhesion, friction, wear, knee joint after arthroplasty, FEM

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The aim of this contribution is to examine the S-continued fraction method of obtaining bounds on the effective dielectric constant εe of a two-phase composite for the case where the dielectric coefficients ε1and ε2 of both components are either complex or real. The starting point for our study is a power expansion of εe(z) at(z)=0 (z)=ε2/ε1-1. The obtained S-continued fraction bounds have an interesting mathematical structure convenient for theoretical and numerical investigations of εe. They also agree with the earlier estimations reported by Bergman and Milton. Specific examples of calculation of bounds on εe by theS-continued fraction method are also provided.

Słowa kluczowe:

composite medium, bounds, dielectric constants, Stieltjes function

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Three problems are solved for a nonlinear model of elastic plates with transverse shear deformations. The material of the plate may be anisotropic. An existence theorem is formulated and proved for a class of boundary conditions. A uniqueness theorem is given for small loadings. The dual problem is derived and the minimax or Lagrangian approach is discussed.

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The aim of thikocvzeń article is to present the list of books by Polish scientists on applied mechanics in a rather broad sense. An effort was made to cover the last century. Previous Polish sources, until 1874, were collected by Kucharzewski (1894). A list of the main journals in applied mechanics is also given, essentially covering the period starting after the Second World War.

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On the basis of the paper [1] two topics are discussed. Firstly, exact formulae for the homogenized coeffi-cients of a layered thermopiezoelectric composite are derived. Secondly, by applying the Ritz method, the local problems are solved approximately. Specific cases are also examined and illustrated.

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Słowa kluczowe:

Epi-convergence in the strong topology of W11(Ω), space HB(Ω), homogenization of perfectly plastic plates, limit analysis and homogenization, periodically inhomogeneous material, relaxation of boundary conditions

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In [9] the formulae were derived for the effective moduli of a piezoelectric composite exhibiting fine periodic structure. The static case considered was studied by the method of F-convergence, cf.[l]. Next, in [10] these results were extended by investigating the dynamic behaviour. The same formulae for the effective moduli were obtained by using the method of Bloch expansions. The aim of this contribution is to present our preliminary results concerning homogenization of the equations of the linear thermopiezoelectricity. To such a problem the method of F-convergence is not applicable. Therefore the relevant analysis was performed by using the method of two-scale asymptotic developments. Our analysis leads to interesting conclusions related to the effective moduli and to the change of the initial condition for the temperature of the homogenized body.

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This paper consists of two parts. In the first part the method for the choice of a bilinear form rendering a non-linear operator potential has been developed. The method constitutes an extension of Magri's approach, the last being valid for linear operators only.

The second part of the paper is concerned with the method of adding the adjoint operator. It has been proved that a system of two coupled operator equations consisting of a given non-linear operator equation and the equation determined by the adjoint of its Frechet derivative is described by a potential operator. The variational functional has been derived. Some particular cases have been discussed.

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Equations of plane compressible flow of perfectly-plastic solids are derived from a three-dimensional, tensorially nonlinear theory of Sawczuk and Stutz. In plane flow the flow rule reduces to a linear relation. The flow law is, in general, not associated with the yield condition. The system of stress and velocity equations may be hyperbolic, parabolic or elliptic depending upon the material constants and dilatancy. The second order effects manifest in the expressions describing the stress and velocity fields, the yield condition and the power of dissipation.

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