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  1. 9 International Journal of Applied Mechanics and Engineering
  2. 8 Inżynieria Rolnicza
  3. 7 Acta Mechanica et Automatica
  4. 6 Acta Agrophysica
  5. 6 International Agrophysics
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  1. 1 2023
  2. 2 2022
  3. 2 2021
  4. 1 2020
  5. 6 2019
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  1. 5 Dobosz S. M.
  2. 5 Grabarczyk A.
  3. 5 Major-Gabryś K.
  4. 4 Bohdziewicz J.
  5. 4 Horabik J.
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1
Content available remote Analysis of optimality conditions for some topology optimization problems in elasticity
100%
Trabucho L.
International Journal of Applied Mathematics and Computer Science
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2002
|
tom 12
|
nr 1
127-137
EN
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bendso e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known.
2
Content available "PIES" in problems of 2D elasticity with body forces on polygonal domains
100%
Bołtuć A. , Zieniuk E.
Journal of Theoretical and Applied Mechanics
|
2011
|
tom Vol. 49 nr 2
369-384
EN
The paper presents a thorough review of the effective approach to solving problems of plane elasticity with body forces of different types. The proposed method bases on generalization of the parametric integral equation system (PIES), which was successfully applied to solving boundary problems without body forces. The main aim of the mentioned generalization was to create such an approach which does not require physical discretization of the domain, or division it into cells, like it is done in the classic boundary element method (BEM). First, only problems defined on polygons were considered. The paper also contains the analysis of the accuracy of obtained solutions in comparison with analytical or other numerical results.
PL
W pracy zaprezentowano i gruntownie zweryfikowano efektywny sposób rozwiązywania zagadnień z zakresu płaskiej teorii sprężystości z siłami masowymi różnego typu. Zaproponowany sposób polega na uogólnieniu parametrycznego układu równań całkowych (PURC), wcześniej z sukcesem stosowanego do rozwiązywania zagadnień brzegowych bez sił masowych. Celem uogólnienia było zastosowane takiego podejścia, które charakteryzowałoby się brakiem konieczności fizycznej dyskretyzacji obszaru czy dzielenia go na komórki, jak jest to stosowane w klasycznej metodzie elementów brzegowych (MEB). W pracy w pierwszej kolejności ograniczono się do zagadnień zdefiniowanych na obszarach wielokątnych. W pracy dokonano analizy dokładności otrzymywanych rozwiązań w porównaniu do wyników analitycznych oraz numerycznych.
3
Content available Three-dimensional elastic and elasto-plastic frictional contact analysis of turbomachinery blade attachments
100%
Zboiński G. , Ostachowicz W.
Journal of Theoretical and Applied Mechanics
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2001
|
tom Vol. 39 nr 3
769-790
EN
The paper presents a summary of the research on three-dimensional contact analysis of turbomachinery blade attachments in the elastic and elasto-plastic range. In that context the paper deals with theoretical, methodological and phenomenological description of the problem. The paper focuses on the applied variational formulation of contact problems of elasticity and elasto-plasticity and the corresponding finite element methods, utilizes contact mechanics algorithms as well as describes displacement, stress, contact and slip states within real turbomachinery blade attachments. Non-linear character of contact mechanics procedures and influence of these nonlinearities on stress and deformation within the attachments are treated with special care.
PL
Trójwymiarowa analiza kontaktowa z tarciem zamocowań łopatek maszyn wirnikowych w zakresie sprężystym i sprężysto-plastycznym. Niniejsza praca przedstawia podsumowanie wyników badań nad trójwymiarową analizą kontaktu w zamocowaniach łopatek maszyn wirnikowych w zakresie sprężystym i sprężystoplastycznym. W tym kontekście zaprezentowane zostały istotne aspekty analizy związane z teoretycznym, metodologicznym i fenomenologicznym opisem problemu. Praca koncentruje się na zastosowanych sformułowaniach wariacyjnych problemów kontaktowych sprężystości i sprężysto-plastyczności, odpowiadających im metodach elementów skończonych, zaproponowanych algorytmach kontaktowych, a także opisach stanów przemieszczeń, naprężeń, kontaktu i poślizgów w rzeczywistych zamocowaniach łopatek turbinowych. Ze szczególną uwagą potraktowano problemy nieliniowego charakteru algorytmów kontaktowych oraz wpływu tych nieliniowości na naprężenia i odkształcenia w zamocowaniu.
4
Content available remote Application of PIES and Rectangular Bezier Surfaces to Complex and Non-homogeneous Problems of Elasticity with Body Forces
100%
Boltuc A. , Zieniuk E.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
|
2010
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tom Vol. 14, No 4
363-376
EN
This paper presents a variety of applications of an effective way to solve boundary value problems of 2D elasticity with body forces. An overview of the approach is presented, its numerical implementation, as well as a number of applications, ranging from problems defined on elementary shapes to complex problems, e.g. with non-homogeneous material. The results obtained by the parametric integral equation system (PIES) were compared with the analytical and numerical solutions obtained by other computer methods, confirming the effectiveness of the method and its applicability to a variety of problems.
5
Content available remote DD-MIC(0) preconditioning of rotated trilinear FEM elasticity systems
100%
Georgiev I. , Margenov S.
Computer Assisted Mechanics and Engineering Sciences
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2004
|
tom Vol. 11, No. 2-3
197-209
EN
New results about preconditioning of rotated trilinear nonconforming FEM elasticity systems in the case of mesh anisotropy are presented. The solver of the arising linear system is based on the constructed efficient preconditioner of the coupled stiffness matrix. Displacement decomposition of the stiffness matrix is used as a first step of the algorithm. At the second step, modified incomplete factorization MIC(0) with perturbation is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained block-diagonal matrix. The derived condition number estimates and the presented numerical tests well illustrate the behaviour of the theoretically studied algorithms as well as their robustness for some more realistic benchmark problems.
6
Content available remote Auxetic materials — A review
100%
Carneiro V. H. , Meireles J. , Puga H.
Materials Science Poland
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2013
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tom Vol. 31, No. 4
561--571
EN
Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson’s ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown.
7
Content available Measurement of Molding Sand Elasticity
100%
Major-Gabryś K. , Grabarczyk A. , Dobosz S. M. , Jakubski J. , Morek J. , Beňo J.
Journal of Casting & Materials Engineering
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2018
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tom Vol. 2, no. 2
38--44
EN
The progressive mechanization and automation of industrial equipment is the driving force of progress, not only in the field of production but also in the measuring and control equipment. In mold production, the automation of processes such as forming molds and cores along with their assembly has led to increases in serial production, reductions in defects, and the shortening of molding times, among others. Thanks to automation in mold and core departments and the use of all sorts of manipulators, mold production in foundries has gained momentum. Unfortunately, in addition to the mentioned advantages, there are also new challenges as to the quality and properties of the molding and core sands used in highly automated foundries.This article presents recent research on molding sand elasticity. The topic was introduced as an attempt to answer the new needs of highly mechanized foundries. The article discusses a new method of measuring the resistance of molding materials to undergoing mechanical deformation (molding sand elasticity), with an additional analysis of the bending strengths of the tested samples. Precise measurements, test sample preparation, and interpretation of the received results are presented in the article.
8
Content available Micromechanical model of auxetic cellular materials
100%
Janus-Michalska M.
Journal of Theoretical and Applied Mechanics
|
2009
|
tom Vol. 47 nr 4
737-750
EN
An effective anisotropic continuum formulation for auxetic cellular materials is the objective of this paper. A skeleton is modelled as a plane beam elastic structure with stiff joints. The skeleton topology, forming concave polygons, is responsible for negative Poisson’s ratio effect. The essential macroscopic features of mechanical behaviour are inferred from the deformation response of a representative volume element using the framework of micromechanical analysis. The strain energy of a unit cell is calculated by adding the tensile, shearing and bending strain energy of individual members. The equivalent continuum is based on averaging this energy, thus formulating the basis for computing the anisotropic stiffness matrix. The structural mechanics methodology and ANSYS finite element code are applied to solve the beam model of the skeleton. Graphical representation of certain material constants such as Young’s modulus, Poisson’s ratio, shear modulus and generalized bulk modulus is given. The results of included parametric study may be used for proper choice of geometric and material data of the skeleton for a given structural application of the anisotropic continuum.
PL
Celem pracy jest sformułowanie efektywnego anizotropowego continuum sprężystego dla materiałów komórkowych o ujemnym współczynniku Poissona. Szkielet materiału jest modelowany przez płaską strukturę belkową połączoną w sztywnych węzłach tworzącą układ wielokątów wklęsłych. Kąty wklęsłe w strukturze materiału odpowiadają za efekt ujemnego współczynnika Poissona. Poprzez zastosowanie modelu mikromechanicznego istotne cechy mechaniczne materiału komórkowego są wyprowadzone z wyników analizy komórki reprezentatywnej. Potencjał sprężysty szkieletu komórki jest wyznaczony jako suma energii w belkach tworzących szkielet od ich rozciągania, ścinania i zginania. Efektywne continuum jest oparte na uśrednianiu potencjału sprężystego, co jest podstawą konstruowania macierzy sztywności. Metoda analizy strukturalnej przeprowadzona za pomocą programu MES-ANSYS jest stosowana dla modelu belkowego szkieletu. Jako wynik tej analizy przedstawiono graficznie rozkłady modułu Younga, współczynnika Poissona, modułu na ścinanie i uogólnionego współczynnika ściśliwości objętościowej. Studium parametryczne umożliwia prześledzenie wpływu parametrów geometrycznych struktury i charakterystyk materiału szkieletu na własności kontinuum zastępczego jako materiału o zastosowaniu strukturalnym.
9
Content available remote Topology optimization of quasistatic contact problems
100%
Myśliński A.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 2
269-280
EN
This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.
10
Content available Applications of differential calculus in economics. A few simple examples for first-year students
100%
Biernacki M.
Didactics of Mathematics
|
2016
|
nr 13(17)
5-12
EN
First-year students usually ask whether they really need mathematics. This paper presents several simple examples applying differential calculus in microeconomics, which allow students to perceive that learning mathematics during their studies of economics does “pay off”.
11
Wyznaczanie charakterystyk sprężystych metalowego sprzęgła podatnego skrętnie
100%
Filipowicz K.
Przegląd Mechaniczny
|
2009
|
tom nr 3
15-20
PL
W pracy przedstawiono opis stanowisk badawczych i metodykę wyznaczania jego sprężystych charakterystyk statycznych i dynamicznych. Zaprezentowano także uzyskane wyniki badań nowych metalowych sprzęgieł podatnych skrętnie.
EN
Description of testing stands and methodology of evaluation of static and dynamic characteristics of torsional flexible couplings have been presented in the paper. There also have been presented new results of investigation of metallic torsional flexible couplin.
12
Content available remote Optimum design of elastic moduli for the multiple load problems
100%
Lewiński T.
Archives of Mechanics
|
2021
|
tom Vol. 73, nr 1
27--66
EN
The paper deals with minimization of the weighted average of compliances of structures, made of an elastic material of spatially varying elasticity moduli, subjected to n load variants acting non-simultaneously. The trace of the Hooke tensor is assumed as the unit cost of the design. Three versions of the free material design are discussed: designing the moduli of arbitrary anisotropy (AMD), designing the moduli of an isotropic material (IMD), designing of Young’s modulus for a fixed Poisson ratio (YMD). The problem is in all cases reduced to the Linear Constrained Problem (LCP) of Bouchitté and Fragalà consisting of two mutually dual problems: stress based and strain based, the former one being characterized by the integrand of linear growth depending on the trial statically admissible stresses. The paper shows equivalence of the stress fields solving the (LCP) problem and those appearing in the optimal body subjected to subsequent load cases.
13
Deformation-enhanced fluctuations of the erythrocyte's spectrin-actin nodes and relation to single molecule measures of spectrin unfolding
100%
Lee J. C. M. , Discher D. E.
Cellular and Molecular Biology Letters
|
2001
|
tom 06
|
nr 2
14
Content available Contact strength of a system of two elastic half spaces with an axially symmetric recess under compression
88%
Monastyrskyy B. , Kaczyński A.
Acta Mechanica et Automatica
|
2010
|
tom Vol. 4, no. 4
64-70
EN
Frictionless contact of two isotropic half spaces is considered one of which has a small smooth circular recess. A method of solving the corresponding boundary value problem of elasticity in axially symmetric case is presented via the function of gap height. The governing integral equation for this function is solved analytically by assuming a certain shape of the initial recess. On the basis of the closed-form solution obtained the strength analysis of a contact couple is performed and illustrated from the standpoint of fracture mechanics.
15
Content available Material symmetry: a key to specification of interatomic potentials
88%
Nalepka K.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2013
|
tom Vol. 61, nr 2
441--450
EN
The paper shows that symmetry forms a basis for relations between different properties of material. In this way, the key quantities for specification of an atomistic model are identified. Material symmetry distinguishes representative processes of small strains. It is proved that the errors in the densities of the energies stored in these processes determine the range of inaccuracies with which an atomistic model recreates processes of small deformations. The errors are equal to the inaccuracies in the eigenvalues of the elasticity tensor, that is in the Kelvin moduli. For cubic crystals, the elementary processes indicated by the symmetry initiate the key paths of large deformations: Bain and trigonal ones. Therefore, the substantial errors in the Kelvin moduli lead to incorrect reconstructing the metastable phases: bcc, sc and bct. The elastic constants commonly used in the literature do not provide such information as the Kelvin moduli. Using the eigenvalues of the elasticity tensor as well as other key properties indicated by the symmetry, the EAM model proposed by A.F. Voter for copper is specified. The obtained potential more accurately reproduces small and large deformations and additionally, correctly describes defect formation as well as Cu dimer properties.
16
Content available remote Modelling and simulation of the curing process of polymers by a modified formulation of the Arruda–Boyce model
88%
Hossain M. , Steinmann P.
Archives of Mechanics
|
2011
|
tom Vol. 63, nr 5-6
621-621
EN
A phenomenologically motivated small strain model and a finite strain general framework to simulate the curing process of polymer have been developed and discussed in our recently published papers [1, 2, 3, 4]. In order to illustrate the capability of the finite strain framework proposed earlier, only the micromechanically-inspired 21-chain model and the phenomenologically motivated Neo-Hookean model (energy function) have been demonstrated so far. The Arruda–Boyce model (well-known as the 8-chain model in the elastic case and Bergström–Boyce model [5, 14] in the viscoelastic case) is a prototype hyperelastic model for polymeric materials. This follow-up contribution presents an extension of the Arruda–Boyce model [6] towards modelling the curing process of polymers. The necessary details, i.e. the stress tensor and the tangent operator, for the numerical implementation within the finite element method, are derived. The curing process of polymers is a complicated process where a series of chemical reactions have been activated, which will convert low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures via the chemical conversion. This paper will model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda–Boyce model. Several numerical examples have been demonstrated to verify our newly proposed, modified approach in case of curing process.
17
Content available remote First-principles study of mechanical, vibrational and thermodynamic properties of magnetic XC compounds (X = Rb, Sr)
88%
Lakdja A. , Benzaidi I. , Sayede A. , Chahed A.
Materials Science Poland
|
2017
|
tom Vol. 35, No. 3
463--469
EN
Lattice dynamic and mechanical properties of hypothetical RbC and SrC compounds were investigated using the ab-initio pseudopotential method and a linear response scheme. The lattice dynamics was studied in the framework of the density functional perturbation theory (DFPT). The dynamical and mechanical stability of the hypothetical RbC and SrC compounds was proved in their equilibrium B1 structure. In addition, the same stability was confirmed in the B3 phase. The thermodynamic properties were also investigated. They exhibited the same trend in both phases, and followed the Debye model. These results were confirmed in the ferromagnetic state, which makes the investigated compounds promising candidates in the spintronic field.
18
Content available remote Lattice model with power-law spatial dispersion for fractional elasticity
88%
Tarasov V.
Open Physics
|
2013
|
tom 11
|
nr 11
1580-1588
EN
A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.
19
Content available remote Theoretical Predictions of Lattice Parameters and Mechanical Properties of Pentaerythritol Tetranitrate under the Temperature and Pressure by Molecular Dynamics Simulations
88%
Tan J. J. , Hu C. , Li Y. , Ge N. , Chen T. , Ji G.
Acta Physica Polonica A
|
2017
|
tom 131
|
nr 2
318-323
EN
Molecular dynamics simulations with condensed-phase optimized molecular potentials for atomistic simulation studies force field are performed to investigate the structure, equation of state, and mechanical properties of high energetic material pentaerythritol tetranitrate. The equilibrium structural parameters, pressure-volume relationship and elastic constants at ambient conditions agree excellently with experiments. In addition, fitting the pressure-volume data to the Birch-Murnaghan or Murnaghan equation of state, the bulk modulus B₀ and its first pressure derivative B'₀ are obtained. Moreover, the elastic constants are calculated in the pressure range of 0-10 GPa at room temperature and in the temperature range of 200-400 K at the standard pressure, respectively. By the Voigt-Reuss-Hill approximation, the mechanical properties such as bulk modulus B, shear modulus G, and the Young modulus E are also obtained successfully. The predicted physical properties under temperature and pressure can provide powerful guidelines for the engineering application and further experimental investigations.
20
Modelling of load-displacement curves obtained from scaffold components tests
88%
Błazik-Borowa E. , Szer J. , Borowa A. , Robak A. , Pieńko M.
|
|
nr 2
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