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1
Content available n-sided polygonal hybrid finite elements involving element boundary integrals only for anisotropic thermal analysis
Cao R. F., Zhao X. J., Lin W. Q., Wang H.
Archives of Mechanics
|
2020
|
Vol. 72, nr 2
109--137
EN
As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.
2
Content available Stress distribution in an anisotropic beam subjected to load
Kyzioł L.
Journal of KONES
|
2018
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Vol. 25, No. 2
207--214
EN
The article presents the physical equations describing the isotropic and anisotropic materials. Orthotropic material and monotropic are special varieties of anisotropy. Constructional steel, pine wood and polyester-glass composite were tested. The beams were made from these materials. The beams were subjected to external loads. The external load caused internal forces in beams. Calculations of stress distribution were carried out by finite element method (Patran – Nastran software). The calculation results allowed for precise illustrate the distribution of stress especially in layered materials. The load is basically a transmitted through the strong layers of composite. This is illustrated in the figures. Wood is materials of a layered structure and is classified as inhomogeneous materials. Whereas steel is considered as a homogeneous material. Passing from the level of microscopic inhomogeneity to the macroscopic homogeneous level is called homogenization. This method formulates the macroscopic description by homogenizing microscopic properties. For the purpose of mathematical description of a material, the real centre can be substituted by a homogeneous centre. The homogenization method is commonly used to describe the properties of rocks, wood, composites, reinforced concrete, as well as human osseous tissues. The description of the mechanical properties of isotropic materials is based on the theory of elasticity, while the anisotropic materials are based on the anisotropic theory of elasticity. Calculations of anisotropic materials are quite complicated (large number of physical quantities) and sometimes-approximate results are obtained.
3
Content available remote The use of Hill anisotropic yield criterion in numerical analysis of bent timber elements reinforced with CFRP strips
Nowak T., Patalas F., Brol J.
Annals of Warsaw University of Life Sciences - SGGW. Forestry and Wood Technology
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2018
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No. 104
221--227
EN
Approaches to modelling heritage timber beams strengthened with CFRP strips are presented in this paper. The numerical analyses presented were completed in the ANSYS 17.0 computation environment, in which the plasticity of wood was defined using the Hill yield criterion and the generalised Hill yield criterion, which take into account the differing yield stresses during compression and tension. The results of a simulation are discussed and compared to results obtained in experimental testing.
4
Content available Micromechanical model of polycrystalline materials with lamellar substructure
Kowalczyk-Gajewska K.
Archives of Metallurgy and Materials
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2011
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Vol. 56, iss. 2
509-522
EN
Micromechanical model of polycrystalline materials with lamellar substructure is presented. The lamellar microstructure of grains is accounted for using the well-established framework developed for layered composites. Within the approach different scale transition rules between the level of lamellar grain and the polycrystalline sample can be employed. The model capabilities are tested using the example of α2 + γ-TiAl intermetallic. Elastic properties and the initial yield surface for the lamellar grain (PST crystal) and for the untextured polycrystal are estimated. Elastic and plastic anisotropy degree is analyzed.
PL
Zaprezentowano model mikromechaniczny materiałów polikrystalicznych o substrukturze lamelarnej. Substruktura laminatu obserwowana dla pojedynczego ziarna została uwzględniona przy wykorzystaniu tradycyjnego podejścia przyjmowanego w przypadku kompozytów warstwowych. W ramach proponowanego podejścia stosowane być mogą różne schematy przejścia mikro-makro z poziomu ziarna o substrukturze laminatu do poziomu polikryształu. Możliwości modelu zostały przetestowane na przykładzie intermetaliku α2 + γ-TiAl. Wyznaczono własności sprężyste i początkową powierzchnię płynięcia pojedynczego kryształu o substrukturze lamelarnej i polikryształu bez tekstury. Przeanalizowano stopień anizotropii własności sprężystych i plastycznych.
5
Content available Analysis of fracture toughness of structural timber. Part I. Theory and experimental tests
Kyzioł Lesław
Polish Maritime Research
|
2010
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nr 3
53--58
EN
This paper presents fundamentals of fracture mechanics of anisotropic materials. Fracture toughness of anisotropic materials, e.g. structural timber, depends a. o. on state of stress, environment, temperature and changes due to ageing, therefore in such materials cracking process runs in various ways. Timber is characterized by eighteen coefficients which determine its fracture toughness in contrast to metals for which this number is as low as three. In this part of considerations a way of conducting the tests of specimens subjected to cracking as well results of the tests of natural and modified timber, are presented.
6
Content available Analysis of fracture toughness of modified timber. Part II. Mathematical description
Kyzioł L.
Polish Maritime Research
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2010
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nr 4
59-63
EN
This paper presents results of fracture toughness tests on DCB specimens made of natural and modified pine wood. The energy release coefficients G�[alfa] were calculated for both the materials under TL and RL crack propagation modes and the 1st mode of loading. Relations between the energy release coeffcients G�[alfa]I and the stress intensity factors K�[alfa]I have been determined. The obtained test results are presented in the form of tables and diagrams.
7
Content available remote Cowin-Mehrabadi Theorem in six dimensions
Ahmad F.
Archives of Mechanics
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2010
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Vol. 62, nr 3
215-222
EN
The Cowin-Mehrabadi Theorem concerning normals to the planes of symmetry of an anisotropic material is generalized to six dimensions. Commutation of the reflection matrix with the 6×6 matrix representing the elasticity tensor in the six-dimensional formulation of the elasticity tensor, provides the condition for the existence of a plane of symmetry. This condition implies the existence of at least two isochoric states for every class except the triclinic one. A simple proof is presented of the fact that an axis of symmetry An, with n > 4 must be an axis of isotropy.
8
Content available remote Phenomenological Description of the Effect of Micro-Shear Banding in Micromechanical Modelling of Polycrystal Plasticity
Kowalczyk-Gajewska K., Pęcherski R. B.
Archives of Metallurgy and Materials
|
2009
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Vol. 54, iss. 4
1145-1156
EN
The rigid-plastic crystal plasticity model accounting for the effect of micro-shear banding mechanism on the reduction of the global strain hardening rate is presented. The instantaneous contribution of micro-shear bands in the rate of plastic deformation is described by means of the constitutive function fMS that depends on the type of strain path specified by the current direction of strain rate tensor. The capabilities of the model are explored by studying the strain-stress behavior of polycrystalline material together with the crystallographic texture evolution in the polycrystalline element.
PL
Przedstawiono sztywno-plastyczny model plastyczności kryształów uwzględniający wpływ mikropasm ścinania na redukcje globalnego modułu umocnienia. Chwilowy udział mikro-pasm ścinania w prędkości deformacji plastycznej został opisany poprzez dodatkowa konstytutywna funkcje fMS, która zależy od schematu odkształcenia zdefiniowanego przez aktualny kierunek tensora prędkości odkształceń. Zbadano możliwości proponowanego modelu mikromechanicznego w ramach analizy odpowiedzi materiału polikrystalicznego z uwzględnieniem rozwoju tekstury krystalograficznej.
9
Content available remote Experimental study with a Digital Image Correlation (DlC) method and numerical simulation of an anisotropic elastic-plastic commercially pure titanium
Toussaint F., Tabourot L., Vacher P.
Archives of Civil and Mechanical Engineering
|
2008
|
Vol. 8, no 3
131-143
EN
In this paper, the tensile behaviour of a commercially pure titanium is studied using a full-field strain measurement. A fine analysis of the measured strain fields is carried out in order to determine the intrinsic behaviour of the material. An elastic-plastic model taking material anisotropy into account is proposed. On the basis of experimental results, the parameters of this model are identified then introduced into a FEM code in order to simulate the behaviour of titanium. To assess the performance of the approach, the numerical results are finally analysed and compared with measurements coming from image processing. A quite satisfactory agreement between simulation and experiment is obtained.
PL
Podczas prób rozciągania blachy z handlowo czystego tytanu badano rozkład odkształceń za pomocą analizy obrazu i identyfikacji położenia przez korelację kontrastu. Metoda pozwoliła na wyznaczenie odkształceń podczas rozciągania na całej powierzchni próbki, łącznie ze strefą przewężenia, dla trzech kierunków rozciągania. Na podstawie pomiarów wyznaczono krzywe umocnienia, współczynniki anizotropii oraz przedstawiono równania konstytutywne badanego materiału, obejmujące izotropowy zakres sprężysty oraz anizotropowy zakres plastyczny. Do opisu właściwości anizotropowych zastosowano warunek Hilla z 1948 r. Poprawność modelu oceniono na podstawie modelowania MES próby rozciągania.
10
Content available remote Plasticization of a Counded Layer of Anisotropic and Loose Material
Malujda I.
Machine Dynamics Problems
|
2006
|
Vol. 30, No. 4
48-59
EN
The present paper attempts to formulate strength criterion of an anisotropic and loose medium. This criterion is the main element of a mathematical model describing the said plasticization processes of a bounded layer of such materials taking into account the influence of heat. This condition is the basis for determining actual parameters of forming the material and deciding on the design characteristics of machinery used for plasticization. The factor responsible for critical stress in rolled wood (i.e. stress being a result of a destructive force) is a yield point of wood during a stretching trial. This resistance is a basis for evaluating the technological value of composite materials (wood is classified as such) and it depends on the temperature and anatomical direction of along which load is applied. In case of sawdust a measure expressing its critical stress can be its yield point, determined empirically during a compression trial under influence of temperature. In case of both of the discussed resistance criteria, a rise in temperature is a factor of greatest importance.
11
Content available remote Badania numeryczne wpływu wartości kąta natarcia ostrza na proces formowania wióra podczas skrawania materiałów kruchych
Jonak J., Podgórski J., Gajewski J.
Eksploatacja i Niezawodność
|
2004
|
nr 4
5-8
PL
W artykule przedstawiono wyniki symulacji procesu skrawania anizotropowych ciał kruchych ostrzem o różnej wartości kata natarcia. Badano proces propagacji szczeliny towarzyszącej odspajaniu przez ostrze większych elementów wióra. Analizę prowadzono z wykorzystaniem Metody Elementów Skończonych w analizie naprężeń oraz w oparciu o metodę " traconych elementów " dla analizy propagacji szczelin.
EN
The results of cutting anisotropic fragile substance simulations are presented in this article. Analysis using finally elements methods in stresses was described.
12
Content available remote The influence of internal restrictions on the elastic properties of anisotropic materials
Kowalczyk-Gajewska K., Ostrowska-Maciejewska J.
Archives of Mechanics
|
2004
|
Vol. 56, nr 3
205-232
EN
The influence of internal restrictions on the elastic properties of anisotropic materials described by Hooke's law is discussed. Spectral decomposition of the stiffness tensor and the compliance tensor is applied. Possible types of restrictions imposed on the deformation modes are considered. An algorithm for accounting for these restrictions in a constitutive law that minimizes stiffening of the material is proposed. As examples, the volume-isotropic materials and fiber-reinforced materials are analyzed.
13
Content available remote Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials
Dłużewski P., Jurczak G., Antunez H.
Computer Assisted Mechanics and Engineering Sciences
|
2003
|
Vol. 10, No. 1
69-79
EN
A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative - instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models.
14
Content available remote The plane single crystal under off-axis uniaxial tension
Chenaoui A., Sidoroff F., Darrieulat M., Hihi A.
Archives of Mechanics
|
2002
|
Vol. 54, nr 3
223-244
EN
The tensile behaviour of a rigid-plastic single crystal obeying Schmid's law with isotropic hardening is investigated for an off-axis tensile test in one of its symmetry planes (plane single crystal). Identification of the active slip systems allows the determination of the plastic spin and the resulting evolution of the crystallographic directions. This results in the description of the tensile behaviour-stress and strain response, onset of instability - depending upon the initial orientation of the crystal and the hardening law.
15
Content available remote The influence material's anisotropy on the initial direction for crack propagation in plate under tension
Bozhydarnyk V.V., Sulym G.
Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
|
2000
|
z. 54 [179]
11-20
EN
A calculation model for evaluating the limit equilibrium state of reinforced anisotropic plates with craks, subjected to tensile loading, has been formulated. The model incorporates the propsed criterional equations and a method for determining the stress intensity factors near small cracks in the reinforced plates. The model was verified on the concrete problems.
16
Equilibrium configurations of magnetic flux lines in strongly anisotropic superconductors
Rogula D., Sztyren M.
Journal of Technical Physics
|
2000
|
Vol. 41, no 2
89-100
EN
The string model is applied to networks of magnetic flux lines in a strongly anisotropic superconducting medium. The notion of vectorial anisotropic string tension is introduced. It is shown that, contrary to the case of isotropic string, the tension is not tangent to the flux line. The equilibrium configurations of flux lines pinned to the anisotropic material are examined. The existence of spontaneously bent extremals, energetically more favorable than straight lines, is proven. The question of degeneracy of the solutions is discussed.
17
Content available remote On the order of singularity at V-shaped notches in anisotropic bodies
Blinowski A., Rogaczewski J.
Archives of Mechanics
|
2000
|
Vol. 52, nr 6
1001-1010
EN
The self-similar problem of stress singularity at the notch in infinite two-dimensional elastic orthotropic body was considered. The considerations were restricted to the notches symmetrically oriented with respect to the axes of orthotropy. Both, the extension and shear modes were studied. It was confirmed that in the limiting case of zero opening angle (semi-infinite crack), the order of singularity is the same as in the case of isotropic material -r^-1/2. This is not true in the case of finite opening angles. If the orientation of the notch axis is parallel to the axis of maximal stiffness, the order of singularity is lower than that for the case of perpendicular orientation. In the last case, if the ratio E[T]/E[L] is small enough, then the order of singularity in tension does not practically decrease with growing opening angle 2alpha up to alpha [is approximately equal to] pi/4.
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