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1

A new mixed-field theory for bending and vibration analysis of multi-layered composite plate

Lezgy-Nazargah M., Salahshuran S.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 3

818--832

EN

A novel mixed-field theory with relatively low number of unknown variables is introduced for bending and vibration analysis of multi-layered composite plates. The presented plate theory is derived from a parametrized mixed variational principle which is introduced recently by the first author. A global-local kinematic with a layer-independent number of variables is assumed for the description of the displacements of the plate. The considered kinematic stratifies the displacement and transverse stress continuity conditions at the mutual interfaces of the layers. It also fulfill the homogenous boundary conditions of the shear stresses on the upper/lower surfaces of the plates without using the shear correction factor. One-unknown variable fields which satisfy a priori the continuity conditions at the adjacent interfaces between layers and the zero boundary conditions on the bounding surfaces are considered for the approximation of the transverse shear stresses. The transverse normal stress along the total thickness of the multi-layered plate is approximated via a quadratic polynomial. The presented mixed-field plate theory has been validated through comparison of the bending and vibration analysis results with those obtained from the three-dimensional (3D) theory of elasticity and the results of the other classical and high-order plate theories.

2

Analiza możliwości zastosowania ultradźwiękowej termografii w podczerwieni w badaniach nieniszczących wielowarstwowych kompozytów aramidowych

Świderski W., Pracht M., Vavilov V.

Problemy Techniki Uzbrojenia

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2015

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R. 44, z. 134

7--21

PL

W artykule przedstawiono opis matematyczny algorytmu wymuszenia cieplnego generowanego źródłem ultradźwiękowym, zastosowanego w nieniszczących badaniach metodą aktywnej termografii w podczerwieni. Algorytm został użyty w numerycznym modelowaniu przepływu ciepła w opracowanym programie ThermoSon przeznaczonym do rozwiązywania zagadnień badań termicznych. Przeprowadzono symulacje numeryczne wykrywania defektów w wielowarstwowym kompozycie aramidowym, stosując ultradźwiękowe źródło wymuszenia cieplnego oraz wstępnie oceniono możliwości tej metody.

EN

The paper includes a mathematical algorithm describing a heat extortion process generated by an ultrasonic source used in non-destructive testing method of active infrared thermography. This algorithm has been used at numerical modelling of heat propagation in developed ThermoSon program designed to solve problems of thermal testing. There are carried out numerical simulations for detection of defects in multi-layer aramide composite that was heated by an ultrasonic source and a preliminary evaluation of this method usability.

3

Pękanie kompozytów warstwowych z materiałów o charakterystyce nieliniowej

Jaroniek M., Niezgodziński T.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2011

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z. 99

98-100

EN

Fabrication of the functionally graded materials (FGM) can be obtained by layered mixing of two materials of different thermo-mechanical properties with different volume ratios gradually changed from layer to layer such that first layer has only a few particles of the other phase and last has maximum volume ratio of this other phase. The material (FGM) is functionally graded thermal and stress barrier. Fracture problems in the layer can be studied using J integral in finite element method, because it is not path independent Consider a laminate composite in plane stress conditions, multi-layered beam bonded to planes. The fracture mechanics problem will be analysed using the photoelastic visualisation of the fracture events in a model structure.

4

Badania elastooptyczne oraz analiza odkształceń i naprężeń kompozytów warstwowych

Jaroniek M.

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

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2007

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Z. 357

3-156

EN

In the present paper the elastic and plastic defonnation in multi-layered composites of finite thickness has been analysed. Advanced mechanical and structural applications require accurate assessment of the damage state of materials during the fabrications as well as during the service. Due to the complex nature of the internl structure of the material, composites (including the layered composite) often fail in a variety of modes. The failure modes very often are influenced by the local material properties that may develop in time under heat and pressure, local defect distribution, process inducing residual stress, and other factors. Consider a laminate composite in pIane stress conditions, multi-layered beam bonded to planes having shear modulus Gi and Poisson's ratio VI respectively, subjected to bending. The behaviour of the cracks depends on the cracks configuration, size, orientation, material properties, and loading characteristic. The fracture mechanics problem will be attacked using the photoelastic visualisation of the fracture events in a model structure. The proposed analytical and experimental method will be developed for a layered composite fracture problem. Fabrication of the model of the TBC with FGM can be obtained by layered mixing of two photoelastic materials of different thenno-mechanical properties with different volume ratios gradually changed fonn layer to layer such that first layer has only a few particles of the other phase and last has maximum volume ratio of this other phase. The specimen can be built as layered beam, for example, glass layer at the bottom next particles of the same glass in the epoxy in several layers of various volume ratio of the glass in epoxy and pure epoxy at the top. The beam can be loaded in 4 point bending to generate cracks propagate through the FGM layer. Photoelastic examination of each state may be obtained for various crack configuration due to applied mechanical load (and if epoxy thermal expansion coefficient is different than the glass thermal expansion coefficient also thermal load should be applied). The development of the failure criterion for a particular application is also very important for the predictions of the crack path and critical loads. Recently, there has been a successful attempt to formulate problems of multiple cracks without any limitation. This attempt was concluded with the series of papers summarising the undertaken research for isotropic and non-homogeneous class of problems. In the present paper the elastic and plastic defonnation has been analysed using the Muskhelishvili' s complex potentials method. The elastostatic stress field is required to satisfy the well-known equilibrium equations using two analytic functions ψ(z) and χ(z). The distribution of stresses and displacements has been calculated using the finite element method (FEM). Finite element calculations were perfonned in order to verify the experimentally observed the isochromatic distribution during cracks propagation. The geometry and materials of models were chosen to correspond to the actual specimens used in the experiments. The numerical calculations were carried out using the finite element program ANSYS 6.1, 9, by applying the substructure technique. Two different methods were used: solid modeling and direct generation. For comparison the numerical and experimental isochromatic fringes distribution was shown in this paper. It is possible to fabricate a model using various photoelastic materials to model multi layered structure. Photoelasticity has shown to be promising in stress analysis of bearns with various number and orientation of cracks. Finite element calculations (FEM) were performed in order to verify the experimentally observed branching phenomenon and the isochromatic distribution observed during cracks propagation. The agreement between the finite element method predicted isochromatics-fringe pattems distribution and those determined photoelasticaly was found to be within 3ফ percent. Crack propagation in multi-layered composites of finite thickness is especially challenging and open field for investigation. The development of the failure criterion for a particular application is also very important for the predictions of the crack path and critical loads. Recently, there has been a successful attempt to formulate problems of multiple cracks without any limitation. This attempt was concluded with the series of papers surnmarising the undertaken research for isotropic and non-homogeneous class of problems. Crack propagation in multi-layered composites of finite thickness is especially challenging and open field for investigation.

5

Analiza teoretyczna i badania elastoplastyczne pękania kompozytów warstwowych

Jaroniek M.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

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2001

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Z. 73

183-194

PL

W kompozytach warstwowych składających się z różnych materiałów własności mechaniczne poszczególnych warstw zmieniają się w zależności od stosowanej technologii wykonania materiału. W kompozytach tego typu ocena wytrzymałości jest utrudniona ze względu na technologicznie narzuconą niejednorodność struktury. W przypadku elementów kompozytowych, składających się z warstw o różnych własnościach mechanicznych w przypadku rys lub szczelin strukturalnych, wokół szczelin powstaja strefy uszkodzeń hamowane lub rozwijane pod wpływem zamian stanu naprężenia oraz wzajemnego oddziaływania warstw. Analiza stanu naprężeń w takich elementach umożliwia opracowanie kryterium zniszczenia, odporności na pękanie poszczególnych warstw, ustalenie, jaki wpływ na hamowanie lub rozwój rys mają własności wytrzymałościowe struktury zmieniające się wzdłuż grubości. Analize stanu naprężeń w takich elementach umożliwia opracowanie kryterium zniszczenia, odporności na pękanie poszczególnych warstw, ustalenie, jaki wpływ na hamowanie lub rozwój rys mają własności wytrzymałościowe struktury zmieniające się wzdłuż grubości.

EN

Advanced mechanical and structural applications require accurate assessment of the damage state of materials during the fabrications as well as during the service. Due to the complex nature of the internal structure of the material, composites including the layered composite often fail in a variety of modes. The failure modes very often are influenced by the local material properties that may develop in time under heat and pressure, local defect distribution, process induced residual stress, and other factors. Consider a laminate composite in plane stress conditions, multi-layered beam bonded to planes having shear modulus Gi and Poissons ratio VI respectively, subjected to bending. The behaviour of the cracks depends on the cracks configuration, size, orientation, material properties and loading characteristic. The facture mechanics problem will be attacked using the photoelastic visualization of the facture events in a model structure. The proposed work will developd facture mechanics tools for a layered comosite facture problem.