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1

Finite element model and test results for punching shear failure of RC slabs

Lewiński Paweł, Więch Przemysław P.

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 2

80--95

EN

The nonlinear finite element analysis of pin-supported reinforced concrete slabs of moderate thickness is the main subject of this paper. This is an important issue of the mechanics of concrete structures. Thus, a nonlinear FE analysis of RC slab models subjected to punching shear was initiated and the comparison of the numerical and test results was made. The prediction engine of the crack pattern due to bending and extension is incorporated in the Mindlin-type (moderately thick) slab model together with other nonlinear features. This is in order to formulate an alternative model of RC slab in relation to the layered models or fully three-dimensional models. New formulas were applied for 3D constitutive relationships for concrete and for tension stiffening effect. Prediction of punching shear was facilitated by Podgórski’s failure criterion for concrete. On the one hand, a considerable advantage of the proposed approach is a relatively low numerical effort in comparison with the existing models, while on the other hand the applied model clearly describes the physical behaviour of a real slab. A supporting test programme for validation was run. Three RC slabs with a system of double-headed studs as the reinforcement against punching were tested by the authors in ITB Strength Tests Laboratory. The results for the units constructed as square slabs with a central short column subjected to full-scale tests were initially compared with assessments based on standard provisions and technical approvals. As a result of this approach, the overall prediction of the nonlinear behaviour of the test model, including the model of shear failure, is in accordance with the experimental data.

2

Comprehensive study of free vibration of rectangular mindlin’s plates with rotationally constrained edges using dynamic timoshenko trial functions

Verma Y.

Engineering Transactions

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2018

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Vol. 66, iss. 2

129--160

EN

A comprehensive theoretical study of the free vibration of rotationally restrained rectangular uniform isotropic Mindlin’s plate is presented. The plate mode shape is assumed to be a weighted combination of the product of the Timoshenko beam functions in the either direction, which are previously generated for rotationally constrained boundary conditions. The effect of the uniformly distributed rotational spring constant (modelling the edge) participates in the potential energy of the plate. The Rayleigh-Ritz method has been used to generate the natural frequencies and plate mode shapes for various intermediate boundary conditions, asymptoting to those of the plates with all possible (six) classical boundary conditions. Plates with various thickness ratios have been studied to converge the results to the corresponding Kirchhoff’s frequencies. The eigenvectors from the eigenvalue problem have been scrutinized to establish the beam-wise modal participation from either direction into the final plate mode shape. The square Mindlin’s plate mode shapes have been generated to establish the various types of frequencies; which have been innovatively named and categorized as the (i) single frequencies, (ii) repeated frequencies (identical twins) and (iii) non-repeated frequencies(fraternal twins). Plates with different rectangular aspect ratios have been also analysed to show the deviation in the frequencies and mode shapes from the square plate. Also, their asymptotic behaviour to the corresponding Timoshenko beam at extreme aspect ratios has been established.

3

Free Vibration Analysis of Mindlin Plates Resting on Pasternak Foundation Using Coupled Displacement Method

Rajesh K., Saheb K. M.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 1

107--128

EN

The authors developed a simple and efficient method, called the Coupled Displacement method, to study the linear free vibration behavior of the moderately thick rectangular plates in which a single-term trigonometric/algebraic admissible displacement, such as total rotations, are assumed for one of the variables (in both X,Y directions), and the other displacement field, such as transverse displacement, is derived by making use of the coupling equations. The coupled displacement method makes the energy formulation to contain half the number of unknown independent coefficients in the case of a moderately thick plate, contrary to the conventional Rayleigh-Ritz method. The smaller number of undetermined coefficients significantly simplifies the vibration problem. The closed form expression in the form of fundamental frequency parameter is derived for all edges of simply supported moderately thick rectangular plate resting on Pasternak foundation. The results obtained by the present coupled displacement method are compared with existing open literature values wherever possible for various plate boundary conditions such as all edges simply supported, clamped and two opposite edges simply supported and clamped and the agreement found is good.

4

Płyta Mindlina na trójparametrowym, inercyjnym podłożu sprężystym Własowa-Leontiewa pod obciążeniem impulsem siły

Ataman M., Szcześniak W.

TTS Technika Transportu Szynowego

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2017

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R. 24, nr 12

223--227, CD

PL

W artykule omówiono zadanie płyty o średniej grubości, z zastosowaniem teorii Mindlina, w przypadku dynamicznym. Sprężysta płyta o średniej grubości jest prostokątna i spełnia warunki brzegowe swobodnego podparcia na obwodzie. Dodatkowo płyta spoczywa na podłożu odkształcalnym Własowa-Leontiewa. Przyjęty model jednokierunkowego podłoża jest trójparametrowy i uwzględnia, oprócz współczynnika sprężystego osiadania, inercję podłoża oraz ścinanie w gruncie. Obciążenie analizowanego układu stanowi impuls siły Diraca, przyłożony w dowolnym punkcie na górnej powierzchni płyty.

EN

The paper deals with vibrations of the elastic Mindlin thick plate resting on the inertial Vlasov-Leotiev foundation. Inertial model of foundation is defined by three parameters: k , c, and m0. The plate is subjected to the impulse of force. Analytical solution of the problem is presented in the paper. Natural and forced vibrations of the plate are analysed.

5

Magneto-thermo-mechanical buckling analysis of Mindlin plate reinforced with FG-carbon nanotubes

Kolahchi R., Esmailpour M., Safari M.

Archives of Civil Engineering

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2016

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Vol. 62, nr 3

89--104

EN

A buckling analysis of temperature-dependent embedded plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a magnetic field is investigated. The SWCNTs are distributed as uniform (UD) and three types of functionally graded nanotubes (FG), in which the material properties of the nano-composite plate are estimated based on the mixture rule. The surrounding temperature-dependent elastic medium is simulated as Pasternak foundation. Based on the orthotropic Mindlin plate theory, the governing equations are derived using Hamilton's principle. The buckling load of the structure is calculated based on an exact solution by the Navier method. The influences of elastic medium, magnetic field, temperature and distribution type, and volume fractions of SWCNT are shown on the buckling of the plate. Results indicate that CNT distribution close to the top and bottom are more efficient than that distributed near the mid-plane for increasing the stiffness of the plates.

PL

Badana jest analiza wyboczenia wbudowanych płyt zależnych od temperatury wzmacnianych jednościennymi nanorurkami węglowymi (SWCNT) poddawanych polu magnetycznemu. Nanorurki SWCNT są rozpowszechniane jako jednolite (UD), a także istnieją trzy typy rozmieszczenia FG (FGA, FGO, FGX). W celu uzyskania równoważnych właściwości materiałowych nanokompozytów dwufazowych (tj. polimer jako matryca i nanorurka węglowa jako wzmocnienie), stosuje się zasadę mieszaniny. Do modelowania matematycznego obecnej struktury stosuje ortotropową teorię płyty Mindlina. W tej teorii odkształcenie normalne i przy ścinaniu są rozpatrywane w kategoriach przemieszczenia punktu materiału na płaszczyźnie środkowej i obrotów normalnej i środkowej płaszczyzny w kierunku osi X i Y. W celu uzyskania obowiązujących równań, stosowana jest metoda energetyczna i zasada Hamiltona. Całkowita energia potencjalna płytki CNTRC to suma energii odkształcenia i pracy wykonanej przez ośrodek elastomerowy i pole magnetyczne. W przypadku energii odkształcenia, zależności przemieszczania w wyniku naprężenia są definiowane w celu uproszczenia. Ośrodek sprężysty zależny od temperatury otoczenia jest stymulowany jako podłoże Pasternaka ze stałą sprężyny i ścinania. Ponieważ ośrodek elastomerowy jest stosunkowo miękki, zakłada się, że sztywność fundamentu jest zależna od temperatury. Ponadto, w przypadku płytki poddawanej stałemu polu magnetycznemu, bierze się pod uwagę przyłożoną siłę masową oraz ocenia się elementy siły Lorentza na jednostkę płytki. Na koniec, korzystając z zasady Hamiltona i integrując wg części, uzyskuje się obowiązujące równania w zakresie wypadkowych naprężeń. Następnie, obliczając wypadkową naprężenia pod względem przemieszczenia i obrotów, uzyskuje się ostateczną formę obowiązujących równań.

6

A 16-node locking-free Mindlin plate resting on two-parameter elastic foundation – static and eigenvalue analysis

Buczkowski R., Taczała M., Kleiber M.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 2

99--114

EN

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

7

Mindlin plates resting on two-parameter tensionless elastic foundation

Buczkowski R., Torbacki W., Tkaczyk T.

Foundations of Civil and Environmental Engineering

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2002

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No. 2

15-26

EN

The paper presents a finite element model for bending analysis of thick plates resting on two-parameter elastic foundation. The formulation of the problem takes into account the shear deformation of the plate and unilateral contact conditions between the plate and the foundation. The numerical model is based on the eigh-teen-node zero-thickness isoparametric interface element interacting with quadratic Lagrange nine-node Mindlin plate elements. A rectangular plate with free edges resting on a two-parameter elastic tensionless foundation is used to verify the accuracy of the proposed model.

PL

Przedstawiono opis pewnego modelu MES służącego do analizy zginania płyt grubych spoczywających na sprężystym podłożu dwuparametrowym. Przedstawione sformułowanie uwzględnia efekt ścinania płyty oraz warunki kontaktu jednostronnego występującego między płytą a podłożem. Model numeryczny jest oparty na 18-węzłowym izoparametrycznym elemencie skończonym o zerowej grubości. Dla potwierdzenia słuszności zaproponowanego algorytmu wybrano przykład posadowienia swobodnej płyty (bez warunków podparcia) na podłożu w warunkach kontaktu jednostronnego.