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Contribuição ao estudo de painéis reforçados: comparação entre o método da chapa ortotrópica e o método dos elementos finitos.; Contribution to the study of reinforced panels: comparison between orthotropic plate method and the finite element method.

Galindo Orozco, Juan Carlos
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 05/12/2008 PT
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46.25%
Métodos convencionais, tais como o método da chapa ortotrópica, têm sido aplicados por muitos anos no estudo de painéis reforçados pela sua simplicidade e facilidade de aplicação na determinação de tensões agentes nas fases iniciais da espiral projeto. Não estão disponíveis na literatura, porém, análises comparativas do método da chapa ortotrópica com procedimentos numéricos utilizando elementos finitos (MEF) que permitam a determinação da acurácia ou da ordem de grandeza dos desvios inerentes à aplicação desta metodologia. O presente trabalho apresenta análises comparativas entre estas duas metodologias na solução de painéis reforçados submetidos a carga lateral uniforme, tipicamente aplicados a estruturas navais (chapa em apenas um dos lados com reforçadores em T). Com este objetivo foram construídos modelos de painéis simplesmente apoiados e engastados (modelagem com elementos de viga e casca) com diferentes espaçamentos e diferentes inércias de reforçadores, configurando uma ampla matriz de análise paramétrica. Os resultados de deflexões e tensões nas vigas e chapas obtidos dos modelos MEF foram parametrizados em função das variáveis da chapa ortotrópica (razão de aspecto virtual), (coeficiente de torção) e K (parâmetro adimensional de tensões e de deflexão). Esta parametrização permite gerar curvas numéricas de tensão e deflexão dos modelos em estudo. As curvas numéricas assim geradas são comparadas com as curvas propostas pelo método da chapa ortotrópica para painéis reforçados simplesmente apoiados...

Dynamic instability of imperfect laminated sandwich plates with in-plane partial edge load

Chakrabarti,Anupam; Sheikh,Abdul Hamid
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2010 EN
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46.13%
Dynamic instability of laminated sandwich plates having inter-laminar imperfections with in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. A linear spring-layer model is used to model the inter-laminar imperfection by considering in-plane displacement jumps at the interfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C1 continuity of transverse displacement (w) i.e., w and its derivatives should be continuous at the common edges between two elements, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.

Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

Ghugal,Yuwaraj Marotrao; Kulkarni,Sanjay Kantrao
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2013 EN
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46%
Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory

Asemi,S.R.; Mohammadi,M.; Farajpour,A.
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2014 EN
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45.92%
Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. In the present work, the posbuckling response of orthotropic single-layered graphene sheet (SLGS) is investigated in a closed-form analytical manner using the nonlocal theory of Eringen. Two opposite edges of the plate are subjected to normal stresses. The nonlocality and geometric nonlinearity are taken into consideration, which arises from the nanosized effects and mid-plane stretching, respectively. Nonlinear governing differential equations (nonlocal compatibility and equilibrium equations) are derived and presented for the aforementioned study. Galerkin method is used to solve the governing equations for simply supported boundary conditions. It is shown that the nonlocal effect plays a significant role in the nonlinear stability behavior of orthotropic nanoplates. Unlike first and second postbuckling modes, nonlocal effects decrease with the increase of lateral deflection at higher postbuckling modes. It is also observed that the nonlocality and nonlinearity is more pronounced for higher postbuckling modes.

Stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension

Kotooussov, A.; Lew, Y.
Fonte: Pergamon-Elsevier Science Ltd Publicador: Pergamon-Elsevier Science Ltd
Tipo: Artigo de Revista Científica
Publicado em //2006 EN
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45.92%
The stress singularities in angular corners of plates of arbitrary thickness with various boundary conditions subjected to in-plane loading are studied within the first-order plate theory. By adapting an eigenfunction expansion approach a set of characteristic equations for determining the structure and orders of singularities of the stress resultants in the vicinity of the vertex is developed. The characteristic equations derived in this paper incorporate that obtained within the classical plane theory of elasticity (M.L. Williams’ solution) and also describe the possible singular behaviour of the out-of-plane shear stress resultants induced by various boundary conditions.; http://www.elsevier.com/wps/find/journaldescription.cws_home/297/description#description; Andrei Kotousov and Yaw Tong Lew; Copyright © 2005 Elsevier Ltd All rights reserved.

An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core

Pandit, M.; Sheikh, A.; Singh, B.
Fonte: Elsevier Science BV Publicador: Elsevier Science BV
Tipo: Artigo de Revista Científica
Publicado em //2008 EN
Relevância na Pesquisa
46.09%
An improved higher order zigzag theory is proposed for the static analysis of laminated sandwich plate with soft compressible core. The variation of in-plane displacements is assumed to be cubic for both the face sheets and the core and transverse displacement is assumed to vary quadratically within the core while it remains constant through the faces. The core is considered to behave as a three-dimensional elastic medium to incorporate the effect of transverse normal deformation. A computationally efficient C0 finite element is also proposed for this model. Numerical examples of laminated composite and sandwich plate are provided for different thickness ratios and aspect ratio to illustrate the accuracy of the present formulation by comparing the present results with the three-dimensional elasticity solutions. Some new results are also presented. The performance of the present model is excellent in calculating displacements and stresses for a wide range of sandwich plate problems with transversely flexible core.; http://www.elsevier.com/wps/find/journaldescription.cws_home/505649/description#description; Mihir K. Pandit, Abdul H. Sheikh and Bhrigu N. Singh

On the Effect of Plate Thickness on Post-Overload Fatigue Crack Growth

Codrington, J.
Fonte: Kluwer Academic Publ Publicador: Kluwer Academic Publ
Tipo: Artigo de Revista Científica
Publicado em //2009 EN
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45.97%
Plate thickness can have a profound effect on fatigue crack growth following the application of an overload cycle. A modified strip-yield model is presented for determining the effects of plate thickness based on the mechanism of plasticity-induced crack closure and first-order plate theory. This approach eliminates the need for any empirical or fitting parameters. Comparisons are made with experimental data for the case of a single tensile overload applied under otherwise constant ∆Κ loading. The theoretical crack growth predictions are found to be in good agreement with the experimental data.; John Codrington

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

Pandit, M.; Sheikh, A.; Singh, B.
Fonte: Professional Engineering Publishing Ltd Publicador: Professional Engineering Publishing Ltd
Tipo: Artigo de Revista Científica
Publicado em //2008 EN
Relevância na Pesquisa
55.94%
This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.; M K Pandit, A H Sheikh and B N Singh; Copyright ©2008 Professional Engineering Publishing. All rights reserved.

Analysis of laminated sandwich plates based on an improved higher order zigzag theory

Pandit, M.; Sheikh, A.; Singh, B.
Fonte: University of Porto; Portugal Publicador: University of Porto; Portugal
Tipo: Conference paper
Publicado em //2008 EN
Relevância na Pesquisa
56.08%
A finite element model based on an improved higher order zigzag plate theory developed by the authors is refined in this study and applied to bending and vibration response of soft core sandwich plates. The theory satisfies interlayer transverse shear stress continuity including transverse shear stress free condition at the plate top and bottom surfaces and transverse normal compressibility of the core. The in-plane displacements vary cubically through the entire thickness, while transverse displacement is assumed to vary quadratically within the core. In order to have a better computational benefit, a C0 finite element formulation is adopted. This is refined through satisfaction of certain constrains variationally using a penalty function approach. The performance of the model is demonstrated by comparing the present results with 3D elasticity solutions and other available results.; M K Pandit, A H Sheikh, and B N Singh; Also published in: Journal of Sandwich Structures & Materials [serial online], 2009; June 5:www1-20

Transverse singular effects in V-shaped notches stressed in mode II

Harding, S.; Kotooussov, A.; Lazzarin, P.; Berto, F.
Fonte: Kluwer Academic Publ Publicador: Kluwer Academic Publ
Tipo: Artigo de Revista Científica
Publicado em //2010 EN
Relevância na Pesquisa
45.96%
The concept of a stress singularity is a cornerstone of modern fracture mechanics. A new mode of stress singularity, the out-of-plane singular mode or K O mode, was recently identified for V-shaped notches subjected to in-plane loading. This new mode is coupled with the shear mode and related to Poisson’s effect. The previous studies based on the first order plate theory focused on the derivation of a characteristic equation describing the strength of this singularity and provide no information regarding the intensity, extent and relevance of this mode to practical problems. This paper aims to fill this gap. The approach utilises the 3D finite element method and a standard regression technique for characterisation of the notch singular modes. A comprehensive study of the influence of Poisson’s ratio, plate thickness and notch opening angle on the value of the notch stress intensity factor associated with this mode is conducted for infinite plates. Additionally, to demonstrate the relevance of this new singular mode to practical problems an investigation of the out-of-plane mode and associated three-dimensional effects are presented for the case of a welded lap joint. Main areas of further research are also identified.; Steven Harding...

Dynamic instability of imperfect laminated sandwich plates with in-plane partial edge load

Chakrabarti, A.; Sheikh, A.
Fonte: Univ Sao Paulo Publicador: Univ Sao Paulo
Tipo: Artigo de Revista Científica
Publicado em //2010 EN
Relevância na Pesquisa
46.05%
Dynamic instability of laminated sandwich plates having inter-laminar imperfections with inplanepartial edge loading is studied for the first time using an efficient finite element platemodel. The plate model is based on a refined higher order shear deformation plate theory, wherethe transverse shear stresses are continuous at the layer interfaces with stress free conditions atplate top and bottom surfaces. A linear spring-layer model is used to model the inter-laminarimperfection by considering in-plane displacement jumps at the interfaces. Interestingly the platemodel having all these refined features requires unknowns at the reference plane only. However,this theory requires C1 continuity of transverse displacement (w) i.e., w and its derivatives shouldbe continuous at the common edges between two elements, which is difficult to satisfy arbitrarilyin any existing finite element. To deal with this, a new triangular element developed by theauthors is used in the present paper.; Anupam Chakrabarti and Abdul Hamid Sheikh

Application of refined plate theory to fracture and fatigue

Kotooussov, A.; Codrington, J.
Fonte: Bentham Science Publishers; Online Publicador: Bentham Science Publishers; Online
Tipo: Parte de Livro
Publicado em //2010 EN
Relevância na Pesquisa
45.88%
The work presented here is a compendium of theoretical results obtained by the authors between 2005 and 2009. Among these results are comprehensive analysis of the three-dimensional elastic stress and displacement fields near a tip of a through-the-thickness crack, generalization of the classical strip-yield model for plates having a finite thickness, and development of an analytical approach for calculating the plasticity-induced crack closure and crack growth rates at constant and variable amplitude loading. As an application of the developed approach, new predictive models of various non-linear fatigue crack growth phenomena in plates of finite thickness were developed. These include computational models of crack growth under small-scale yielding conditions and constant amplitude loading, growth of a fatigue crack emanating from a sharp notch, and crack growth retardation phenomenon following an overload cycle. All theoretical predictions were extensively compared with previous numerical and experimental studies demonstrating a great potential of the refined plate theory in the analysis of fracture and fatigue problems.; Kotousov, A. and Codrington J.

Finite element modeling of a plate with localized piezoelectric sensors and actuators

Abreu,G. L. C. M. de; Ribeiro,J. F.; Steffen, Jr.,V.
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2004 EN
Relevância na Pesquisa
56.01%
This paper presents the numerical modeling of a plate structure containing bonded piezoelectric material. Hamilton's principle is employed to derive the finite element equations using the mechanical energy of the structure and the electrical energy of the piezoelectric material. Then, a numerical model is developed based on Kirchhoff's plate theory. A computational program is implemented for analyzing the static and dynamic behavior of composite plates with piezoelectric layers symmetrically bonded to the top and bottom surfaces. A set of numerical simulations is performed and the results are compared with those from analytical formulation available in the literature and with software ANSYS® .

Boundary element method applied to the bending analysis of thin functionally graded plates

Damanpack,A. R.; Bodaghi,M.; Ghassemi,H.; Sayehbani,M.
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/05/2013 EN
Relevância na Pesquisa
46.01%
The present work introduces the boundary element method applied to the bending analysis of functionally graded plates. It is assumed that material properties are graded through the thickness direction of the plate according to a power law distribution. The neutral surface position for such plate is determined and the classical plate theory based on the exact neutral surface position is employed to extract the equilibrium equations. A direct approach based on the Green's identity is used to formulate boundary element method. By introducing a novel approach, domain integrals which arise from distributed transverse loads are transformed into boundary integrals. In case studies, three geometrical shapes including, rectangular, circular and elliptic for functionally graded plates with/without hole are considered. Comparative studies are first carried out to evaluate the sufficiency of the proposed method for bending analysis of isotropic and functionally graded plates subjected to the transverse loads. Then, a series parametric study is performed to examine the influences of the power of functionally graded material, boundary conditions and geometrical parameters on the deformation and stress of functionally graded plates.

Isogeometric finite element analysis of functionally graded plates using a refined plate theory

Nguyen-Xuan, H.; Tran, Loc V.; Thai, Chien H.; Kulasegaram, S.; Bordas, S. P. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/2013
Relevância na Pesquisa
45.96%
We propose in this paper a novel inverse tangent transverse shear deformation formulation for functionally graded material (FGM) plates. The isogeometric finite element analysis (IGA) of static, free vibration and buckling problems of FGM plates is then addressed using a refined plate theory (RPT). The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which achieve easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field of four degrees of freedom per each control point and retains the computational efficiency while ensuring the high accuracy in solution.

Isogeometric finite element analysis of laminated composite plates based on a four variable refined plate theory

Tran, Loc V.; Thai, Chien H.; Gan, Buntara S.; Nguyen-Xuan, H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/03/2014
Relevância na Pesquisa
45.96%
In this paper, a novel and effective formulation based on isogeometric approach (IGA) and Refined Plate Theory (RPT) is proposed to study the behavior of laminated composite plates. Using many kinds of higher-order distributed functions, RPT model naturally satisfies the traction-free boundary conditions at plate surfaces and describes the non-linear distribution of shear stresses without requiring shear correction factor (SCF). IGA utilizes the basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which achieve easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The static, dynamic and buckling analysis of rectangular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation.; Comment: arXiv admin note: substantial text overlap with arXiv:1310.1847

A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak

Bakharev, F. L.; Nazarov, S. A.; Sweers, G. H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/03/2012
Relevância na Pesquisa
45.88%
Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend both on the type of boundary conditions and the sharpness exponent of the peak.; Comment: 12 pages, 1 figure, submitted to Math. Mech. Compl. Sys

A multilayered plate theory with transverse shear and normal warping functions

Loredo, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.05%
A multilayered plate theory which takes into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear behaviour, the fifth is related to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho-Parmerter and (a modified version of) Beakou-Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal stretching, are also considered. All these theories can be emulated by the kinematic field of the present model thanks to the adaptation of the five warping functions. Results of all these theories are confronted and compared to analytical solutions, for the bending of simply supported plates. Various plates are considered, with special focus on very low length-to-thickness ratios: an isotropic plate, two homogeneous orthotropic plates with ply orientation of $0$ and $5$ degrees, a $[0/c/0]$ sandwich panel and a $[-45/0/45/90]_s$ composite plate. Results show that models are more accurate if their kinematic fields (i) depend on all material properties (not only the transverse shear stiffnesses) (ii) depend on the length-to-thickness ratio (iii) present a coupling between the $x$ and $y$ directions.; Comment: arXiv admin note: text overlap with arXiv:1311.1463

On a consistent finite-strain plate theory based on 3-D energy principle

Dai, Hui-Hui; Song, Zilong
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/07/2014
Relevância na Pesquisa
46.16%
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both geometrical and material nonlinearity) and by a series expansion, we deduce a vector plate equation with three unknowns, which exhibits the local force-balance structure. The success relies on using the 3-D field equations and bottom traction condition to derive exact recursion relations for the coefficients. Associated weak formulations are considered, leading to a 2-D virtual work principle. An alternative approach based on a 2-D truncated energy is also provided, which is less consistent than the first plate theory but has the advantage of the existence of a 2-D energy function. As an example, we consider the pure bending problem of a hyperelastic block. The comparison between the analytical plate solution and available exact one shows that the plate theory gives second-order correct results. Comparing with existing plate theories, it appears that the present one has a number of advantages, including the consistency, order of correctness, generality of the loadings, applicability to finite-strain problems and no involvement of unphysical quantities.

Development and applications of a quadratic isoparametric finite element for axisymmetric stress and deflection analysis

Janucik, F. X.
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Tese de Doutorado
EN_US
Relevância na Pesquisa
46.06%
The theory and computer program for an axisymmetric finite element for static stress and deflection analysis is presented. The element is an eight noded isoparametric quadrilateral based on the displacement method which is capable of representing quadratic variation of element boundaries and displacements. Element stiffness properties are developed for linear elastic small displacement theory using homogeneous isotropic material. Test cases are compared with theoretical solutions from the theory of elasticity to identify program capabilities and limitations. Ability to analyse axisymmetric problems and to represent curved element boundaries has been demonstrated. Example problems including a cylindrical pressure vessel, a disk of uniform thickness subjected to centrifugal body force, and stress concentrations in a cylindrical rod due to a spherical inclusion are presented. In each of these cases program predicted deflection and stress values were within 2% of theoretical values. Limitations which have been identified include the prediction of discontinuous stresses at adjacent element boundaries, failure to match original element boundary stress conditions in substructure analyses, and the necessity of double precision calculations to correctly analyse problems whose theoretical solutions obey small displacement plate theory. Analysis of a spherical pressure vessel resulted in predicted displacements within 4% of theoretical values while stresses on element boundaries varied by 60% from theoretical values. Substructure analysis for the spherical inclusion problem resulted in prediction of boundary stresses which were incompatible with those originally obtained. Techniques to overcome this difficulty are proposed but are not tested. The inability to obtain reasonable results for flexural problems was found to be due to round off error in the single precision technique used for solving the structure equilibrium relations. Use of double precision calculations resulted in displacements and stresses within .25% and 4.% respectively of theory for the case of a clamped circular plate loaded by a uniform pressure normal to its surface.