Papers by Luiz Carlos Facundo Sanches
Boundary Elements and Other Mesh Reduction Methods XXIX, 2007
In this work, the plate bending formulation of the boundary element method (BEM) based on the Rei... more In this work, the plate bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis is extended to the analysis of zoned plates in order to model a building floor structure. In the proposed formulation each sub-region defines a beam or a slab and depending on the way the subregions are represented, one can have two different types of analysis. In the simple bending problem all sub-regions are defined by their middle surface. On the other hand, for the coupled stretching-bending problem all sub-regions are referred to a chosen reference surface, therefore eccentricity effects are taken into account. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. The bending and stretching values defined on the interfaces are approximated along the beam width, reducing therefore the number of degrees of freedom. Then, in the proposed model the set of equations is written in terms of the problem values on the beam axis and on the external boundary without beams. Finally some numerical examples are presented to show the accuracy of the proposed model.
In this work, the plate bending formulation of the boundary element method - BEM, based on the Re... more In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner?s hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.
Abstract. A recent method developed by means of the spatial Fourier transform generalizes the Bou... more Abstract. A recent method developed by means of the spatial Fourier transform generalizes the Boundary Element Methods (BEM) to the so-called Fourier-BEM. This approach is available for all cases as long as the differential operator is linear and has constant coefficients and is possible for all variants of the BEM. Via convolution and Parceval’s theorem, which states the equivalence of energy terms in the original space and in the Fourier space, the idea is to avoid the inverse Fourier transform of the fundamental solution and to work directly with the Fourier transformed fundamental solution. No inverse transform and no fundamental solution in the original space are required. Alternative Boundary Integral Equations (BIE) can be established in the Fourier transformed domain. A Galerkin approach lead to matrices identical to those obtained via the standard BIE and does not require a second integration. The elements and shape functions also can be transformed to the Fourier domain. I...
Synergismus Scyentifica Utfpr, Sep 1, 2009
Differential and integral elastic plates equations are frequently performed using numerical metho... more Differential and integral elastic plates equations are frequently performed using numerical methods like the Finite Element Method (FEM) or the Boundary Element Method (BEM). One of the main differences between these techniques is a direct treatment of boundary value problem in BEM analysis. It must be pointed out that corner forces are introduced in the direct boundary integral equation when polygonal plates are studied using classical theory. This parameter appears as a consequence of classical plate hypothesis in which curvatures are related with the second derivative of the out-of-plane displacement and it is the necessary condition to reduce boundary variables. However, when thick plate theory is considered curvatures are not directly related with out-of-plane displacement derivative and no corner forces are introduced even in BEM analysis. Further, three boundary conditions should be satisfied in thick plate analysis rather than two of classical theory. This study intends to present results obtained from plate bending problems using classical and thick plate theories in order to understand the differences in plate behavior due the features above mentioned. The classical plate analysis will be performed using Danson's fundamental solutions and Reissner theory will be used in thick plate's analysis with Weeën's fundamental solution. The numerical implementation is carried out for continuous or discontinuous isoparametric linear elements. A classical example is solved to show the aim of this paper and the results are compared with those available in the literature.
Synergismus Scyentifica Utfpr, Sep 1, 2009
Proceedings of the 23rd ABCM International Congress of Mechanical Engineering, 2015
Proceedings of the XXXVI Iberian Latin American Congress on Computational Methods in Engineering, 2015
Mathematical Problems in Engineering, 2007
A direct version of the boundary element method (BEM) is developed to model the stationary dynami... more A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane) and for the out-of-plane state (bending). These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corre...
... two fundamental solutions were proposed and they approaches to the Danson and Bezine-Stern so... more ... two fundamental solutions were proposed and they approaches to the Danson and Bezine-Stern solutions for thin plates when the thickness approaches to zero. ... Mitarbeiter, Leandro Palermo Junior, Leandro Palermo Junior [Orientador], João Batista de Paiva, Renato Soliani. ...
O presente trabalho trata do estudo das formulacoes estatica e dinâmica estacionaria de um modelo... more O presente trabalho trata do estudo das formulacoes estatica e dinâmica estacionaria de um modelo de folhas poliedricas, atraves da implementacao do Metodo dos Elementos de Contorno (MEC) na analise de pecas de parede fina e no modelamento do sistema de laje composta "Steel Deck". Elementos planos contendo os estados de flexao (placa) e extensao (membrana) foram associados para representar o modelo final de folhas poliedricas. A analise e feita em regime elastico linear mediante a hipotese de pequenas deformacoes e com equilibrio na posicao nao deslocada. O modelo final assume uma associacao de lâminas (folhas poliedricas) no espaco, onde em cada lâmina estao associados os estados de flexao e extensao. O sistema final de equacoes e obtido tratando-se cada folha poliedrica individual, como uma sub-regiao do MEC. Nas equacoes de cada sub-regiao, apos as transformacoes de coordenadas, procede-se a compatibilizacao de deslocamentos e equilibrio de forcas sobre as mesmas. O tratamento numerico foi feito atraves da formulacao direta do Metodo dos Elementos de Contorno, utilizando-se elementos isoparametricos lineares continuos e descontinuos e gerando-se as equacoes integrais em pontos de colocacao no contorno e fora do dominio. Com o proposito de mostrar a validade da formulacao, foram resolvidos exemplos estaticos e dinâmicos estacionarios de estados planos, placas finas, pecas de parede fina e do sistema de lajes composta "Steel Deck". Na analise dinâmica estacionaria sao determinadas as Funcoes de Resposta em Frequencia. Das informacoes contidas nas FRF, sao obtidas as frequencias naturais e os modos proprios de vibracao correspondentes. O procedimento e validado atraves de comparacoes com resultados analiticos e numericos disponiveis na literatura Abstract
Mathematical Problems in Engineering, 2007
A direct version of the boundary element method (BEM) is developed to model the stationary dynami... more A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane) and for the out-of-plane state (bending). These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).
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Papers by Luiz Carlos Facundo Sanches