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S17 O Método dos Elementos de Contorno em Engenharia |
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Title:
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B.E.M. WITH GALERKIN TECHNIQUE, HYPERSINGULAR AND VECTORIAL FORMULATION, FOR 2D POTENTIAL PROBLEMS TO CALCULATE THE TANGENTIAL DERIVATIVE USING LINEAR ELEMENTS
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Summary :
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B.E.M. WITH GALERKIN TECHNIQUE, HYPERSINGULAR AND VECTORIAL FORMULATION, FOR 2D POTENTIAL PROBLEMS TO CALCULATE THE TANGENTIAL DERIVATIVE USING LINEAR ELEMENTS.
PLÍNIO FLEURY JR.
FACULDADE DE ENGENHARIA DA UERJ. DEP. DE ENGENHARIA MECÂNICA
R. SÃO FRANCISCO XAVIER 524 CEP 20550-013, RIO DE JANEIRO, R.J., BRASIL
E-MAIL: LAIDE@OPENLINK.COM.BR
WEBE J. MANSUR
COPPE/UNIVERSIDADE FEDERAL DO RIO DE JANEIRO. PROGRAMA DE ENGENHARIA CIVIL
CAIXA POSTAL 68506 CEP 21945-970, RIO DE JANEIRO, R.J., BRASIL
E-MAIL: WEBE@COC.UFRJ.BR
CÓDIGO DO TEMA S17 - O MÉTODO DOS ELEMENTOS DE CONTORNO EM ENGENHARIA.
ABSTRACT. THIS WORK PRESENTS A COMPUTATIONAL METHODOLOGY FOR BOUNDARY ELEMENT METHODS (B.E.M.) USING A VECTORIAL AND HYPERSINGULAR FORMULATION TO 2D POTENTIAL PROBLEMS (HEAT TRANSFER, FLUID TRANSFER, SOUND, PERCOLATION ETC.)(MANSUR AND OTHERS 1997) APPLYING THE GALERKIN TECHNIQUE AND LINEAR ELEMENTS (GRAY 1998) TO CALCULATE THE POTENTIAL, THE NORMAL DERIVATIVE AND THE TANGENTIAL DERIVATIVE. THE HYPERSINGULAR FORMULATION CAN FURNISH THE TANGENTIAL DERIVATIVE DIRECTLY, WHICH CAN BE USEFUL WHEN ONE WANT BOTH THE NORMAL AND TANGENTIAL DERIVATIVES IN ORDER TO OBTAIN THE RESULTANT FLUX. ALTHOUGH HAD BEEN SUBJECT OF INTENSIVE STUDIES (BÉZINE 1978, BREBBIA AND OTHERS 1989, FLEURY AND OTHERS 1998, GUIMARÃES AND OTHERS 1994, INGLER AND OTHERS 1990, STERN 1979 AND TELLES AND OTHERS 1993) THE HYPERSINGULAR FORMULATION UNTIL TODAY HAS VARY CONCEPTUAL ASPECTS NOT TOTALLY EXPLORED AND A METHODOLOGY NOT EXPERIMENTED. HERE IS STUDIED THE USE OF GALERKIN TECHNIQUE AND A VECTORIAL FORMULATION SHOWING THAT THE INCREASE OF WORK WITH DOUBLE INTEGRATION IS COMPENSATED BY LESS SINGULARITIES IN THE FIRST INTEGRATION AND NONE IN THE SECOND.
KEY WORDS: BOUNDARY ELEMENTS METHOD, HYPERSINGULAR FORMULATION, GALERKIN INTEGRALS.
BIBLIOGRAPHY
BÉZINE, G., 1978, BONDARY INTEGRAL FORMULATION FOR PLATE FLEXURE WITH ARBITRARY BOUNDARY CONDITIONS, MECHANICS RESARCH COMMUNICATIONS,5 (4): 197-206.
BREBBIA, C.A.,AND J., DOMINGUEZ, 1989, BOUNDARY ELEMNTS: INTRODUTORY COURSE, COMPUTATIONAL MECHANICS PUBLICATIONS, SOUTHAMPTON AND BOSTON.
FLEURY JR., P., MANSUR,W.J., AZEVEDO, J.P.S., 1998, A TÉCNICA DE GALERKIN COM ELEMENTOS LINEARES E FORMULAÇÃO HIPERSINGULAR DO M.E.C. PARA FENÔMENOS DE POTENCIAL, III SIMPÓSIO MINEIRO DE MECÂNICA COMPUTACIONAL, OURO PRETO, MG, BRASIL, V1, 411.
GUIMARÃES,S. AND TELLES, J.C.F., 1994, “ON HYPER-SINGULAR BOUNDARY ELEMENT FORMULATION FOR FRACTURE MECHANICS APPLICATIONS? ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 13,353-363.
GRAY L.J., 1998.EVALUATION OF SINGULAR AND HYPERSINGULAR GALERKIN INTEGRALS: DIRECT LIMITS AND SYMBOLIC COMPUTATION, COMPUTATIONAL MECHANICS PUBLICATIONS, BOUDARY ELEMNT METHODS, V. SLADEK AND J. SLADEK, SOUTHAMPTON, UK & BOSTON, USA.
INGLER, M. S. AND RUDOLPHI, T.J., 1990, “SOLUTION OF POTENTIAL PROBLEMS USING COMBINATIONS OF REGULAR DERIVATIVES AND DERIVATIVE BOUNDARY INTEGRAL EQUATIONS?APPL.MATH. MODELLING,14,536-543.
MANSUR,W.J., FLEURY JR., P., AZEVEDO, J.P.S., 1997, “A VECTOR APPROACH TO THE HYPER-SINGULAR BEM FORMULATIONS FOR LAPLACE’S EQUATION IN 2D? THE INTERNATIONAL JOURNAL OF BOUNDARY ELEMENT METHODS COMMUNICATIONS, VOL 8, N, 4, PAG, 239-250.
STERN, M., 1979, A GENERAL BOUNDARY INTEGRAL FORMULATION FOR NUMERICAL SOLUTIONS OF PLATE BENDING PROBLEMS, INT. J. SOLIDS STRUCTURES, 15,769-782.
TELLES,J. C. F., AND PRADO, A. A., 1993, HYPER-SINGULAR FORMULATION FOR 2-D POTENTIAL PROBLEMS, CHAP. 6 OF ADVANCED FORMULATIONS IN BOUDARY ELEMENT METHODS, ELSEVIER, LONDON..
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Author :
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Júnior, Plínio Fleury
Mansur, Webe J.
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