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COB41 NUMERICAL SIMULATION OF FLUID FLOW BY THE CONTROL VOLUME-FINITE ELEMENT METHOD
J.B. Campos silva(*) & L. F. M. Moura(**)
(*) Departamento de Engenharia Mecânica, Faculdade de Engenharia - UNESP - Ilha Solteira
CEP 15.385-000 Ilha Solteira - SP, Brasil - E-mail: jbcampos@feis.unesp.br
(**) Departamento de Engenharia Térmica e de Fluidos - FEM/UNICAMP - Campinas
CEP 13.081-970 Barão Geraldo/Campinas -SP, Brasil - E-mail: felipe@fem.unicamp.br
A control volume-finite element method (CVFEM) to simulate unsteady, incompressible and viscous fluid flows using nine-noded quadrilateral elements is presented. The mathematical modeling of flows is the Navier-Stokes equations in primitive variables u-v-p. The set of non-linear partial differential equations was integrated and after using interpolation functions and the time discretization, the algebraic system of equations was solved by using the frontal method of solution. The obtained results of some benchmark problems compared favorable with available results from the literature.
Keywords: Finite Element, Control Volume, Navier-Stokes Equations, Primitive Variables, Computational Fluid Dynamics.
COB76 OBTENCIÓN DE LA MATRIZ DE RIGIDEZ SECANTE EN MECÁNICA NO LINEAL DEL SÓLIDO / DERIVATION OF THE SECANT STIFFNESS MATRIX FOR NON LINEAR FINITE ELEMENT ANALYSIS OF SOLIDS
William Matias & Eugenio O ~ Nate y
Departamento de Engenharia Civil, Universidade de Bras'ilia - ENC/UnB
CEP 70910--900 Bras'ilia, Brasil - E-mail: taylor@guarany.cpd.unb.br
In this paper the general non symmetric parametric form of the secant stiffness matrix for non linear analysis of solids using finite element method is derived. A convenient symmetric expression for a particular value of the parameters is obtained. The geometrically non linear formulation is based on a Generalized Lagragian approach. Detailed expressions of all the relevant matrices involved in the analysis of 3D solids are obtained. The potential of using the secant stiffness matrix for developing new solution algorithms for non linear structural problem is also discussed. Examples of application are given for the non linear analysis of pin joined frames and 2D solids.
Keywords: geometric nonlinear analysis, secant stiffness matrix, Generalized Lagragian description
COB79 A SIMPLE LOCKING-FREE THREE-NODE SHELL FINITE ELEMENT
R.J. Marczak1 and A.M. Awruch2
1 Departamento de Eng. Mecânica - Universidade Federal do Rio Grande do Sul
Rua Sarmento Leite, 425, 90050-170, Porto Alegre-RS, Brazil - E-mail: rato@Qvortex.ufrgs.br
2 Departamento de Eng. Civil - Universidade Federal do Rio Grande do Sul Av. Osvaldo Aranha, 99, 3o andar, 90035-190, Porto Alegre-RS, Brazil
A simple triangular shell finite element with fifteen degrees of freedom for the analysis of general shell structures is presented in this work. The element uses a substitute transverse shear strain field to avoid locking, and is formulated on the basis of RSDS-element (Resultant Stress Degenerated Shell Element) approach, which leads to very simple strain-displacement expressions. The substitute shear strain field is derived assuming constant shear strains along the sides of the element, similar to the MITC (Mixed Interpolation in Tensorial Componentes) procedure. All integrations can be performed using only one point Gaussian rule, leaving the element with one non-comunicable zero energy mode, which does not affect the results. This procedure allows the use of symbolic engines to derive analytic expressions for stiffness matrices, reducing computational cost of the analysis by a significative amount.
Keywords: Finite element method, plates and shells, shear locking.
COB103 STRESS PREDICTIONS FOR SHORT FLAT BARS WITH PROJECTIONS SUBJECTED TO SHEAR LOADING
M. K. Pipelzadeh & S. J. Hardy
Department of Mechanical Engineering, University of Wales, Swansea, SA2 8PP, U. K.
The finite element method has been used to obtain stress concentration factor data for flat ' T' shaped components subjected to shear loading with local restraints being applied. This paper presents and describes the stress contours developed as a result of the shear load for a typical geometry. In addition, the stress concentration factor (SCF) data are used to obtain prediction equations using a multiple linear regression model. These equations provide guidelines for the assessment of the SCF by designers. The contours show the localised and large stress gradients in the vicinity of the fillet region. The ratio of the length to depth (or slenderness ratio) of the shank region is generally less than 3:1. For these short components particularly under shear (or bending) loads, primary bending stresses are no longer dominant and the transverse shear becomes an important secondary effect.
Keywords: Shear loading, stress concentration factor, finite element analysis, flat bars with projections.
COB109 ELASTIC CONTACT WITH FRICTION AS A CONDITIONAL MINIMIZATION PROBLEM / CONTATO ELÁSTICO COM ATRITO COMO UM PROBLEMA DE MINIMIZAÇÃO CONDICIONAL
Alberto Luiz Serpa1;2 & Fernando Iguti2
1. Eaton Limited - Transmissions Division, Rua Clark, 2061 - Valinhos - SP, C.P. 304,
13279-400, Brazil - E-mail: albertolserpa@eaton.com
2. Department of Computational Mechanics, Faculty of Mechanical Engineering,
Unicamp, C.P. 6122, Campinas - SP, 13083-970, Brazil - E-mail: serpa@fem.unicamp.br
This work presents a study of contact with friction between elastic bodies under the assumptions of infinitesimal elasticity. This is a non-linear problem due to the unilateral constraints (interpenetration of bodies) and friction. The solution can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to model the equations of elasticity. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-interpenetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to stick and slip conditions, equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised an approach called here as a conditional dependent constrained minimization problem. An Augmented Lagrangian Method is used. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration.
Keywords: Finite Element, Contact Problem, Mathematical Programming, Augmented Lagrangian / Elementos
Finitos, Problema de Contato, Programa¸c~ao Matem'atica, Lagrangiano Aumentado.
COB 155 ANALYSIS OF COLD ROLL FORMING OF THIN SHEET METAL FOR SOME ROLL-STANDS
Sylvie Idrissi-Ronel, Theophile Mehinto & Gerard Chalant
Laboratoire ‘Mécanique, Matériaux, Environnement’ (L.M.M.E.) , Faculté de Technologie
Avenue d’Estrée-BP 792-97337 CAYENNE -France E-mail: 105606.3500@compuserve.com
The cold-roll-forming of thin sheets is a forming process where initialy flat sheet is drawn along through roll stands which may have a complex form. The cold-roll-forming is a three dimensionnal problem with large transformations, elasto-plastic behaviour with contact and friction . The objectif of the model is to have a better knowledge of sheet strains, in order to obtain a product with optimised mecanical and geometrical qualities. The proposed method simulates the cold-roll-forming process by a two dimensionnal analysis on the sheet cross section resolved by linear finite elements, coupled with a three dimensionnal analysis of the sheet between adjacent roll stands. Complex profiles were modeled with this method.
Keywords: Finite Element, Large Deformations, elastoplastic behaviour, Contact, Cold-Roll-Forming.
COB182 The Preconditioned Conjugate Gradient Method for the Solution of Sparse Matrices: Finite Element Method Applications
Cesareo de La Rosa Siqueira
Naval Engineering Department, University of São Paulo - USP, CEP: 05508-900 São Paulo, Brazil - E-mail: cesareo@usp.br
Julio R. Meneghini
Mechanical Engineering Department, University of São Paulo -USP, CEP: 05508-900 São Paulo, Brazil - E-mail: jmeneg@usp.br
This paper presents the Preconditioned Conjugate Gradient Method (PCG) for the solution of sparse matrices and its application in the Finite Element Method. The Preconditioned Conjugate Gradient Method was implemented for the solution of a heat transfer problem in an unstructured mesh. The stiffness matrix generated by the Finite Element Method is sparse and banded. The results obtained for a conduction problem were in very good agreement with the analytical results. The performance of PCG is also compared with the unpreconditioned version of the algorithm in terms of CPU time for different computer platforms. This result is of practical importance when dealing with transient problems where saving time is essential as so many iterations are involved. As an example of this class of problems, the authors are implementing the method to study vortex shedding phenomenon using a 2D discrete vortex method including viscous diffusion in an unstructured finite element mesh.
Keywords: Preconditioned conjugate gradient, finite elements.
COB194 ANÁLISE DINÂMICA DE PLACAS E CASCAS ATRAVÉS DE ELEMENTOS FINITOS QUADRILATERAIS QUADRÁTICOS COM INTEGRAÇÃO NUMÉRICA CONSISTENTE / DYNAMIC ANALYSIS OF PLATES AND SHELLS THROUGH QUADRILATERAL QUADRATIC FINITE ELEMENTS WITH CONSISTENT NUMERICAL INTEGRATION
Amarildo Tabone Paschoalini, Loir Afonso Moreira & Fernando Iguti
Departamento de Engenharia Mecânica, Faculdade de Engenharia - UNESP/FEIS
CEP 15.385-000 Ilha Solteira, Brasil - E-mail: tabone@feis.unesp.br
The purpose of this work is a comparative performance study of plates and shells dynamic analysis, considering consistent numerical integration, of the Serendipity and Lagrangean isoparametric quadrilateral quadratic finite element families, obtained both from the Ahmad’s formulation; one intends to establish, between both elements, which is the most adequate to start the development of a subparametric hierarchical element, based on the p mesh refinement concept, intending to remove the excessive rigidity characteristic of the Ahmad’s element for thin plates and shells problems. One could notice from the obtained results that the Lagrangean family element has a consistently better performance than the Serendipity family element, particularly for thin plates and shells problems.
Keywords: Finite Elements Method, Numerical Integration, Structural Analysis, Shell, Plate.
Método dos elementos finitos, Integração numérica, Análise estrutural, Casca, Placa.
COB358 MALHAS ADAPTATIVAS DE ELEMENTOS FINITOS: APLICAÇÃO À ANÁLISE DE TENSÕES EM ELASTICIDADE BIDIMENSIONAL / ADAPTIVE FINITE ELEMENT MESHES: APPLICATION TO STRESS ANALYSIS IN TWO-DIMENSIONAL ELASTICITY
D.E.de Sá Nery, P.A.B. de Sampaio e R.J. Jospin
Instituto de Engenharia Nuclear /CNEN, caixa postal 68550 cep 21945-970 Rio de Janeiro-Brasil-E-mail: reinaldo@cnen.gov.br
An adaptive remeshing procedure for finite element plane stress analysis is presented. A variant of the Zienkiewicz and Zhu a posteriori error estimator is used to guide a Delaunay mesh generator based on Bowyer’s algorithm. The remeshing scheme is designed to create nearly optimal meshes containing a controlled number of elements. The numerical examples presented demonstrate the good performance of the Zienkiewicz and Zhu error estimator and the effectiveness of the remeshing scheme proposed.
Keywords : Finite Elements, Error Estimator, Adaptive Remeshing, Plane Stress, Linear Elasticity
Elementos Finitos, Estimador de Erros, Remalhagem Adaptativa, Tensões Planas, Elasticidade Linear
COB403 STRUCTURAL DYNAMIC ANALYSIS OF NONLINEAR MULTIBODY SYSTEMS BY A TIME-DISCONTINUOUS GALERKIN FORMULATION
J. G. Damilano & J. A. A. Duarte
Instituto de Aeronáutica e Espaço - CTA/IAE/ASE-E, CEP 12228-904 S. J. Campos, SP, Brazil
This work presents a study for structural dynamic analyses of nonlinear multibody systems, by a time- discontinuous Galerkin finite element method. A single-field formulation is used with the displacements approximated as a parabolic function continuous within each time slab, but discontinuous across time levels. Since the resulting system of equations is prone to high frequency oscillations the algorithm presented is well suited for the solution of such problems as it provides unconditional stability, third order accuracy and high frequency numerical damping. For conservative systems the relative difference in total energy at each time step is used as error indicator and an adaptive time stepping procedure is used to select the proper time step size. The solution for a linear oscillator gives access to the applicability of the algorithm to more complex problems and then the scheme is applied to a strongly nonlinear oscillator whose results are in excellent agreement with their analytical counterparts. The scheme allows the freedom to choose whatever initial time step size, since it searches for the best time step size that will provide the desired accuracy.
Keywords: Structural Dynamics; Adaptive Time Integration; Discontinuous Galerkin.
COB420 CONTACT PROBLEMS IN PLATES UNDERGOING LARGE DEFLECTIONS, USING A higher ORDER PLATE theory
Jackson Luís Barp
Departamento de Engenharia Mecânica - Centro de Ciências Tecnológicas -UNISINOS
CEP 93.022-000 São Leopoldo, RS, Brasil - E-mail: jbarp@stihl.com.br
Marco Antônio Luersen
Departamento de Mecânica, NuPES - Núcleo de Pesquisa em Engenharia Simultânea - CEFET-PR
CEP 80.230-901 Curitiba, PR, Brasil - E-mail: luersen@nupes.cefetpr.br
Carlos Alberto de Campos Selke
GRANTE - Grupo de Análise de Tensões - Departamento de Engenharia Mecânica - UFSC
CEP 88.040-900, Florianópolis, SC, Brasil - Email: selke@grante.ufsc.br
This work presents an incremental finite element formulation for contact problems of plates undergoing large deflections, with unilateral constraints, such as rigid foundations. A nine node lagrangian type isoparametric finite element, based on the Lo, Christensen and Wu higher order plate theory, is obtained using this formulation. The penalty method is used to solve the variational inequality that usually arises in contact problems, and the solution depends on the penalty parameter. Using the finite element obtained, bending problems of beams and plates, with their lateral displacements constrained by walls, are numerically solved, and the results are compared with solutions available in the literature.
Keywords: Contact, plate theories, finite elements.
COB504 DINÂMICA DE CASCAS CILÍNDRICAS CONTENDO FLUIDO EM FLUXO CIRCULAR: SOLUÇÃO DO PROBLEMA EM REGIME PERMANENTE / DYNAMIC OF THE CYLINDRICAL SHELL CONTAINE FLUID AT CIRCULAR FLUX: SOLUTION OF THE PROBLEM AT STEADY STATE
D.S.Aguiar e J.C. Menezes
CTA - ITA - IEM – Departamento de Projetos. CEP: 12228-904 – São José dos Campos – S.P, EMAIL: menezes@mec.ita.cta.br
This work present the solution and numerical results of the governing equations of a viscous fluid in steady state circunferencial motion. To describe the motion of the fluid, Navier-Stokes and Continuit equations are used (Panton,R.L.1984). The numerical solution is basead on the studies of Taylor e Hughes (Taylor e Hughes,1981), who employed the Finite Element Method for the two-dimension solution of the flow. Three velocity components are considered in a cylindrical coordinate system. To validate the results, the problem of a concentric journal bearing is solved , which shows a predictable press and velocities profile.
Keywords: Fluxo circular, regime permanente, método dos elementos finitos, dinâmica dos fluido/ circular flow, steady state, finite element method, fluid dynamic.
COB855 APLICAÇÃO DO MÉTODO DE ELEMENTOS FINITOS COM O AUXÍLIO DE SISTEMA ESPECIALISTA / APPLICATION OF FINITE ELEMENT METHOD AIDDED BY EXPERT SYSTEMS
Michael J. Fernandes, Lauro F. S. Ignácio Jr. & Edison da Rosa
Departamento de Engenharia Mecânica - Universidade Federal de Santa Catarina - UFSC
CP. 476 - Campus Universitário, Florianópolis, SC, Brasil - CEP 88040-900
E-mail: michael@grante.ufsc.br, lf@grante.ufsc.br, darosa@emc.ufsc.br
This paper presents an expert system to help the tasks of modelling physical problems through the finite element method. The construction of the modelling system is associated with two modules. The first one is an expert system that helps in the numerical model building , and the other one is a model manager that controls the whole process remaining, i. e., the model manager gets the geometry from a CAD modeller, based on ACIS standard, and perform a mesh generation. The user, following the advices received from the expert system, applies the loads and boundary conditions. After that, a finite element package reads this data, and solve the problem using adaptive methods to take accurate results.
Keywords: Expert Systems, Knowledge Based Systems, Structural Analysis, Finite Element Method, Preprocessor, Modelling / Sistemas especialistas, Sistemas baseados em Conhecimento, Análise Estrutural, Método de Elementos Finitos, Pré-processador, Modelagem.
COB988 MODELAGEM DA INTERAÇÃO QUASI-ESTÁTICA ENVOLVENDO SÓLIDOS ELÁSTICOS E RÍGIDO-PLÁSTICOS COM ÊNFASE NO FENÔMENO DE CONTATO / QUASISTATIC INTERACTION OF ELASTIC AND RIGID PLASTIC SOLIDS WITH EMPHASIS ON CONTACT PHENOMENA
Reynaldo Taylor-de-Lima & Wladmir Sybine
Departamento de Engenharia Civil - Pontifícia Universidade Católica do Rio de Janeiro, Rua Marques de São Vicente, 225.
CEP 22.453-900 Rio de Janeiro, RJ - Brasil, e-mail: taylor@civ.puc-rio.br / sybine@civ.puc-rio.br
Interaction and contact between solids are relevant phenomena in the context of structural engineering. In this field, loads are transmited by contact to structures which, in their turn, transmit loads to foundations by contact between bodies. In metal forming computations, such phenomena also play a major role. A good description of the interaction between workpiece and tools is of fundamental importance for a realistic simulation of fabrication processes. Actualy, contact mechanics have many applications in structural and mechanical engineering and contact models can be generated by the variational principles of solid mechanics. The present work describes a finite element model, based on a treatment of boundary conditions by penalty functions, developed in order to analyse the quasi-static interaction between a rigid solid and a deformable solid. The model is verified in its simpler version through the analysis of the Signorini’s problem without friction. It is extended, in order to take into account the inelastic behavior of the deformable solid in the domain of finite strains, through rigid-plastic constitutive equations. In the extended version the model is verified by the analysis of a metal forming process.
Keywords: contact mechanics / finite elements / metal forming computation - mecânica de contato / elementos finitos / conformação mecânica computacional
COB995 A-POSTERIORI ERROR ESTIMATORS FOR STRONGLY NONLINEAR PROBLEMS
Felix Christian Guimarães Santos
Departamento de Engenharia Mecânica - Universidade Federal de Pernambuco
CEP 50740-530 Recife, Brasil - e-mail: fcgs@dmat.ufpe.br
The use of auxiliary linear problems in order to estimate the approximation error of finite element discrete solutions to nonlinear elliptic problems has been one of the most reliable and robust way of assessing the accuracy of a discrete model. There has been an understanding that if an implicit estimator is asymptotically exact for linear problems, then it will be so when being used for nonlinear problems through a suitable auxiliary problem. In this work we prove that
statement for a wide class of implicit estimators.
Keywords: Finite element method, Nonlinear PDE's, A-posteriori estimators.
COB1160 A DIRECTIONAL ERROR ESTIMATOR FOR ADAPTIVE LIMIT ANALYSIS
Lavinia Borges1, Raúl Feijóo2 & Nestor Zouaini1
1 Programa e Departamento de Engenharia Mecânica, COPPEIEE- UFRJ - Cx. Postal 68503 - Ilha do
Fundão, Rio de Janeiro,RJ - Brasil - CEP:21945-970. E-mail: lavinia@serv.com.ufrj.br
2 Laboratório Nacional de Computação Científica, Rua Lauro Müller, 455 - Botafogo, Rio de janeiro, RJ
- Brasil CEP:22290-160. E-mail: feij@alpha.lncc.br
We present some results on finite element adaptive mesh-refinement strategies for limit analysis, using a posteriori error estimator based on local directional interpolation error and recovering of the second derivatives of the finite element solution. The abstract framework of the adopted error estimation techniques is discussed. Some possibilities of derivatives recovery are considered, including the proposal of a directional error estimator. We apply the above abstract formulation to finite element models of limit analysis.
Keywords: Finite elements, limit analysis, error estimator, adaptive mesh, elementos finitos análise limite, estimative
de erro, malhas adaptadas.
COB1266 MODELO CONSTITUTIVO PARA DANO EM MATERIAIS FRÁGEIS / CONSTITUTIVE MODEL FOR DAMAGE IN BRITTLE MATERIALS
Roque Luiz Pitangueira1 e Raul Rosas e Silva2
1 Departamento de Engenharia de Estruturas - UFMG - Av. do Contorno, 842 - 2o. andar CEP 30110-060, Belo Horizonte, Brasil - E-mail:roque@dees.ufmg.br
2 Departamento de Engenharia Civil - PUC-Rio - Rua Marquês de São Vicente, 225
CEP 22453-900, Rio de Janeiro, Brasil - E-mail:raul@civ.puc-rio.br
A simple constitutive model which includes heterogeneity and size effects is presented. Distributed and discrete approaches for modeling of damage in brittle materials are discussed. Different implementations of the distributed approach are established, according to the choice of the initial compliance matrix, the treatment of the damage direction variation during the analysis, the approximation of the tangent constitutive relation, and the local damage evolution laws in tension and compression. The implications of the different approximations of constitutive tensors in a tangent formulation are adressed in a numerical example.
Keywords: Constitutive, Damage, Fracture, Localization, Size effect, Dano, Fratura, Localização, Efeito de Tamanho