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• Numerical modelling of sheet metal forming problems

  E. Oñate, C. Agelet de Saracibar

  (1991). Numerical Modelling of Material Deformations Processes, C. Sturgess et al (Eds.), Springer Verlag, London

  
  

  Abstract

  Stamping of sheet-metal parts by means of punches and dies is a standard manufacturing process. However, despite its broad application in industry, the design of forming processes is still largely based on experimental techniques, such as the use of circular grid systems (Keeler 1968) or forming limit diagrams (Hecker 1973, Keeler 1974).

  Abstract
  Stamping of sheet-metal parts by means of punches and dies is a standard manufacturing process. However, despite its broad application in industry, the design of forming processes [...]

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• Finite Streifenmethode für Mindlinsche Platten und axialsymmetrische Schalen

  E. Oñate, B. Suárez, E. Hinton

  (1990). Finite Elemente Programme für Platten und Schalen, Springer-Verlag, Berlin, Germany

  
  

  Abstract

  Viele Konstruktionen besitzen konstante geometrische Eigenschaften entlang einer bestimmten Richtung. Derartige prismatische Strukturen sind bei Platten weit verbreitet, bei denen der Querschnitt der Platte in Längsrichtung oft konstant bleibt. Bei axialsymmetrischen Schalen bleibt der Querschnitt der Schale in Umfangsrichtung ebenfalls konstant (siehe Bild 2.1). Falls die Materialeigenschaften der Struktur ebenfalls in der gleichen Richtung konstant sind, kann die Berechnung durch eine Kombination der Methode der finiten Elemente und Fourierreihenentwicklung vereinfacht werden, um das transversale und longitudinale Verhalten zu erfassen.

  Abstract
  Viele Konstruktionen besitzen konstante geometrische Eigenschaften entlang einer bestimmten Richtung. Derartige prismatische Strukturen sind bei Platten weit verbreitet, bei [...]

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• Adaptive Mesh Refinement Techniques for Structural Problems

  E. Oñate, J. Castro

  (1990). The Finite Element Method in the 1990's, E. Oñate et al (Eds.), CIMNE/Springer Verlag

  
  

  Abstract

  In this paper some adaptive mesh refinement (AMR) strategies for finite element analysis of structural problems are discussed. Two mesh optimality criteria based on the equal distribution of: (a) the global error, and (b) the specific error over the elements are studied. It is shown that the correct evaluation of the rate of convergence of the different error norms involved in the AMR procedures is essential to avoid oscillations in the refinement process. The behaviour of the different AMR strategies proposed is compared in the analysis of some structural problems.

  Abstract
  In this paper some adaptive mesh refinement (AMR) strategies for finite element analysis of structural problems are discussed. Two mesh optimality criteria based on the equal [...]

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• Finite element analysis of sheet metal forming problems using a viscous voided shell formulation

  E. Oñate, C. Agelet de Saracibar

  (1988). Modelling of Metal Forming Processes, J.L. Chenot y E. Oñate (Eds.), Kluwer Academic Publisher, pp. 163-178

  
  

  Abstract

  A formal analogy between the equations of pure plastic and viscoplastic flow theory for void containing metals and those of standard non linear elasticity is presented. It is shown how by direct simplifications of the general equations, the standard incompressible flow expressions for non voided metals are obtained. The general formulation is particularized for the analysis of sheet metal forming problems and details of the viscous voided shell and membrane formulations for dealing with the axisymmetric case are given. Finally, some examples of applications of pure and hemispherical stretching and deep drawing of a circular sheet axe presented.

  Abstract
  A formal analogy between the equations of pure plastic and viscoplastic flow theory for void containing metals and those of standard non linear elasticity is presented. It [...]

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• Stabilization techniques for finite element analysis of convection-diffusion problems

  E. Oñate, M. Manzan

  (2000). Convection Heat Transfer, B. Sundén and G. Comini (Eds.), WIT Press, Southampton, United Kingdom

  
  

  Abstract

  The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get a physical solution. This has pushed researchers to develop various stabilization algorithms used in every day practice by numerical analysts. In this chapter some methods are presented along with a new finite increment calculus approach to obtain the different algorithms using higher order conservation equations.

  Abstract
  The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get [...]

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• An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients

  E. Oñate, J. García-Espinosa, S. Idelsohn

  (1998). New Advances in Adaptive Computational Methods in Mechanics, P. Ladeveze and J.T. Oden (Eds.), Elsevier

  
  

  Abstract

  In this paper the FIC method is used as the basis for a new “alpha-adaptive” procedure (where alpha denotes the stabilization parameters) for obtaining stable solution in advective-diffusive problems where arbitrary sharp transverse gradients are present. The new stabilization thechnique can be viewed as an alternative class of adaptive methods where the numerical solution is enhanced by searching “adaptively” the optimal value of the streamline and transverse (crosswing) stabilization parameters while keeping the mesh and the finite element approximation unchanged. Indeed the basic alpha-adaptive process can be enhanced by combining it with standard h, p or hp adaptive schemes. In the first part of the paper the basis of the FIC stabilized method for advectivediffusive problems are explained. Next the algorithm for computing the streamline and transverse stabilization parameters via the new “alpha-adaptive” procedure is described. Finally, the efficiency and accuracy of the new approach are shown in two examples of application.

  Abstract
  In this paper the FIC method is used as the basis for a new “alpha-adaptive” procedure (where alpha denotes the stabilization parameters) for obtaining stable [...]

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• Possibilities of parallel computing in the finite element analysis of industrial forming processes

  E. Oñate

  (1997). Vector and Parallel Processing - VECPAR'96, Palma J.M.L.M., Dongarra J. (eds) Vector and Parallel Processing — VECPAR'96. VECPAR Lecture Notes in Computer Science, vol. 1215, pp 258-294, Springer, Berlin, Heidelberg

  
  

  Abstract

  The paper presents an overview of the possibilities of parallel computing for the analysis of industrial forming processes using the finite element method. The theoretical and computational aspects of the various finite element formulations are presented in some detail as well as the different strategies for parallehzation of the solver, the mesh generation, the error simulation and the mesh adaption modules. Some examples of parallel analysis of powder compaction and sheet stamping processes using parallel finite element codes developed at CIMNE are finally presented.

  Abstract
  The paper presents an overview of the possibilities of parallel computing for the analysis of industrial forming processes using the finite element method. The theoretical [...]

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• Discrete Volume Method. A variational approach for brittle fracture

  V. Cardoso, E. Oñate, S. Botello

  Monograph CIMNE (2019). M184

  
  

  Abstract

  The Discrete Element Method has been used to simulate fracture dynamics beacuse its inherent capacity to reproduce multi-body interaction, but in the case of elasticity mechanics the microparameters of the numerical model, required to replicate the properties of the material, are difficult to calibrate. On the other hand, damage models based on finite element strategies can easily reproduce the properties of the media but they can not simulate the dynamics of multiple fractures. We propose a numerical approach, the Discrete Volume Method, to simulate fracture of brittle materials without the disadvantages mentioned, by combining the benefits of variational formulations and the numerical convenience of discrete element method to capture the dynamics of cracks. The Discrete Volume Method does not have microparameters, since the displacements are computed using the material properties and the fracture mechanism is controlled by an auxiliary damage field. Within this work we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures the Control Volume Function Approximation (CVFA), and the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate. A similar strategy is used to get the damage field solution. In order to coupling both fields, displacement and damage, we use a finite increment arrangement for reducing the resdidual of elastic equation within each time step. We develop a numerical formulation for time discretization based on the analytical solution of the differential equation resulting from assuming a continuous variation of internal forces of the system between time steps. Finally, we show the effectiveness of the methodology by performing numerical experiments and comparing the solutions with published results. 

  Abstract
  The Discrete Element Method has been used to simulate fracture dynamics beacuse its inherent capacity to reproduce multi-body interaction, but in the case of elasticity mechanics [...]

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• Finite volume for stress analysis upon polygonal, unstructured and non conforming meshes

  V. Cardoso Nungaray, S. Botello, F. Zarate, E. Oñate

  Rev. int. métodos numér. cálc. diseño ing. (2019). Vol. 35, (4), 47

  
  

  Abstract

  Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures 1) the Control Volume Function Approximation (CVFA), and 2) the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate.

  Abstract
  Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons [...]

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• Ship hydrodynamics

  E. Oñate, J. García-Espinosa, S. Idelsohn

  (2004). Encyclopedia of Computational Mechanics, E. Stein, R. de Borst and T.J.R. Hughes (Eds.), John Wiley & Sons Ltd, Vol. 3, Chapter 18, pp. 579 - 607

  
  

  Abstract

  This chapter presents an overview of some computational methods for analysis of ship hydrodynamics problems. Attention is focused on the description of a stabilized finite element formulation derived via a finite calculus procedure. Both arbitrary Lagrangian-Eulerian (ALE) and fully Lagrangian forms are presented. Details of the treatment of the free-surface waves and the interaction between the ship structure and the sea water are also given. Examples of application to a variety of ship hydrodynamics problems are shown.

  Abstract
  This chapter presents an overview of some computational methods for analysis of ship hydrodynamics problems. Attention is focused on the description of a stabilized finite [...]

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