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A residual correction method based on finite calculus

  • Oñate, Eugenio
  • Taylor, RL
  • Zienkiewicz, O.C.
  • Rojek, Jerzy
In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar convection‐diffusion problem and the problem of elasticity at the incompressible or quasi‐incompressible limit. The formulation permits the use of equal interpolation for displacements and pressure on linear triangles and tetrahedra as well as any low order element type. To add additional stability in the solution, pressure gradient corrections are introduced as suggested from developments of sub‐scale methods. Numerical examples are included to demonstrate the performance of the method when applied to typical test problems.
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A general stabilized formulation for incompressible fluid flow using finite calculus and the finite element method

  • Oñate, E.
  • García, J.
  • Bugeda, G.
  • Idelsohn, S.R.
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.
Proyecto:


Posibilidades de las nuevas tecnologías de información y comunicaciones en el sector de la construcción

  • Oñate, Eugenio
  • (presenter), Javier
  • Zárate, Francisco
Se presenta una breve panorámica de las posibilidades de las nuevas Tecnologías de la Información y las Comunicaciones en el sector de la construcción. Tras unas reflexiones sobre el valor intrínseco de la información y las comunicaciones, se describe el impacto que está teniendo Internet en los nuevos métodos de trabajo, de comercio, de formación y, en general, de intercambio de información a todos los niveles en las actividades de los técnicos del sector de la construcción. Finalmente se especula sobre las posibilidades de las TIC para generar entornos de trabajo inteligentes que generen y gestionen conocimiento para la solución de problemas prácticos.
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Langrangian formulation for incompressible fluids using finite calculus and the finite element method

  • Oñate, Eugenio
  • Idelsohn, S.R.
  • Pin, F.
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM) and a lagrangian description. The necessary stabilization for dealing with the incompressibility condition is introduced via the so called finite calculus (FIC) method. Both a quasi-implicit algorithm and a fractional step scheme are described. Examples of application of the lagrangian flow description are presented.
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Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements

  • Oñate, E.
  • Miquel, J.
  • Zárate, F.
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of  curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation.
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The particle finite element method. An overview

  • Oñate, E.
  • Idelsohn, S.R.
  • Pin, F.
  • Aubry, R.
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
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Finite calculus formulation for incompressible solids using linear triangles and tetrahedra

  • Oñate, Eugenio
  • Rojek, J.
  • Taylor, RL
  • Zienkiewicz, OC
Many finite elements exhibit the so‐called ‘volumetric locking’ in the analysis of incompressible or quasi‐incompressible problems.In this paper, a new approach is taken to overcome this undesirable effect. The starting point is a new setting of the governing differential equations using a finite calculus (FIC) formulation. The basis of the FIC method is the satisfaction of the standard equations for balance of momentum (equilibrium of forces) and mass conservation in a domain of finite size and retaining higher order terms in the Taylor expansions used to express the different terms of the differential equations over the balance domain. The modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem. The FIC approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective–diffusive and fluid flow problems. The same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra. Examples of application of the new stabilized formulation to linear static problems as well as to the semi‐implicit and explicit 2D and 3D non‐linear transient dynamic analysis of an impact problem and a bulk forming process are presented.
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Possibilities of the particle finite element method for fluid-structure interaction problems with free surface waves

  • Oñate, Eugenio
  • Idelsohn, Sergio
  • Del Pin, Facundo
  • Aubry, Romain
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Proyecto:


Ship hydrodynamics

  • Oñate, Eugenio
  • García-Espinosa, Julio
  • Idelsohn, Sergio
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.
Proyecto:


A general stabilized formulation for incompressible fluid flow using finite calculus and the finite element method

  • Oñate, Eugenio
  • García-Espinosa, Julio
  • Bugeda, Gabriel
  • Idelsohn, Sergio
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.
Proyecto:


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