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• Rotation-free finite element for the non-linear analysis of beams and axisymmetric shells

  F. Flores, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 5297–5315

  
  

  Abstract

  In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbour (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic-plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic-plastic materials and large strains.

  Abstract
  In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions [...]

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• Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus

  E. Oñate, F. Zarate, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (13-16), pp. 1793–1825

  
  

  Abstract

  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.

  Abstract
  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]

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• Stabilized formulation for the advection-diffusion-absorption equation using finite calculus and linear finite elements

  E. Oñate, J. Miquel, G. Hauke

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 3926–3946

  
  

  Abstract

  A stabilized finite element method (FEM) for the 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. The basis of the method is detailed for the 1D problem. It is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter. A critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given. More accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives. A straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. The extension to the multi-dimensional case is briefly described. Numerical results for 1D and 2D problems are presented showing the efficiency and accuracy of the new stabilized formulation.

  Abstract
  A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing [...]

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• Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion

  F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

  Fire and Materials (2015). Vol. 39 (6), pp. 570-584

  
  

  Abstract

  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classifi cations d ue to the  competing ef fects of gasifica ti on, charring, flame inhibition and melt flow/dripping. For numerical investigation, the particle finite element method (PFEM) is used. Its capability to model the complex fire behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efficie nt p lasticiser; adding PTFE p reve nts dripping  by causing a flo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasification and dripping. The thermal impact of both the burner and the flame is approximated taking into account flame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the fire behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi fi cations and t he exti nc tion times are well predicted.

  Abstract
  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol [...]

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• Cracking of a concrete arch dam due to seasonal temperature variations

  I. de-Pouplana, L. Gracia, F. Salazar, E. Oñate

  F. Salazar's Conference proceedings (2017). 6

  
  

  Abstract

  A finite element thermomechanical analysis of a concrete arch dam has been carried out to predict the extent of cracking due to temperature variations. A linear elastic analysis allows us to find out the areas exceeding the tensile strength of the concrete. Then, a smeared crack approach based on a non-local damage model is used to accurately predict the pattern of the damage at the dam. Additionally, joint elements are introduced in the damaged regions of the wall to analyze the evolution of the crack aperture over the year.

  Abstract
  A finite element thermomechanical analysis of a concrete arch dam has been carried out to predict the extent of cracking due to temperature variations. A linear elastic analysis [...]

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• Fluid-structure interaction using the Particle Finite Element Method

  S. Idelsohn, E. Oñate, F. Pin, N. Calvo

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (17-18), pp. 2100-2123

  
  

  Abstract

  In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.

  Abstract
  In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]

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• Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach

  E. Oñate, J. Arteaga, J. García-Espinosa, R. Flores

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 339-362

  
  

  Abstract

  A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on the evaluation of the energy rate (the power) of the FE residuals of the momentum and incompressibility equations. The residuals are computed using recovered values of the derivatives of the velocity and pressure variable obtained via a nodal derivative recovery technique. Two mesh adaptation procedures based on: a) the equi-distribution of the residual power among the elements in the mesh and b) the equi-distribution of the density of the total residual power are presented. The stabilized form of the Navier-Stokes equations using a finite calculus (FIC) formulation is solved with a fractional step FE scheme. This allows the use of linear triangles and tetrahedra with an equal order interpolation for the velocity and pressure variables. A nodal-based approach is used for computing the residual power integrals. The examples show the ability of the error estimation and the mesh adaptation process to capture the high gradients of the solution in the vecinity of boundary layers and in zones of high vorticity of the fluid for both steady state and transient flow situations.

  Abstract
  A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on [...]

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• Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows

  E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

  Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (19-20), pp. 1777–1800

  
  

  Abstract

  We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.

  Abstract
  We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]

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• Unified Lagrangian formulation for elastic solids and incompressible fluids. application to fluid-structure interaction problems via the PFEM

  S. Idelsohn, J. Marti, A. Limache, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197, pp. 1762–1776

  
  

  Abstract

  We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. In our work the FSI problem is solved via the Particle Finite Element Method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.

  Abstract
  We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and [...]

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• Transmisión de Calor Apuntes

  E. Oñate, F. Zarate

  Personal Repository of Francisco Zarate (2000). 3

  
  

  Abstract
  Apuntes de Clase

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