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• Efectos de los terremotos en las construcciones

  E. Oñate, J. Canet

  (1986). Riesgos Naturales en Ingeniería, E. Alonso et al (Eds.), Ediciones UPC

  
  

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• A total lagrangian formulation for the geometrically non-linear analysis of shells

  J. Oliver, E. Oñate

  (1984). Flexible Shells, E.L. Axelrad, F.A. Emmerlind (Eds.), Berlín

  
  

  Abstract

  The analysis of structures subjected to large displacements by means of the finite element method has attracted the attention of many researchers in recent years and different publications have been reported in the literature [1-8] In this work the authors suggest an alternative finite element formulation for the analysis of shells process of the structure is defined via a total Lagrangian approach. Stresses and strain over the shell surface are defined using a local set of Cartesian axes based on the principal curvature directions of the shell middle surface. This allows to obtain useful explicit expressions of the finite element matrices in a simple manner. Additionally, normal to the midsurface before deformation are assumed to remain straight but not necessarily to the midsurface after deformation, thus allowing for shear deformation effects. Finally, it is worth pointing out that no restrictions are made on the magnitude of the curvatures. This is of special interest for the analysis of non-shallow shells using a small number of elements. The formulation uses two dimensional finite elements for the analysis of 3-D shells. The discretization over the shell thickness is eliminates using what is usually known as “degenerated element technique” [2,4]. This allows for a substantial reduction in the number of variables and eliminates the possibility of ill-conditions of the element matrices which takes place when using 3-D elements and the thickness of the shell is small. In the first part of this work the formulation for 3-D shells is presented. Then a series of examples of shells undergoing large displacements are presented.    

  Abstract
  The analysis of structures subjected to large displacements by means of the finite element method has attracted the attention of many researchers in recent years and different [...]

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• Stabilized solution of the multidimensional advection-diffusion-absorption equation using linear finite elements

  E. Oñate, J. Miquel, F. Zárate

  Computers and Fluids (2007). Vol. 36 (1), pp. 92-112, 2007

  
  

  Abstract

  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.

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

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• Updated Lagrangian mixed finite element formulation for quasi and fully incompressible fluids

  E. Oñate, J. Carbonell

  Computational Mechanics (2014). Vol. 54 (6), pp. 1583-1596, 2014

  
  

  Abstract

  We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing equations for the conservation of momentum and mass are given in both differential and variational form. The finite element interpolation uses an equal order approximation for the velocity and pressure unknowns. The procedure for obtaining stabilized FEM solutions is outlined. The solution in time of the discretized governing conservation equations using an incremental iterative segregated scheme is described. The linearization of these equations and the derivation of the corresponding tangent stiffness matrices is detailed. Other iterative schemes for the direct computation of the nodal velocities and pressures at the updated configuration are presented. The advantages and disadvantages of choosing the current or the updated configuration as the reference configuration in the Lagrangian formulation are discussed.

  Abstract
  We present a mixed velocity-pressure finite element formulation for solving the updated Lagrangian equations for quasi and fully incompressible fluids. Details of the governing [...]

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• The particle finite element method. An overview

  E. Oñate, S. Idelsohn, F. Del Pin, R. Aubry

  International Journal of Computational Methods (2004). Vol. 1 (2), pp. 267-307

  
  

  Abstract

  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.

  Abstract
  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 [...]

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• Materiales compuestos - Simulación del comportamiento anisótropo

  E. Car, S. Oller, E. Oñate

  (2002). Análisis y Cálculo de Estructuras de Materiales Compuestos, Oller S. (Ed.), pp. 95-144, CIMNE, Barcelona, Spain

  
  

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• Stochastic analysis of an impact problem

  F. Zárate, J. Hurtado, E. Oñate

  (1999). I. Doltsinis (Ed.), CIMNE, Barcelona, Spain

  
  

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• Efficient computational aspects for analyses of sheet stamping problems

  G. Duffett, P. Cendonya, J. Rojek, E. Oñate

  (1997). Recent Developments in Computational and Applied Mechanics. A Book in Honour of John B. Martin, B. D. Reddy (Ed.), CIMNE

  
  

  Abstract

  Efficiency and accuracy are vital for the acceptable simulation of large scale industrial sheet stamping problems. Two aspects, implemented within the explicit dynamic program STAMPACK, that effectively address this problem are described: an anisotropic plasticity material model combined with a thin shell element that contains only displacement degrees of freedom and an effective drawbead formulation based on an elastic-plastic analogy

  Abstract
  Efficiency and accuracy are vital for the acceptable simulation of large scale industrial sheet stamping problems. Two aspects, implemented within the explicit dynamic program [...]

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• Enhanced prediction of structural instability points using a critical displacement method

  E. Oñate, W. Matias Silva

  (1995). Advances in Finite Element Technology, N.-E. Wiberg (Ed.), CIMNE, Barcelona

  
  

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• A review of some finite element families for thick and thin plate and shell analysis

  E. Oñate

  (1994). Recent Developments in Finite Element Analysis, Hughes J., Oñate E. and Zienkiewicz O. (Eds.), CIMNE, Barcelona

  
  

  Abstract

  This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing the adequate constrains the original thick plate element evolve into DK forms adequate for this situations only. This evolution process allows to revisite some classical elements like the Morley triangle and also to derive simple plate and shell triangles and quadrilates with only translational degrees of freedom as nodal variables.

  Abstract
  This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing [...]

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