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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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• Simple and accurate two-noded beam element for composite laminated beams using a refined zigzag theory

  E. Oñate, A. Eijo, S. Oller

  Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213–216, pp. 362–382

  
  

  Abstract

  In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical Timoshenko beam theory and the refined zigzag kinematics proposed by Tessler ''et al.'' [[#cite-22|[22]]]. The element has just four kinematic variables per node. Shear locking is eliminated by reduced integration. The accuracy of the new beam element is tested in a number of applications to the analysis of composite laminated beams with simple supported and clamped ends under point loads and uniformly distributed loads. An example showing the capability of the new element for accurately reproducing delamination effects is also presented.

  Abstract
  In this work we present a new simple linear two-noded beam element adequate for the analysis of composite laminated and sandwich beams based on the combination of classical [...]

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• P1/P0+ elements for incompressible flows with discontinuous material properties

  E. Oñate, P. Nadukandi, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191-206

  
  

  Abstract

  We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant pressure field'' and ''a prescribed linear field'' that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behaviour for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf-sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier-Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper. The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.

  Abstract
  We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant [...]

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• Lagrangian versus Eulerian integration errors

  S. Idelsohn, E. Oñate, N. Nigro, P. Becker

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191–206; (preprint)

  
  

  Abstract

  The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.

  Abstract
  The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible [...]

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• Surface tension problems solved with the Particle Finite Element Method using large time-steps

  J. Giménez, N. Nigro, S. Idelsohn, E. Oñate

  Computers and Fluids (2016). (preprint) Vol. 141, pp. 90-104

  
  

  Abstract

  In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [3] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.

  Abstract
  In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology [...]

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• Analysis of post-tensioned structures by means of a constitutive serial-parallel rule of mixtures

  S. Jiménez, L. Barbu, S. Oller

  Monograph CIMNE (2018). M178

  
  

  Abstract

  The main objective of this thesis is to present a novel methodology for the analysis of post-tensioned concrete structures, based on the potential offered by the use of the Serial-Parallel Rule of Mixtures when modelling composite materials. The advantages of this methodology are studied in comparison to the available approaches, i.e. the formulation proposed by the standards used in the design of structures and the mechanism used in numerical simulation based on the finite element method (FEM). The Serial-Parallel Rule of Mixtures allows the modelization of each component material in depth, working as a constitutive model manager in order to simulate the composite material being studied. The prestressed concrete is modelled as a composite material with long fibres where the fibre orientation is defined by the steel tendon direction. Therefore, the most suitable constitutive model can be used in each case. In the present thesis this is: for the matrix - concrete an isotropic damage model and for the fibre - steel a viscoelasticity model, achieving an extraordinary accuracy in the micro-scale. The analysis is based on the FEM, which combined with the Serial-Parallel Rule of Mixtures theory allows the study of large-scale structures, taking into account the specific geometric requirements of the construction. Three application examples are included which are used for validating the methodology and the potential of this approach. The first two cases are two isostatic beams that allow the comparison with the results obtained through the study using analytical methods. Finally, the third case shows the results obtained recently for the analysis of a Benchmark, in which the behaviour of a mock-up of a reactor containment building has been studied.

  Abstract
  The main objective of this thesis is to present a novel methodology for the analysis of post-tensioned concrete structures, based on the potential offered by the use of the [...]

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• Analysis of time dependent problems using exponential basis functions

  B. Movahedian, B. Boroomand

  (2011). Research Report, Nº PI364

  
  

  Abstract

  In this research we present a method based on using Exponential Basis Functions (EBFs) to solve a class of time dependent engineering problems. The solution is first approximated by a summation of EBFs satisfying the differential equation and then completed by satisfying the time dependent boundary conditions as well as the initial conditions through a collocation method. This can be performed by considering two approaches. In the first one the solution is split into three parts, i.e. a homogeneous solution obtained by homogeneous boundary conditions, a homogeneous solution obtained by non-homogeneous solution and finally a particular solution induced by source terms. In the second approach the solution is split into two parts, i.e. a homogeneous solution and a particular solution induced by source terms. The two approaches are then employed to construct a time marching algorithm for the solution of problems over a long period of time. We shall present the details of the application of the two approaches introduced to some mathematical and engineering problems. The details of the time marching algorithm proposed are explained. Several problems are solved to show the capabilities of the approaches used. Some benchmark problems are also devised and solved for further studies. It is shown that the one of the introduced approaches is capable of solving a class of problems with moving boundaries.

  Abstract
  In this research we present a method based on using Exponential Basis Functions (EBFs) to solve a class of time dependent engineering problems. The solution is first approximated [...]

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• Exponential basis functions in solution of incompressible fluid problems with moving free surfaces

  S. Zandi, B. Boroomand, S. Soghrati

  (2011). Research Report, Nº PI363

  
  

  Abstract

  In this report, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation established on pressure, as a potential equation, is employed. In this method, the approximate solution is expressed by a linear combination of exponential basis functions (EBFs), with complex-valued exponents, satisfying the governing equation. Constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique. The numerical solution is performed in a time marching approach using an implicit algorithm. In each time step, the governing equation is solved at the beginning and the end of the step, with the aid of an intermediate geometry. The use of EBFs helps to find boundary velocities with high accuracy leading to a precise geometry updating. The developed Lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems. Non-linear sloshing fluids in rigid rectangular two-dimensional basins are particularly addressed.

  Abstract
  In this report, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation [...]

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