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• Extended rotation-free shell triangles with transverse shear deformation effects

  F. Zárate, E. Oñate

  Computational Mechanics (2012). Vol. 49 (4), pp. 487-503

  
  

  Abstract

  The paper extends recent work of the authors to include transverse shear effects on rotation-free triangular element for plates (Oñate and Zárate in Int J Numer Methods Eng 83(2):196–227, 2010). Two new shell triangular elements are presented, the EBST+ and the EBST+1. Transverse shear deformation effects are important for thick shells, as well when the shell is laminated or formed by composite material. The ingredients for the element formulation are: a Hu-Washizu type mixed functional and linear interpolation for the displacement field. In both elements presented a finite volume approach is used for computing the bending moments and the curvatures over a patch of elements. The nodal translational degrees of freedom of the original enhanced basic shell triangle (EBST) are extended with the two shear deformation angles via two different approaches. The first one uses a linear interpolation of the rotation angles inside the element (EBST+) and the second one assumes a constant field for the rotation angles (EBST+1). For the thin shell case the shear angles vanish and the new elements reproduce the good behaviour of the original thin EBST element. As a consequence the elements can reproduce the solutions for thick to thin shells situations without exhibiting shear locking. The numerical solution for the thick shell case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin EBST element. Examples of the good performance of the new rotation-free shell triangles are given.

  Abstract
  The paper extends recent work of the authors to include transverse shear effects on rotation-free triangular element for plates (Oñate and Zárate in Int J Numer [...]

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• A coupled PFEM–Eulerian approach for the solution of porous FSI problems

  A. LARESE, R. Rossi, E. Oñate, S. Idelsohn

  Computational Mechanics (2012). Vol. 50 (6), pp. 805-819

  
  

  Abstract

  This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a Lagrangian model for the structural behavior and an Eulerian approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an Eulerian fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.

  Abstract
  This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well [...]

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• Possibilities of the particle finite element method for fluid–soil–structure interaction problems

  E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

  Computational Mechanics (2011). Vol. 48 (3), pp. 307-318

  
  

  Abstract

  We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid–solid and solid–solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.

  Abstract
  We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure [...]

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• On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field

  S. Idelsohn, M. Mier-Torrecilla, N. Nigro, E. Oñate

  Computational Mechanics (2010). Vol. 46 (1), pp. 115-124

  
  

  Abstract

  Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure fields. We show the importance of using discontinuous pressure fields to avoid errors in the incompressibility condition near the interface.

  Abstract
  Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure [...]

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• A monolithic Lagrangian approach for fluid–structure interaction problems

  P. Ryzhakov, R. Rossi, S. Idelsohn, E. Oñate

  Computational Mechanics (2010). Vol. 46 (6), pp. 883-899

  
  

  Abstract

  Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

  Abstract
  Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique [...]

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• The generalized finite point method

  B. Boroomand, M. Najjar, E. Oñate

  Computational Mechanics (2009). Vol. 44, pp. 173-190

  
  

  Abstract

  In this paper we propose a new mesh-less method based on a sub-domain collocation approach. By reducing the size of the sub-domains the method becomes similar to the well-known finite point method (FPM) and thus it can be regarded as the generalized form of finite point method (GFPM). However, unlike the FPM, the equilibrium equations are weakly satisfied on the sub-domains. It is shown that the accuracy of the results is dependent on the sizes of the sub-domains. To find an optimal size for a sub-domain we propose a patch test procedure in which a set of polynomials of higher order than those chosen for the approximations/interpolations are used as the exact solution and a suitable error norm is minimized through a size tuning procedure. In this paper we have employed the GFPM in elasto-static problems. We give the results of the size optimization in a series of tables for further use. Also the results of the integrations on a generic sub-domain are given as a series of library functions for those who want to use GFPM as a cheap and fast integral-based mesh-less method. The performance of GFPM has been demonstrated by solving several sample problems.

  Abstract
  In this paper we propose a new mesh-less method based on a sub-domain collocation approach. By reducing the size of the sub-domains the method becomes similar to the well-known [...]

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• Orthotropic rotation-free basic thin shell triangle

  J. Valdes-Vazquez, E. Oñate

  Computational Mechanics (2009). Vol. 44 (3), pp. 363-375

  
  

  Abstract

  A methodology for the geometrically nonlinear analysis of orthotropic shells using a rotation-free shell triangular element is developed. The method is based on the computation of the strain and stress fields in the principal fiber orientation of the material. Details of the definition of the fiber orientation in a mesh of triangles and of the general formulation of the orthotropic rotation-free element are given. The accuracy of the formulation is demonstrated in examples of application.

  Abstract
  A methodology for the geometrically nonlinear analysis of orthotropic shells using a rotation-free shell triangular element is developed. The method is based on the computation [...]

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• Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM

  S. Idelsohn, J. Marti, A. Souto-Iglesias, E. Oñate

  Computational Mechanics (2008). Vol. 43 (1), pp. 125-132

  
  

  Abstract

  The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.

  Abstract
  The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular [...]

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• Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods

  C. Felippa, E. Oñate

  Computational Mechanics (2007). Vol. 39 (2), pp. 91-111

  
  

  Abstract

  This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions

  Abstract
  This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, [...]

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• An improved finite point method for tridimensional potential flows

  E. Ortega, E. Oñate, S. Idelsohn

  Computational Mechanics (2007). Vol. 40 (6), pp. 949-963

  
  

  Abstract

  At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.

  Abstract
  At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical [...]

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