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• Advances in the particle finite element method (PFEM) for solving coupled problems in engineering

  E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, J. Marti, J. Carbonell, P. Ryzhakov, B. Suárez

  (2011). Particle-Based Methods, Computational Methods in Applied Sciences, Springer, E. Oñate and R. Owen (Eds.), Vol. 25, pp. 1-48

  
  

  Abstract

  We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points 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 are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.

  Abstract
  We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering [...]

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• The CIMNE model for generating knowledge on computational engineering and its transfer to society

  E. Oñate

  (2017). Research Report, Nº PI417

  
  

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• Langrangian formulation for incompressible fluids using finite calculus and the finite element method

  E. Oñate, S. Idelsohn, F. Pin

  (2003). Kuznetsov Y., Neittanmaki P. and Pironneau O. (Eds.),CIMNE, Barcelona, Spain

  
  

  Abstract

  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.

  Abstract
  We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM) and a lagrangian description. The necessary stabilization for [...]

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• The CIMNE model for generating knowledge on computational engineering and its transfer to society

  E. Oñate

  (2017). Research Report, Nº PI417

  
  

  Abstract

  We present an overview of the model implemented by the International Centre for Numerical Methods in Engineering (CIMNE, www.cimne.com ) for  the generation of scientific and technical knowledge on computational engineering, understood in the broad sense, the subsequent generation of product resulting from the research activities and the transfer of these products to society for their exploitation in the industrial sector. We present examples of application of the CIMNE model to a number of academic, scientific and industry activities of CIMNE.

  Abstract
  We present an overview of the model implemented by the International Centre for Numerical Methods in Engineering (CIMNE, www.cimne.com ) for  the generation of scientific [...]

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• Estudio de estimación de parámetros constitutivos en el método de elementos discretos o de partículas

  C. Recarey, E. Oñate, J. Miquel, F. Zárate, J. Rojek, S. Burrell

  Monograph CIMNE (2005). M93

  
  

  Abstract

  Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación de rocas, suelos, medios granulares y otros materiales. El movimiento de elementos esféricos se describe por medio de las ecuaciones de dinámica del cuerpo rígido. Se emplea en la formulación una integración explícita, la cual, brinda una buena eficiencia computacional.

  Abstract
  Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación [...]

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• Numerical simulation of multifluid flows with the particle finite element method

  M. Mier, S. Idelsohn, E. Oñate

  Monograph CIMNE (2010). M115

  
  

  Abstract

  In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations.

  Abstract
  In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have [...]

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• Computational model of the human urinary bladder

  V. Monteiro, E. Oñate, S. Oller

  Monograph CIMNE (2014). M148

  
  

  Abstract

  The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. It is considered a major medical problem once this disease has high rates of reoccurrence, often leading to the extirpation of this organ. The most refined solution to replace this organ is the ileal bladder, which consists of a neobladder made of the patient’s intestinal tissue. Unfortunately this solution presents not only functional mechanical problems, described on the literature as voiding and leaking problems, but also biological ones (i.e. bone loss, given the absorption by the intestine of substances that should be eliminated from the organism). Urged by the urological community of the Hospital Clinic de Barcelona and backgrounded by its experience in the numerical simulation of biomedical structures, the Center of Numerical Methods in Engineering (CIMNE) had the initiative to provide the research of the mechanics of the urinary bladder and the simulation of fluid structure interaction (FSI) to account for the filling and voiding of this organ with urine. The Finite Element Method (FEM) simulation of the real bladder and the comprehensive understanding of the mechanics of this organ and its interaction with urine will give the possibility to propose geometrical improvements and study suitable materials for an artificial solution to address the cases on which the bladder needs to be removed. To reach this goal, first we proceeded to the bibliographic review of mathematical models of the urinary apparatus and to a comprehensive study of the physiology and dynamics of the bladder. A review of the major urological structures, kidney, ureter and urethra, takes place. To consider boundary conditions other surrounding structures to the urinary system are also studied. In the second part of the thesis, we propose the numerical model to study the human urinary bladder. The behavior of the detrusor muscle during filling and voiding of the bladder with urine and its ability to promote the storage of urine under low pressure need to be accurately represented, requiring the implementation of a non-linear constitutive model. The mathematical model needs to be capable to simulate the mechanical variables that govern this organ and the properties of the urine. The nonlinear behavior of living tissues is implemented and validated with examples from the literature. The quasi-incompressibility property of urine and the navierstokes equations for the fluid are taken into account. The geometry of the bladder needs to be taken into account, and the implementation of a 3D computational model obtained from the computerized tomography of a cadaver male adult is considered. The data has been treated to consider boundary conditions. Two models have been conceived: one meshed with four nodes tetrahedral and another meshed with shell elements. FSI must work for the simulation of filling and voiding of the bladder. Due to the close densities of the materials the scheme used to solve fluid-structure needs to be carefully selected. The proposed numerical model and the filling and voiding analysis are finally validated with standardized urodynamic tests. The final part of the thesis, the simulation of a neobladder is presented, being the first step to simulate numerically artificial materials for bladder replacement.

  Abstract
  The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. [...]

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• Development and applications of the finite point method to compressible aerodynamics problems

  E. Ortega, E. Oñate, S. Idelsohn

  Monograph CIMNE (2014). M143

  
  

  Abstract

  This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.

  Abstract
  This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating [...]

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• Lagrangian formulation for fluid-structure interaction problems using the particle finite element method

  E. Oñate, S. Idelsohn, M. Celigueta

  (2006). Verification and Validation Methods for Challenging Multiphysics Problems, CIMNE, pp. 125-150

  
  

  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 an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points (called particles) 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 of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. Examples of application of the PFEM 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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• Finite Element Analysis of Membrane Structures

  R. Taylor, E. Oñate, P. Ubach de Fuentes

  (2005). Recent Advances in Textile Membranes and Inflatable Structures, Springer Verlag, pp. 47 - 68

  
  

  Abstract

  This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Cauchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.

  Abstract
  This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation [...]

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