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• Locking in the imcomprenssible limit: pseudo-divergence-free Element Free Galerkin

  Y. Vidal, P. Villon, A. Huerta

  (2003). Research Report, Nº PI233

  
  

  Abstract

  Locking in finite elements has been a major concern since its early developments. It appears because poor numerical interpolation leads to an over-constrained system. This paper proposes a new formulation that asymptotically suppresses locking for the Element Free Galerkin (EFG) method in incompressible limit, i.e. the so-called volumetric locking. Originally it was claimed that EFG did not present volumetric locking. However, recently, performing a modal analysis, the senior author has shown that EFG presents volumetric locking. In fact, it is concluded that an increase of the dilation parameter attenuates, but never suppresses, the volumetric locking and that, as in standard finite elements, an increase in the order of reproducibility (interpolation degree) reduces the relative number of locking modes. Here an improved formulation of the Element Free Galerkin method is proposed in order to a alleviate volumetric locking. Diffuse derivatives are defined in the thesis of the second author and their convergence to the derivatives of the exact solution, when the radius of the exact solution, when the radius of the support goes to zero (for a fixed dilation parameter) it’s proved. Therefore, diffuse solution, converges to the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation functions are defined that asymptotically verify the incompressibility condition. Modal analysis and numerical results for classical benchmark test in solids corroborate this issue.

  Abstract
  Locking in finite elements has been a major concern since its early developments. It appears because poor numerical interpolation leads to an over-constrained system. This [...]

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• Goal-Oriented adaptivity for shell structures

  P. Díez, I. Morata, A. Huerta

  (2003). Research Report, Nº PI234

  
  

  Abstract

  The reliable computation of shell structures requires a tool to assess and control the quality of the finite element solution. For practical purposes, the quality of the numerical solution must be measured using a quantity of engineering interest rather than in the standard energy norm. however, the assessment of the error in an output of interest is based on a standard energy norm error estimator. The standard error estimator has to be applied quantity. In shells with assumed-strain models, the combination of primal and dual error estimation is performed differently than in the continuum mechanics case. Moreover, a part form the goal-oriented error estimator, the adaptive process requires a remeshing criterion. This work introduces a specific remeshing criterion for goal-oriented adaptivity and tis particularization to the context of shell elements.

  Abstract
  The reliable computation of shell structures requires a tool to assess and control the quality of the finite element solution. For practical purposes, the quality of the numerical [...]

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• A comparison of two formulations to blend finite elements and mesh-free methods

  A. Huerta, S. Fernández-Méndez, W. Liu

  (2003). Research Report, Nº PI235

  
  

  Abstract

  Mesh-free methods have since their early developments been blended to the finite element formulation in order to benefit from the advantages of both numerical techniques. In this paper, two recently proposed formulations to couple mesh-free and finite element methods are discussed and compared.

  Abstract
  Mesh-free methods have since their early developments been blended to the finite element formulation in order to benefit from the advantages of both numerical techniques. [...]

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• Impossing essential boundary conditions in Mesh-Free Methods

  S. Fernández-Méndez, A. Huerta

  (2003). Research Report, Nº PI236

  
  

  Abstract

  Imposing essential boundary is a key issue in mesh-free methods. The mesh-free interpolation does not verify the Kronocker delta property and, therefore, the imposition of prescribed values is not as straightforward as for the finite element method. The aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in Galerkin based mesh-free methods. Special attention is paid to the mesh-free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the Garlekin weak form. Particular examples are used to analyze and compare their performance in different situations.

  Abstract
  Imposing essential boundary is a key issue in mesh-free methods. The mesh-free interpolation does not verify the Kronocker delta property and, therefore, the imposition of [...]

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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

  (2003). Research Report, Nº PI237

  
  

  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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• A finite calculus formulation of the level set equation

  S. Idelsohn, E. Oñate, S. Ransau

  (2003). Research Report, Nº PI239

  
  

  Abstract

  A finite calculus formulation of the level set equation is presented. Quadratic Galerkin finite elements are used for spatial discretization. A unique stabilization parameter is computed. A time stabilization parameter allowing the use of the forward Euler scheme with Courant number larger than one is presetend.

  Abstract
  A finite calculus formulation of the level set equation is presented. Quadratic Galerkin finite elements are used for spatial discretization. A unique stabilization parameter [...]

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• A finite element model for the simulation of lost foam casting

  G. Houzeaux, R. Codina

  (2003). Research Report, Nº PI242

  
  

  Abstract

  In this paper, we present a numerical model to simulate lost foam casting processes. We first introduce this particular casting in order to catch the different physical processes in play during a casting. We also briefly comment on the possible physical and numerical models to envisage the numerical simulation. Next we present a model which aims at solving “part of” the complexities of the casting, together with a simple energy budget that enables to obtain an equation for the velocity of the metal front advance. Once the physical model is established we develop a finite element method to solve the governing equations. The numerical and physical methodologies are then validated through the solution of a two and a three-dimensional example. Finally, we briefly discuss some possible improvements of the numerical model in order to catch more physical phenomena.

  Abstract
  In this paper, we present a numerical model to simulate lost foam casting processes. We first introduce this particular casting in order to catch the different physical processes [...]

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• Development of local models and their computational implementation for polymer coated steel sheets

  J. Rojek, M. Luege, E. Oñate

  (2004). Research Report, Nº PI265

  
  

  Abstract

  This report present review of the state of the art of numerical modelling of polymers and polymer coated metal laminates and gives details of selected numerical models including those that will be used in the work in the project POLYCOAT. The first sections studied in the project. Basic mechanical and thermal properties of the polymers are reviewed. Then constitutive models developed for polymers are reviewed based on literature and own work. Details of selected models are given. Deformation behaviour of polymer coated metal laminates is considered with special attention to the phenomena observed at the polymer-metal interface. The numerical models for the interface are presented finally.

  Abstract
  This report present review of the state of the art of numerical modelling of polymers and polymer coated metal laminates and gives details of selected numerical models including [...]

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• El valor del cálculo en los sistemas de ayuda a la toma de decisiones en ingeniería

  E. Oñate

  Revista de Obras Públicas (2004). Vol. 151 (3449), pp. 41-48

  
  

  Abstract

  El artículo revindica el valor de los métodos de cálculo que se enseñan en las Escuelas de Ingeniería, como herramientas indispensables en los nuevos sistemas de ayuda a la toma de decisiones (SAD). Los SAD integran base de datos, métodos de cálculo y módulos de inteligencia artificial, y su utilización se extiende cada día más para ayuda al diseño y gestión de infraestructuras y servicios de ingeniería. En el texto se describen varios desarrollos y aplicaciones recientes de SAD en ingeniería civil. El artículo acaba con una reflexión sobre los límites de los SAD. The paper stresses the value of the computational methods taught in engineering faculties as indispensable tools within the new decision support systems (DSS). The DSS integrate data bases, computational methods and artificial intelligence modules. They are increasingly used for supporting the design and management of civil constructions and services in engineering. The paper describes recent developments and applications of DSS in civil engineering. The text ends up with a discussion on the limits of the DSS. 

  Abstract
  El artículo revindica el valor de los métodos de cálculo que se enseñan en las Escuelas de Ingeniería, como herramientas indispensables [...]

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• The efects of VaR position limits on endogenous price formation in financial markets

  G. Peffer

  (2004). Research Report, Nº PI263

  
  

  Abstract

  This paper sets out to study the impact that market risk limits have on the price dynamics in securities markets. We start out from a standard model in which trading patterns are determined for utility-maximising investors in non-clearing markets with a particularly simple price formation mechanism. To make trading conditions more realistic, we add borrowing and short-selling constraints and incorporate a stochastic information arrival process into the standard model. We present a VaR position limit formulation that allows us to integrate market risk limit considerations into our model and solve the respective utility maximization problems. Simulation results are then discussed which show an increase in price instability in a scenario of widespread adoption of VaR as a mechanism to limit portfolio risk.

  Abstract
  This paper sets out to study the impact that market risk limits have on the price dynamics in securities markets. We start out from a standard model in which trading patterns [...]

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