COLLECTIONS

Documents published in Scipedia

• ED-Elas2D: An Educational Program for Computer-aided Training in Structural Analysis Using the Finite Element Method

  B. Suarez, E. Blanco, L. Gil, P. Zapata, E. Oñate

  European Journal of Engineering Education (1998). Vol. 23 (2), pp. 243-254

  
  

  Abstract

  In this paper, a methodology for computer-aided training of structural problems by the finite element method is presented. The resulting educational program, named ED-Elas2D, has been developed by a group of researchers at the School of Civil Engineering at the Technical University of Catalonia (UPC) in Barcelona, UPC. The program combines the standard concept which appears in the traditional teaching of finite element methods for structural analysis, such as the introduction to the basic structural theory, data definition (pre-processor), description of the analysis procedure (processor) and interpretation of results (post-processor). The program is addressed to both students who enrol in the study on finite element methods and to academic and technical staff in universities and companies who wish to update their knowledge of finite element techniques. The educational program ED-Elas2D works in the Windows system and it is characterized by its interactivity and graphic utilities.

  Abstract
  In this paper, a methodology for computer-aided training of structural problems by the finite element method is presented. The resulting educational program, named ED-Elas2D, [...]

  • 10
  •  read

• A finite element model for thermomechanical analysis in casting processes

  D. Celentano, S. Oller, E. Oñate

  Journal of Physique IV (1993). Vol. 3 (C7), pp. 1171-1180

  
  

  Abstract

  This paper summarizes the recent work of the authors in the numerical simulation of casting processes. In particular, a coupled thermomechanical model to simulate the solidification problem in casting has been developed [7,8,9]. The model, based on a general isotropic thermoelasto-plasticity theory and formulated in a macroscopical point of view, includes generalized phase-change effects and considers the different thermomechanical behaviour of the solidifying material during its evolution from liquid to solid. For this purpose, a phase-change variable, plastic evolution equations and a temperature-dependent material constitutive law have been defined. Some relevant aspects of this model are presented here. Full thermomechanical coupling terms have been considered as well as variable thermal and mechanical boundary conditions : the first are due to air gap formation, while the second involve a contact formulation. Particular details concerning the numerical implementation of this model are also mentioned. An enhanced staggered scheme, used to solve the highly non-linear fully coupled finite element equations, is proposed. Furthermore, a proper convergence criterion to stop the iteration process is adopted and, although the quadratic convergence of Newton-Rapshon's method is not achieved, several numerical experiments demonstrate reasonable convergence rates [9]. Finally, an experimental cylindrical casting test problem, including phase-change phenomena, temperature-dependent constitutive properties and contact effects, is analyzed. Numerical results are compared with some laboratory measurements.

  Abstract
  This paper summarizes the recent work of the authors in the numerical simulation of casting processes. In particular, a coupled thermomechanical model to simulate the solidification [...]

  • 5
  •  read

• Análisis no lineal de tanques criogénicos bajo cargas térmicas

  J. Oliver, E. Oñate, J. Peraire, R. Chueca

  Hormigón y Acero (1985). Vol. 155, pp. 99-123

  
  

  • 2
  •  read

• La formulación del flujo viscoplástico y sus diversas aplicaciones prácticas por el método de los elementos finitos

  E. Oñate

  Revista de Obras Públicas (1980). Vol. 127 (3178), pp. 115-129

  
  

  • 4
  •  read

• Diseño óptimo de vasijas de presión usando el método de los elementos finitos y un optimizador no lineal

  J. Middleton, E. Oñate

  ETSIIT (1977). Vol. 11, pp. 309-325

  
  

  Abstract

  Se presenta un esquema de diseño para vasijas de presión metálicas de manera que se minimice la tensión tangencial en la vasija . La geometría final se establece mediante un procedimiento iterativo que optimiza un modelo matemático que expresa la  variación de la tensión tangencial en la vasija. Los parámetros del modelo se calculan para cada interacción a partir de los valores de las tensiones tangenciales en la vasija, determinados por el método de los elementos finitos.

  Abstract
  Se presenta un esquema de diseño para vasijas de presión metálicas de manera que se minimice la tensión tangencial en la vasija . La geometría [...]

  • 8
  •  read

• A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

  H. Garikapati, S. Zlotnik, C. Verhoosel, E. Brummelen, P. Diez

  Computational Mechanics (2019). (Preprint) pp. 1-23

  
  

  Abstract

  Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a postprocessing operation on the explicit solution provided by PGD.We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.

  Abstract
  Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random [...]

  • 12
  •  read

• A new 3D equilibrated residual method improving accuracy and efficiency of flux‐free error estimates

  N. Parés, P. Diez

  Comput. Methods Appl. Mech. Engrg., (2019). (Preprint) Vol. 120, pp. 391-432

  
  

  Abstract

  The paper presents a novel strategy providing fully computable upper bounds for the energy norm of the error in the context of three‐dimensional linear finite element approximations of the reaction‐diffusion equation. The upper bounds are guaranteed regardless the size of the finite element mesh and the given data, and all the constants involved are fully computable. The upper bound property holds if the shape of the domain is polyhedral and the Dirichlet boundary conditions are piecewise‐linear. The new approach is an extension of the flux‐free methodology introduced by Parés and Díez in the paper “A new equilibrated residual method improving accuracy and efficiency of flux‐free error estimates”, which introduces a guaranteed, low‐cost, and efficient flux‐free method substantially reducing the computational cost of obtaining guaranteed bounds using flux‐free methods while retaining the good quality of the bounds. Besides extending the 2D methodology, specific new modifications are introduced to further reduce the computational cost in the three‐dimensional setting. The presented methodology also provides a new strategy to obtain equilibrated boundary tractions, which improves the quality of standard techniques while having a similar computational cost.

  Abstract
  The paper presents a novel strategy providing fully computable upper bounds for the energy norm of the error in the context of three‐dimensional linear finite element approximations [...]

  • 1
  •  read

• Sampling-based stochastic analysis of the PKN model for hydraulic fracturing

  H. Garikapati, C. Verhoosel, E. Brummelen, S. Zlotnik, P. Diez

  Computational Geosciences (2019). (Preprint) Vol. 23 (1), pp. 81-105

  
  

  Abstract

  Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic fracturing process by considering various system parameters to be random. Our analysis is based on the Perkins-Kern-Nordgren (PKN) model for hydraulic fracturing. This baseline model enables computation of high fidelity solutions, which avoids pollution of our stochastic results by inaccuracies in the deterministic solution procedure. In order to obtain the desired degree of accuracy of the computed solution, we supplement the employed time-dependent moving-mesh finite element method with two new enhancements: (i) global conservation of volume is enforced through a Lagrange multiplier; (ii) the weakly singular behavior of the solution at the fracture tip is resolved by supplementing the solution space with a tip enrichment function. This tip enrichment function enables the computation of the tip speed directly from its associated solution coefficient. A novel incremental-iterative solution procedure based on a backward-Euler time-integrator with sub-iterations is employed to solve the PKN model. Direct Monte-Carlo sampling is performed based on random variable and random field input parameters. The presented stochastic results quantify the dependence of the fracture evolution process—in particular the fracture length and fracture opening—on variations in the elastic properties and leak-off coefficient of the formation, and the height of the fracture.

  Abstract
  Hydraulic fracturing processes are surrounded by uncertainty, as available data is typically scant. In this work, we present a sampling-based stochastic analysis of the hydraulic [...]

  • 4
  •  read

• Algebraic and parametric solvers for the power flow problem: towards real-time and accuracy-guaranteed simulation of electric systems

  R. García-Blanco, P. Diez, D. Borzacchiello, F. Chinesta

  Archives of Comp. Meths. Engng. (2018). (Preprint) Vol. 25 (4), pp. 1003-1026

  
  

  Abstract

  The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.

  Abstract
  The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers [...]

  • 3
  •  read

• Algebraic PGD for tensor separation and compression: An algorithmic approach

  P. Diez, S. Zlotnik, A. García-González, A. Huerta

  Comptes Rendus Mécanique (2018). (Preprint) Vol. 346 (7), pp. 501-514

  
  

  Abstract

  Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using a greedy approach combined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensor separation based on solving the Least Squares approximation in a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.

  Abstract
  Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated [...]

  • 4
  •  read