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• Error estimation for adaptive computations on shell structures

  P. Diez, A. Huerta

  European Journal of Finite Elements (2000). Vol. 9 (1-3), pp. 49-66

  
  

  Abstract

  The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. The first is associated with the finite dimensional interpolation space and it is present in any finite element computation. The latter is associated with the piecewise polynomial approximation of a curved surface and is much more relevant in shell problems than in any other standard 2D or 3D computation. In the shells framework, formerly the quality control of the finite element solution has been carried out using flux projection a posteriori error estimators. This technique exhibits two main drawbacks: 1) the flux smoothing averages stress components over different elements that may have different physical meaning if the tangent planes are different and 2) the error estimation process uses only the approximate solution and hence, the discretized forces and the computational mesh: the data describing the real geometry and load is therefore not accounted for. In this work, a residual type error estimator introduced for standard 2D finite element analysis is generalized to shell problems. This allows to easily account for the real original geometry of the problem in the error estimation procedure and precludes the necessity of comparing generalized stress components between non coplanar elements. This estimator is based on approximating a reference error associated with a refined reference mesh. In order to build up the residual error equation the computed solution must be represented (projected) on the reference mesh. The use of thin shell finite elements requires a proper formulation in order to preclude shear locking. Following an idea of Donea and Lamain, the interpolation of the rotations is not unique and requires a particular technique to transfer the information from the computational mesh to the reference mesh. This technique is also developed in this work and may be used in any adaptive evolution problem where the solution must be transferred from one mesh to another.

  Abstract
  The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. [...]

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• Adaptive finite element strategies based on error assessment

  A. Huerta, A. Rodríguez-Ferran, P. Diez, J. Sarrate

  Int. J. Numer. Meth. Engng. (1999). Vol. 46 (10), pp. 1803-1818

  
  

  Abstract

  Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or error indicators. After that, a new spatial discretization must be defined via h, p or r-adaptivity. In principle, any of the approaches for error assessment may be combined with any of the procedures for adapting the discretization. However, some combinations are clearly preferable. The advantages and limitations of the various alternatives are discussed. The most adequate strategies are illustrated by means of several applications in solid mechanics.

  Abstract
  Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed, by means of either error estimators or error [...]

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• A unified approach to remeshing strategies for finite element h-adaptivity

  P. Diez, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (1999). Vol. 176 (1-4), pp. 215-229

  
  

  Abstract

  In h-adaptivity, a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution. Several authors have introduced different remeshing strategies yielding very different results. In this work these methods are included in a unified framework, emphasizing the role of the underlying hypotheses. Moreover, an objective tool to evaluate the accuracy of the resulting finite element solution is presented. Thus, a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions. The different remeshing strategies are compared with well-known numerical examples.

  Abstract
  In h-adaptivity, a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution. Several authors have introduced [...]

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• A posteriori error estimation for standard finite element analysis

  P. Díez, J. Egozcue, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (1998). Vol. 163 (1-4), pp. 141-157

  
  

  Abstract

  A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element refinement. First, an approximation of the energy norm of the error is obtained solving local problems with homogeneous Dirichlet boundary conditions. A later enrichment of the estimation is performed by adding the contributions of projections on a new family of subspaces. This estimate is a lower bound of the measure of the actual error. The estimator does not need to approximate local boundary conditions for the error equation. Therefore, computation of flux jumps is not necessary. Moreover, the estimator can be applied in mixed meshes containing elements of different shapes and its implementation in a standard finite element code is straightforward. The presented results show the effectiveness of the estimator approximating both the distribution and the global measure of the error, as well as its usefulness in adaptive procedures.

  Abstract
  A new residual type estimator based on projections of the error on subspaces of locally-supported functions is presented. The estimator is defined by a standard element-by-element [...]

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• Vulnerabilidad sísmica y toma de decisiones

  J. Egozcue, G. Grande, P. Diez

  Revista Internacional de Cálculo de Estructuras (1997). Vol. 2 (1), pp. 35-58

  
  

  Abstract

  Vulnerability of civil structures and systems under seismic actions have been extensively used and studied in the last decade. However, the goals of those studies are very diverse and it have caused some confusion on the meaning and definition of vulnerability. Naturally, different scopes of vulnerability lead to different methodologies in its study which may be incompatible. The present aim is to analyse the definition of seismic vulnerability in the framework of Bayesian decision making. Three different examples of decision making related to seismic vulnerability, which are qualitatively different, guide the discussion. They have an increasing complexity: decisions on normative seismic design; decisions on insurances against seismic risk and, finally, those decisions that should be taken to lead alarm, mitigation and rescue systems for seismic disasters. The three analised examples correspond to three different decision making schemes, respectively named: a priori, a posteriori and preposterior. In each case the definition of seismic vulnerability depends on the concept of considered utility (cost-benefit), on the involved random states and the scale in which the phenomena are to be considered. Most of the concepts associated with seismic vulnerability are reviewed through these three examples. A conclusion is that seismic vulnerability studies should consider the associated decision making problem. Simultaneously, the study of methodological and estimation aspects on vulnerability are remarked in order to improve both guidelines for seismic design and disaster mitigation.

  Abstract
  Vulnerability of civil structures and systems under seismic actions have been extensively used and studied in the last decade. However, the goals of those studies are very [...]

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• Cimne & Complas 30 Years - 1987 - 2017

  E. Oñate

  Videos of Plenary Lectures presented at the XIV International Conference on Computational Plasticity (COMPLAS 2017).

  
  

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• From fracture to fragmentation

  F. Witel

  Videos of Plenary Lectures presented at the IV International Conference on Particle-Based Methods. Fundamentals and Applications (PARTICLES 2015).

  
  

  Abstract

  The nature of fracture phenomena strongly limits engineering solutions to cases, a little bit beyond the regime of linear fracture mechanics. Nevertheless, fracture in brittle disordered materials, dominated by simultaneously growing and dynamically competing cracks is rather ubiquitous [1,2]. From the dynamics of single crack propagation, through the statistics of crack ensembles to the rapid fragmentation of materials, Discrete Element Methods (DEM) helped to enrich the understanding over the past decades. Models of seemingly simple rigid body dynamics with simple contact and cohesive interactions proved to be surprisingly successful for representing dynamic fracture and fragmentation phenomena, emerging from the complex systems dynamics. Today, applications of DEM make a substantial contribution for explaining the mechanical response and breaking phenomena of heterogeneous materials under various types of loading conditions beyond single crack growth [3,4]. Various particle geometries, material response, ways to treat repulsive and cohesive behaviour and of course loss of cohesion, lead to a flexible tool-set of approaches. Strategies for higher order agglomeration, coupling with other simulation techniques for continuum domains or other particle based methods extended the reach of DEM significantly. Ranging from the slowly changing, sub-critical loads to the highly energetic fragmentation, DEM proved to be an indispensable tool for such investigations. In this talk a brief review on the motivations and basic ideas behind the DEM approach to cohesive particulate matter is given. Different ways of introducing cohesion and its loss are discussed in light of fracture in frictional and non-frictional materials beyond the Griffith length of stable crack growth. Among the widespread applications of DEM for the fracture of heterogeneous materials, focus is given on impact comminution of aggregated matter [4]. By providing an improved understanding of comminution processes e.g. in impact mills, one of the energetically least efficient processes on the global scale could be improved – by the use of particle mechanics. It is shown, that a critical impact velocity vcr exists, separating the fracture from the fragmentation regime. Below the critical velocity, fragmentation by repeated impacts can be described by a Basquin type low cycle fatigue law, above vcr Power-law fragment size distributions emerge. This behaviour is robust even for multi-phase materials. In a comparative study it is finally demonstrated, how the milling efficiency can be increased for the same system only by manipulating the shock wave configurations via vibrating targets.

  Abstract
  The nature of fracture phenomena strongly limits engineering solutions to cases, a little bit beyond the regime of linear fracture mechanics. Nevertheless, fracture in brittle [...]

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• Application of SPH to coupled fluid-solid problems in the petroleum industry

  J. Williams

  Videos of Plenary Lectures presented at the IV International Conference on Particle-Based Methods. Fundamentals and Applications (PARTICLES 2015).

  
  

  Abstract

  This talk addresses the application of SPH to problems of hydro-fracturing and fluid-structure interaction. Simulating a hydraulic-fracture propagating in a rock with in-situ joint sets is particularly challenging. Traditional continuum modeling techniques have the advantage of using classical non- linear material models, however they often fail to accurately capture the complexity of the geometry and path of multiple intersecting fractures. In particular, mesh dependence of the fracture path, closing of an opened fracture and shear, present difficulties using these techniques. The use of the smoothed particle hydrodynamics (SPH) method for these problems is relatively recent. Mesh free methods, such as SPH, have the potential to overcome the previously mentioned difficulties of mesh based methods. Simulation of the initiation and propagation of pressure-driven fractures in brittle rocks is presented in this study. By exploiting techniques commonly used in traditional continuum methods, we have developed an elasto-plastic SPH model, which is based on the Drucker-Prager yield criterion, and the Grady-Kipp damage model. The model is validated against Brazil test data. Results are also presented the Brazil test, uni-axial compressive fracture as well as initial results for intersection of dynamic fractures with intersecting joints.

  Abstract
  This talk addresses the application of SPH to problems of hydro-fracturing and fluid-structure interaction. Simulating a hydraulic-fracture propagating in a rock with in-situ [...]

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• Simulation of finite elasto-plastic strains using the Virtual Element Method

  P. Wriggers

  Videos of Plenary Lectures presented at the XIV International Conference on Computational Plasticity (COMPLAS 2017).

  
  

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• Two-scale characterization of fiber-reinforced polymers with self-heating effect

  K. Terada

  Videos of Plenary Lectures presented at the XIV International Conference on Computational Plasticity (COMPLAS 2017).

  
  

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