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• Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction

  J. Sarrate, A. Huerta, J. Donea

  Comput. Methods Appl. Mech. Engrg., (2001). Vol. 190 (24-25), pp. 3171-3188

  
  

  Abstract

  A new formulation for two-dimensional fluid–rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid body in viscous incompressible flow are studied. The incompressible Navier–Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian–Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation can be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid–rigid body interaction.

  Abstract
  A new formulation for two-dimensional fluid–rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid body in viscous incompressible [...]

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• An improved algorithm to smooth graded quadrilateral meshes preserving the prescribed element size

  J. Sarrate, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2001). Vol. 17 (2), pp. 89-99

  
  

  Abstract

  In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases.

  Abstract
  In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of [...]

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• Error estimation and adaptivity for nonlocal damage models

  A. Huerta, A. Rodríguez-Ferran

  Int. J. Solids and Structures (2000). Vol. 37 (48-50), pp. 7501-7528

  
  

  Abstract

  Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a crucial influence on the structural response. To assess this influence, it is essential to keep finite element discretization errors under control. If not, the effect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint. To ensure the quality of the FE solution, an adaptive strategy based on error estimation is proposed here. It is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. Another important consequence of brittleness is that it leads to structural responses of the snap-through or snap-back type. This requires the use of arc-length control, with a definition of the arc parameter that accounts for the localized nature of quasi-brittle failure. All these aspects are discussed for two particular nonlocal damage models (Mazars and modified von Mises) and for two tests: the Brazilian tensile splitting test and the single-edge notched beam test. For the latter test, the capability of the Mazars model to capture the curved crack pattern observed in experiments – a topic of debate in the literature – is confirmed.

  Abstract
  Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a [...]

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• Enrichment and coupling of the finite element and meshless methods

  A. Huerta, S. Fernández-Méndez

  Int. J. Numer. Meth. Engng. (2000). Vol. 48 (11), pp. 1615-1636

  
  

  Abstract

  A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown.

  Abstract
  A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements [...]

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• Efficient unstructured quadrilateral mesh generation

  J. Sarrate, A. Huerta

  Int. J. Numer. Meth. Engng. (2000). Vol. 49 (10), pp. 1327-1350

  
  

  Abstract

  This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral elements. This automatically generates meshes composed entirely by quadrilaterals over complex geometries (there is no need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function is defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presented to show the efficiency of this algorithm.

  Abstract
  This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into [...]

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• Numerical differentiation for local and global tangent operators in computational plasticity.

  A. Pérez-Foguet, A. Rodríguez-Ferran, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 189 (1), pp. 277-296

  
  

  Abstract

  In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of the constitutive equations are approximated by means of difference schemes. These derivatives are needed to achieve quadratic convergence in the integration at Gauss-point level and in the solution of the boundary value problem. Numerical differentiation is shown to be a simple, robust and competitive alternative to analytical derivatives. Quadratic convergence is maintained, provided that adequate schemes and stepsizes are chosen. This point is illustrated by means of some numerical examples.

  Abstract
  In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of [...]

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• Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-lade model

  A. Pérez-Foguet, A. Rodríguez-Ferran, A. Huerta

  Int. J. Numer. Meth. Engng. (2000). Vol. 48 (2), pp. 159-184

  
  

  Abstract

  In a companion paper Pérez-Foguet, A., Rodríguez-Ferran, A. and Huerta, A. Numerical differentiation for local and global tangent operators in computational plasticity. Computer Methods in Applied Mechanics and Engineering, 2000, in press, the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. Relatively simple models were treated in that reference. The approach is extended here to a complex model: the MRS-Lade model. This plastic model has a cone-cap yield surface and exhibits strong coupling between the flow vector and the hardening moduli. Because of this, differentiating these quantities with respect to stresses and internal variables - the crucial step in obtaining consistent tangent matrices - is rather involved. Numerical differentiation is used here to approximate these derivatives. The approximated derivatives are then used to (1) compute consistent tangent matrices (global problem) and (2) integrate the constitutive equation at each Gauss point (local problem) with the Newton-Raphson method. The choice of the stepsize (i.e. the perturbation in the approximation schemes), based on the concept of relative stepsize, poses no difficulties. In contrast to previous approaches for the MRS-Lade model, quadratic convergence is achieved, for both the local and the global problems. The computational efficiency (CPU time) and robustness of the proposed approach is illustrated by means of several numerical examples, where the major relevant topics are discussed in detail.

  Abstract
  In a companion paper Pérez-Foguet, A., Rodríguez-Ferran, A. and Huerta, A. Numerical differentiation for local and global tangent operators in computational [...]

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• High-order accurate time-stepping schemes for convection-diffusion problems

  J. Donea, B. Roig, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3-4), pp. 249-275

  
  

  Abstract

  The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function are considered for deriving multi-stage time integration schemes involving first time derivatives only, thus easier to implement in conjunction with C0 finite elements than standard time-stepping schemes which incorporate higher-order time derivatives. After a brief discussion of the stability and accuracy properties of the multi-stage Padé schemes and having underlined the similarity between Padé and Runge–Kutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.

  Abstract
  The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods [...]

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• Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers

  A. Rodríguez-Ferran, A. Huerta

  Int. J. Numer. Meth. Engng. (1999). Vol. 46 (12), pp. 2011-2026

  
  

  Abstract

  Various non-linear equation solvers are adapted to handle linear constraints via the Lagrange-multiplier technique. This adaptation process turns out to be quite straightforward for Newton-Raphson methods and rank-two Quasi-Newton methods (BFGS and DFP), but rather more involved for Broyden method. In fact, two Broyden methods can be obtained: the standard one and a modified one, better adapted to the Lagrange-multiplier environment. Some numerical examples are used to assess the relative performance of the various adapted solvers. These tests illustrate the superiority of the modified Broyden method over the standard one.

  Abstract
  Various non-linear equation solvers are adapted to handle linear constraints via the Lagrange-multiplier technique. This adaptation process turns out to be quite straightforward [...]

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• FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation (preprint)

  A. Puigferrat, I. de-Pouplana, E. Oñate

  Computer Methods in Applied Mechanics and Engineering (2020). Vol 365, pp. 112984, DOI: 10.1016/j.cma.2020.112984

  
  

  Abstract

  In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form of the governing equations for the multidimensional transient advection-diffusion-absorption problems obtained via the Finite Increment Calculus (FIC) procedure. The FIC governing equations have a residual form that introduces a characteristic length vector that depends on streamline, absorption and shock capturing stabilization parameters, as well as on a characteristic element size that ensures a stabilized numerical solution using a standard Galerkin FEM. The value of the stabilization parameters is obtained as an extension of the steady-state form. The accuracy of the FIC-FEM formulation is verified in the solution of several transient advection-diffusion-absorption problems using regular meshes of 3-noded triangles and 4-noded quadrilaterals.

  Abstract
  In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form [...]

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