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  • 1.
    Becker, Roland
    et al.
    Université de Pau et des Pays de l'Adour.
    Burman, Erik
    University of Sussex Falmer.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    A hierarchical NXFEM for fictitious domain simulations2011In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 86, no 4-5, p. 549-559Article in journal (Refereed)
    Abstract [en]

    We suggest a fictitious domain method, based on the Nitsche XFEM method of (Comput. Meth. Appl. Mech. Engrg 2002; 191: 5537-5552), that employs a band of elements adjacent to the boundary. In contrast, the classical fictitious domain method uses Lagrange multipliers on a line (surface) where the boundary condition is to be enforced. The idea can be seen as an extension of the Chimera method of (ESAIM: Math. Model Numer. Anal. 2003; 37: 495-514), but with a hierarchical representation of the discontinuous solution field. The hierarchical formulation is better suited for moving fictitious boundaries since the stiffness matrix of the underlying structured mesh can be retained during the computations. Our technique allows for optimal convergence properties irrespective of the order of the underlying finite element method.

  • 2.
    Burman, Erik
    et al.
    Department of Mathematics, University College London, United Kingdom.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Larson, Mats G.
    Department of Mathematics and Mathematical Statistics, Umeå University, Sweden.
    Augmented Lagrangian and Galerkin least-squares methods for membrane contact2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 114, no 11, p. 1179-1191Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations. 

  • 3.
    Cenanovic, Mirza
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization. Jönköping University, School of Engineering, JTH, Product Development.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Larson, Mats G,
    Umeå University.
    Minimal surface computation using a finite element method on an embedded surface2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 502-512Article in journal (Refereed)
    Abstract [en]

    We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace–Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.

  • 4. Christensen, XP.W
    et al.
    Klarbring, A
    Pang, J.S.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    Formulation and comparison of algorithms for frictional contact problems1998In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 42, no 1, p. 145-173Article in journal (Refereed)
  • 5.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Nonconforming rotated Q1 tetrahedral element with explicit time stepping for elastodynamics2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 91, no 10, p. 1105-1114Article in journal (Refereed)
    Abstract [en]

    In this paper, we apply a rotated bilinear tetrahedral element to elastodynamics in R3. This element performs superior to the constant strain element in bending and, unlike the conforming linear strain tetrahedron, allows for row-sum lumping of the mass matrix. We study the effect of different choices of approximation (point- wise continuity versus edge average continuity) as well as lumping versus consistent mass in the setting of eigenvibrations. We also use the element in combination with the leapfrog method for time domain com- putations and make numerical comparisons with the constant strain and linear strain tetrahedra. 

  • 6.
    Hansbo, Peter
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization. Jönköping University, School of Engineering, JTH, Product Development.
    Burman, Erik
    Universiy College London.
    Claus, Susanne
    University College London.
    Larson, Mats G.
    Umeå University.
    Massing, André
    Simula Research Laboratory.
    CutFEM: Discretizing geometry and partial differential equations2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 472-501Article in journal (Refereed)
    Abstract [en]

    We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.

  • 7.
    Hansbo, Peter
    et al.
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Heintz, David
    Chalmers University of Technology and University of Gothenburg.
    Larson, Mats G.
    Umeå University.
    An adaptive finite element method for second-order plate theory2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 81, no 5, p. 584-603Article in journal (Refereed)
    Abstract [en]

    We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P(2)-approximations on simplices for the out-of-plane deformations, using C(0)-continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples.

  • 8.
    Heintz, Per
    et al.
    Chalmers University of Technology.
    Larsson, Fredrik
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Runesson, Kenneth
    Chalmers University of Technology.
    Adaptive strategies and error control for computing material forces in fracture mechanics2004In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 60, no 7, p. 1287-1299Article in journal (Refereed)
    Abstract [en]

    The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self-equilibrating Eshelby (material) stress tensor it turns out that the classical J-integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non-conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single-edged crack, whereby different strategies for computing the J-integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch.

  • 9.
    Larsson, Fredrik
    et al.
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Runesson, Kenneth
    Chalmers University of Technology.
    Space-time finite elements and an adaptive strategy for the coupled thermoelasticity problem2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 56, no 2, p. 261-293Article in journal (Refereed)
    Abstract [en]

    A space-time finite element method for the linear thermo-elasticity problem is outlined. By establishing the appropriate dual problem in space-time. it is possible to establish an exact a posteriori error representation formula based on residuals and the dual solution. In particular, we focus on the error generation in time. An adaptive strategy in the time-domain is proposed, and its performance is investigated with the aid of a numerical example in 2D. In particular. the excellent precision of the error estimate. in terms of the effectivity, index being close to unity, is noted.

  • 10.
    Larsson, Fredrik
    et al.
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Runesson, Kenneth
    Chalmers University of Technology.
    Strategies for computing goal-oriented a posteriori error measures in non-linear elasticity2002In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 55, no 8, p. 879-894Article in journal (Refereed)
    Abstract [en]

    We investigate the characteristics and performance of goal-oriented a posteriori error measures for a class of non-linear elasticity models, while restriction is made to small strain theory. The chosen error measure of the displacement field can be global or local (probing the chosen quantity in a specific spatial point). The error is computable with the aid of the solution of a dual problem whose data depend on the error measure. The main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution. The chosen strategies are compared in terms of accuracy, ease of implementation, reliability and cost-efficiency. A well-known numerical example, the Cook's membrane, is used for the numerical evaluations.

  • 11.
    Larsson, Fredrik
    et al.
    Chalmers University of Technology.
    Runesson, Kenneth
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Time finite elements and error computation for (visco)plasticity with hardening or softening2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 56, no 14, p. 2213-2232Article in journal (Refereed)
    Abstract [en]

    In this paper we investigate the possibility for, and characteristics of, reliable and efficient a posteriori error computation at the integration of the constitutive relations pertinent to (visco)plasticity with softening/hardening. The variational structure admits the use of finite elements in time, which are based on the Discontinuous Galerkin method. An important feature is the possibility to select 'goal-oriented' error measures with great freedom. A key task is to identify and solve an auxiliary problem, that is the dual of the actual (primal) problem. Different strategies for computing the dual solution accurately, yet avoiding excessive cost, are investigated in the paper. In particular, we consider the characteristics at the limit of rate-independent plasticity.

  • 12.
    Möller, Peter
    et al.
    Chalmers University of Technology.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    On advancing front mesh generation in three dimensions1995In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 38, no 21, p. 3551-3569Article in journal (Refereed)
    Abstract [en]

    This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way.

  • 13.
    Nilsson, Bertil
    et al.
    Halmstad University.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
    Adaptive finite element methods for hydrodynamic lubrication with cavitation2007In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 72, no 13, p. 1584-1604Article in journal (Refereed)
    Abstract [en]

    We present an adaptive finite element method for a cavitation model based on Reynolds' equation. A posteriori error estimates and adaptive algorithms are discussed, and numerical examples illustrating the theory are supplied.

  • 14. Salomonsson, Kent
    et al.
    Stigh, Ulf
    An adhesive interphase element for structural analyses2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 76, no 4, p. 482-500Article in journal (Refereed)
    Abstract [en]

    A special purpose finite element is developed for structural simulations of complex adhesively bonded structures. In the interphase element, the adhesive is explicitly regarded as a material phase between two substrates. The element considers large rotations. Furthermore, it considers in-plane straining of the adhesive due to large curvatures of the bonded shells. This feature appears especially important when considering bonding of thin plastically deforming metallic shell structures. Simulations are made on specimens where the adherends deform both elastically and plastically. The results are in good agreement with previously performed experiments. 

  • 15.
    Strömberg, Niclas
    Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
    A method for structural dynamic contact problems with friction and wear2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 58, no 15, p. 2371-2385Article in journal (Refereed)
1 - 15 of 15
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