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  • 1. Abenius, Erik
    et al.
    Andersson, Ulf
    Edelvik, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Eriksson, Lasse
    Ledfelt, Gunnar
    Hybrid time domain solvers for the Maxwell equations in 2D2002In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, p. 2185-2199Article in journal (Refereed)
  • 2.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Strand, Bo
    Solving inverse electromagnetic problems using FDTD and gradient-based minimization2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, p. 650-673Article in journal (Refereed)
  • 3.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    A rotation-free corotational plane beam element for non-linear analyses2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 75, no 6, p. 672-689Article in journal (Refereed)
    Abstract [en]

    This paper presents a plane beam element without rotational degrees of freedom that can be used for the analysis of non-linear problems. The element is based on two main ideas. First, a corotational approach is adopted, which means that the kinematics of the element is decomposed into a rigid body motion part and a deformational part. Next, in the deformational part. the local nodal rotations are extrapolated as a function of the local displacements of the two nodes of the element and the first nodes to the left and right of the element. Six numerical applications are presented in order to assess the performance of the formulation.

  • 4.
    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.

  • 5.
    Bengzon, Fredrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Adaptive finite element approximation of multiphysics problems: a fluid structure interaction model problem2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, no 12, p. 1451-1465Article in journal (Refereed)
    Abstract [en]

    We consider computation of the displacement of an elastic object immersed into a viscous incompressible flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. We derive an a posteriori error estimate for this one way coupled problem using duality techniques. Based on these estimates we develop an adaptive algorithm that automatically constructs a suitable adapted mesh for the fluid and solid domains given goal quantities specified on the solid problem.

  • 6.
    Bergman, Greger
    et al.
    SSAB HardTech.
    Oldenburg, Mats
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    A finite element model for thermomechanical analysis of sheet metal forming2004In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 59, no 9, p. 1167-1186Article in journal (Refereed)
    Abstract [en]

    A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin-walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature-dependent elastic-plastic model with a non-linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one-sided forming and quenching experiment

  • 7.
    Bernland, Anders
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Wadbro, Eddie
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Berggren, Martin
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Acoustic shape optimization using cut finite elements2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 3, p. 432-449Article in journal (Refereed)
    Abstract [en]

    Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

  • 8. Burman, Erik
    et al.
    Claus, Susanne
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, Andre
    Center for Biomedical Computing, Simula Research Laboratory, PO Box 134, NO-1325 Lysaker, Norway.
    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.

  • 9. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    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.

  • 10.
    Burman, Erik
    et al.
    Department of Mathematics, University College London, United Kingdom.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Materials and Manufacturing.
    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. 

  • 11.
    Bängtsson, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    A comparison between two solution techniques to solve the equations of glacially induced deformation of an elastic Earth2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 75, p. 479-502Article in journal (Refereed)
  • 12.
    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.

  • 13. Cenanovic, Mirza
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    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.

  • 14.
    Christensen, P. W.
    et al.
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Klarbring, Anders
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    Pang, Jong Shi
    Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD, USA.
    Strömberg, Niclas
    Department of Mechanical Engineering, Linköping University, Linköping, Sweden.
    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)
    Abstract [en]

    This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code.

  • 15. 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)
  • 16. Compere, Gaetan
    et al.
    Remacle, Jean-Francois
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A mesh adaptation framework for dealing with large deforming meshes2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 82, no 7, p. 843-867Article in journal (Refereed)
    Abstract [en]

    In this paper. we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adaptation library. A new technique combining global node repositioning and mesh optimization in order to perform arbitrarily large deformations is also proposed. We then present several test cases to evaluate the performances of the proposed techniques and to show their applicability to fluid-structure interaction problems with arbitrarily large deformations. Copyright (C) 2009 John Wiley & Sons, Ltd.

  • 17.
    Dazel, Olivier
    et al.
    Université du Maine, Le Mans France.
    Brouard, B.
    Université du Maine, Le Mans France.
    Groby, J. -P
    Université du Maine, Le Mans France.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    A normal modes technique to reduce the order of poroelastic models: application to 2D and coupled 3D models2013In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 96, no 2, p. 110-128Article in journal (Refereed)
    Abstract [en]

    A reduced-order model for structures involving poroelastic materials is proposed in this paper. The approach is based on a separation of the solid and fluid phases of the porous material into separate substructures. For each individual substructure, a decoupled normal mode basis is considered, from which a set of vectors for the decomposition is selected. The preserved modes are completed by an additional family to correct for the influence of the static response of the non-preserved. It is shown that the only neglected phenomenons in the model are the inertia of the non-preserved modes and part of their intercoupling. The following three features render the proposed scheme computationally attractive: (i) real valued matrices are involved in the transformations; (ii) the assembly of complex, frequency dependent matrices is only performed at the stage of solving for a particular frequency; and (iii) the number of normal modes required are selected using a novel method.The computational efficacy is demonstrated, on a simple but realistic 3D case, through numerical results obtained using a reduced number of DOFs, showing a significant reduction of computational cost compared with traditional methods.

  • 18.
    Edlund, Johan
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Strand, Bo
    Iterative solution of a hybrid method for Maxwell's equations in the frequency domain2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 56, p. 1755-1770Article in journal (Refereed)
  • 19. Effenberger, Cedric
    et al.
    Kressner, Daniel
    Engström, Christian
    ETH Zurich, Seminar for Applied Mathematics.
    Linearization techniques for band structure calculations in absorbing photonic crystals2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 89, no 2, p. 180-191Article in journal (Refereed)
    Abstract [en]

    Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques. Copyright © 2011 John Wiley & Sons, Ltd.

  • 20.
    Effenberger, Cedric
    et al.
    ETH Zurich, Switzerland.
    Kressner, Daniel
    ETH Zurich, Switzerland.
    Engström, Christian
    ETH Zurich, Switzerland.
    Linearization techniques for band structure calculations in absorbing photonic crystals2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 89, no 2, p. 180-191Article in journal (Refereed)
    Abstract [en]

    Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spatial discretization using an interior penalty discontinuous Galerkin method, we employ a recently developed linearization technique to deal with the resulting rational matrix eigenvalue problems. In particular, the efficient implementation of Krylov subspace methods for solving the linearized eigenvalue problems is investigated in detail. Numerical experiments demonstrate that our new approach is considerably cheaper in terms of memory and computing time requirements compared with the naive approach of turning the rational eigenvalue problem into a polynomial eigenvalue problem and applying standard linearization techniques. Copyright © 2011 John Wiley & Sons, Ltd.

  • 21.
    Engström, Christian
    et al.
    ETH Zurich, Seminar for Applied Mathematics.
    Wang, Mengyu
    Complex dispersion relation calculations with the applications to absorptive photonic crystals2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, p. 849-863Article in journal (Refereed)
  • 22.
    Engström, Christian
    et al.
    ETH Zurich, Switzerland.
    Wang, Mengyu
    ETH Zurich, Switzerland.
    Complex dispersion relation calculations with the applications to absorptive photonic crystals2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, p. 849-863Article in journal (Refereed)
    Abstract [en]

    A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivityand we relate for this absorptive system the spectral parameter to the time frequency. We transform thenon-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problemand uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact ofthe penalty term numerically and illustrate the high convergence rate of the method.

  • 23. Eriksson, Anders
    Derivatives of tangential stiffness matrices for equilibrium path descriptions1991In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 5, p. 1093-1113Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.

  • 24.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Derivatives of tangential stiffness matrices for equilibrium path descriptions1991In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 5, p. 1093-1113Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.

  • 25. Eriksson, Anders
    Derivatives of tangential stiffness matrices for equilibrium path descriptions1991In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 5, p. 1093-1113Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.

  • 26. Eriksson, Anders
    On improved predictions for structural equilibrium path evaluations1993In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 36, no 2, p. 201-220Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures for higher-order predictions have been introduced in order to improve the convergence speed in a general finite element program for non-linear structural analysis. In addition to higher-order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post-bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re-creation of the tangential stiffness matrix, used for equilibrium iterations. Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods. The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.

  • 27.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On improved predictions for structural equilibrium path evaluations1993In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 36, no 2, p. 201-220Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures for higher-order predictions have been introduced in order to improve the convergence speed in a general finite element program for non-linear structural analysis. In addition to higher-order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post-bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re-creation of the tangential stiffness matrix, used for equilibrium iterations. Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods. The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.

  • 28. Eriksson, Anders
    On improved predictions for structural equilibrium path evaluations1993In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 36, no 2, p. 201-220Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures for higher-order predictions have been introduced in order to improve the convergence speed in a general finite element program for non-linear structural analysis. In addition to higher-order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post-bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re-creation of the tangential stiffness matrix, used for equilibrium iterations. Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods. The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.

  • 29. Eriksson, Anders
    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems1989In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 28, no 6, p. 1317-1334Article in journal (Refereed)
    Abstract [en]

    The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.

  • 30.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems1989In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 28, no 6, p. 1317-1334Article in journal (Refereed)
    Abstract [en]

    The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.

  • 31. Eriksson, Anders
    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems1989In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 28, no 6, p. 1317-1334Article in journal (Refereed)
    Abstract [en]

    The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.

  • 32. Eriksson, Anders
    ON SOME PATH-RELATED MEASURES FOR NON-LINEAR STRUCTURAL F. E. PROBLEMS.1988In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 26, no 8, p. 1791-1803Article in journal (Refereed)
    Abstract [en]

    In the paper, the solution of a non-linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behavior, guiding the iteration strategy in coming steps. Two path-related stiffness measures are derived, giving information concerning the behavior of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.

  • 33.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    ON SOME PATH-RELATED MEASURES FOR NON-LINEAR STRUCTURAL F. E. PROBLEMS.1988In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 26, no 8, p. 1791-1803Article in journal (Refereed)
    Abstract [en]

    In the paper, the solution of a non-linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behavior, guiding the iteration strategy in coming steps. Two path-related stiffness measures are derived, giving information concerning the behavior of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.

  • 34. Eriksson, Anders
    ON SOME PATH-RELATED MEASURES FOR NON-LINEAR STRUCTURAL F. E. PROBLEMS.1988In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 26, no 8, p. 1791-1803Article in journal (Refereed)
    Abstract [en]

    In the paper, the solution of a non-linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behavior, guiding the iteration strategy in coming steps. Two path-related stiffness measures are derived, giving information concerning the behavior of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.

  • 35. Eriksson, Anders
    USING EIGENVECTOR PROJECTIONS TO IMPROVE CONVERGENCE IN NON-LINEAR FINITE ELEMENT EQUILIBRIUM ITERATIONS.1987In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 24, no 3, p. 497-512Article in journal (Refereed)
    Abstract [en]

    In an earlier paper a method for calculation of non-linear structural response was described. A method for selective damping of solution components parallel to critical eigenvectors was proposed, reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the 'dynamic relaxation' approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N-R schemes. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.

  • 36.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    USING EIGENVECTOR PROJECTIONS TO IMPROVE CONVERGENCE IN NON-LINEAR FINITE ELEMENT EQUILIBRIUM ITERATIONS.1987In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 24, no 3, p. 497-512Article in journal (Refereed)
    Abstract [en]

    In an earlier paper a method for calculation of non-linear structural response was described. A method for selective damping of solution components parallel to critical eigenvectors was proposed, reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the 'dynamic relaxation' approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N-R schemes. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.

  • 37. Eriksson, Anders
    USING EIGENVECTOR PROJECTIONS TO IMPROVE CONVERGENCE IN NON-LINEAR FINITE ELEMENT EQUILIBRIUM ITERATIONS.1987In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 24, no 3, p. 497-512Article in journal (Refereed)
    Abstract [en]

    In an earlier paper a method for calculation of non-linear structural response was described. A method for selective damping of solution components parallel to critical eigenvectors was proposed, reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the 'dynamic relaxation' approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N-R schemes. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.

  • 38.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Svanberg, Krister
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimization in simulations of human movement planning2011In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 87, no 12, p. 1127-1147Article in journal (Refereed)
    Abstract [en]

    This paper discusses optimization algorithms in movement simulations for models of humans, humanoid robots or other mechanisms. Targeted movements between two configurations define a dynamically redundant system, for which there is freedom in the choice of control force time variations. A previously developed formulation for the treatment of targeted dynamics for mechanisms was used as a basis. The paper describes the development of an algorithm related to the method of moving asymptotes for the necessary optimization. The algorithm is specifically adapted to problems which are large and non-linear but sparse, and which include very high numbers of design variables as well as constraints. In particular, non-linear equality constraints from dynamic equilibrium equations are important. The optimization algorithm was developed to include these, but also in order to allow successively increasing penalty factors for constraint violations. The resulting setting was shown to be able to handle the systems established, robustly giving convergence to at least a local minimum also for very distant start iterates. The existence of very closely situated local optima, representing very similar movements, was discovered for the problem formulation, calling for an ad hoc method for finding the best of these local optima.

  • 39.
    Esen, Sedat
    et al.
    Luleå tekniska universitet.
    Souers, P.C.
    Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA.
    Vitello, P.
    Energetic Materials Center, Lawrence Livermore National Laboratory, Livermore, CA.
    Prediction of the non-ideal detonation performance of commercial explosives using the DeNE and JWL++ codes2005In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 64, no 14, p. 1889-1914Article in journal (Refereed)
    Abstract [en]

    The non-ideal detonation performance of two commercial explosives is determined using the DeNE and JWL++ codes. These two codes differ in that DeNE is based on a pseudo-one-dimensional theory which is valid on the central stream-tube and capable of predicting the non-ideal detonation characteristics of commercial explosives as a function of the explosive type, rock properties and blasthole diameter. On the other hand, JWL++ is a hydrocode running in a 2-D arbitrary Lagrangian-Eulerian code with CALE-like properties and can determine the flow properties in all stream lines within the reaction zone. The key flow properties (detonation velocity, pressure, specific volume, extent of reaction and reaction zone length) at the sonic locus on the charge axis have been compared. In general, it is shown that the flow parameters determined using both codes agree well. The pressure contours determined using the JWL++ are analysed in detail for two explosives at 165 mm blastholes confined in limestone and kimberlite with a view to further investigate the explosive/rock interface. The DeNE and JWL++ codes have been validated using the measured in-hole detonation velocity data.

  • 40. Estep, Donald
    et al.
    Målqvist, Axel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Tavener, Simon
    Nonparametric density estimation for randomly perturbed elliptic problems II: Applications and adaptive modeling2009In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 80, p. 846-867Article in journal (Refereed)
  • 41.
    Gaborit, Mathieu
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. Le Mans Univ, UMR CNRS 6613, LAUM, Le Mans, France..
    Dazel, O.
    Le Mans Univ, UMR CNRS 6613, LAUM, Le Mans, France..
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Gabard, G.
    Le Mans Univ, UMR CNRS 6613, LAUM, Le Mans, France..
    Coupling of finite element and plane waves discontinuous Galerkin methods for time-harmonic problems2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 116, no 7, p. 487-503Article in journal (Refereed)
    Abstract [en]

    A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation problems. While wave-based methods can significantly reduce the computational cost, especially at high frequencies, their efficiency is hampered by the need to use small elements to resolve complex geometric features. This can be alleviated by using a standard finite element model close to the surfaces to model geometric details and create large, simply-shaped areas to model with a wave-based method. This strategy is formulated and validated in this paper for the wave-based discontinuous Galerkin method together with the standard finite element method. The coupling is formulated without using Lagrange multipliers and results demonstrate that the coupling is optimal in that the convergence rates of the individual methods are maintained.

  • 42.
    Gaborit, Mathieu
    et al.
    University of Le Mans.
    Dazel, Olivier
    Université du Maine, Le Mans France.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. Centre for ECO2 Vehicle Design.
    Gabard, Gwenael
    University of Le Mans.
    Coupling of finite element and plane waves discontinuous Galerkin methods for time-harmonic problems2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 116, no 7, p. 487-503Article in journal (Refereed)
    Abstract [en]

    A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation problems. While wave-based methods can significantly reduce the computational cost, especially at high frequencies, their efficiency is hampered by the need to use small elements to resolve complex geometric features. This can be alleviated by using a standard finite element model close to the surfaces to model geometric details and create large, simply-shaped areas to model with a wave-based method. This strategy is formulated and validated in this paper for the wave-based discontinuous Galerkin method together with the standard finite element method. The coupling is formulated without using Lagrange multipliers and results demonstrate that the coupling is optimal in that the convergence rates of the individual methods are maintained.

  • 43.
    Habbal, Abderrahmane
    et al.
    Laboratoire J.A.Dieudonné, Université de Nice Sophia-Antipolis, France.
    Petersson, Joakim
    Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
    Thellner, Mikael
    Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
    Multidisciplinary topology optimization solved as a Nash game2004In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 61, no 7, p. 949-963Article in journal (Refereed)
    Abstract [en]

    In the present work, multidisciplinary optimization is formulated in the game theory framework. We choose a coupled heat transfer—thermoelastic system as the case study for which a topology design approach is developed. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. The game has two players and the parameterization of the design domain is such that the design variables describe the material density and a parameter which influences the heat flow by convection to the surrounding fluid. The first player controls the structure and the second player controls the temperature distribution in the structure. For the second player, we present mathematical proof of existence of a discrete valued optimal solution and it is concluded that no regularization of the suboptimization problem is needed. We present two numerical examples which illustrate the proposed methodology. One of the examples is also solved by weighting the objectives to a scalar valued objective function and the result is compared with the Nash game solution.

  • 44.
    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. 

  • 45.
    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.

  • 46.
    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.

  • 47.
    Hansbo, Peter
    et al.
    Göteborg, Sweden.
    Heintz, David
    Göteborg, Sweden.
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    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. Copyright (C) 2009 John Wiley & Sons, Ltd.

  • 48.
    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.

  • 49.
    Hörlin, Nils-Erik
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    A symmetric weak form of Biot's equations based on redundant variables representing the fluid, using a Helmholtz decomposition of the fluid displacement vector field2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, no 13, p. 1613-1637Article in journal (Refereed)
    Abstract [en]

    A novel symmetric weak formulation of Biot's equations for linear acoustic wave propagation in layered poroelastic media is presented. The primary variables used are the frame displacement, the acoustic pore pressure, the scalar potential and the vector potential obtained from a Helmholtz decomposition of the fluid displacement. Also a symmetric weak form based on the frame displacement, the pore pressure and the fluid displacement is obtained as an intermediate result. hp finite element simulations of a double leaf partition based on this new weak formulation is verified against simulation results from the classical frame displacement, fluid displacement formulation and a frame displacement pore pressure formulation. All three formulations simulated, displays the same rate of convergence with respect to finite element bases polynomial degree. The novel formulation also extends a previously published frame displacement, pore pressure, scalar fluid displacement potential formulation with an implicit irrotational fluid displacement assumption to a full representation of Biot's equations.

  • 50.
    Hörlin, Nils-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Numerical acoustics.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Numerical acoustics.
    Weak, anisotropic symmetric formulations of Biot's equations for vibro-acoustic modelling of porous elastic materials2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, no 12, p. 1519-1540Article in journal (Refereed)
    Abstract [en]

    In this paper a fully anisotropic symmetric weak formulation of Biot's equations for vibro-acoustic modelling of porous elastic materials in the frequency domain is proposed. Starting from Biot's equations in their anisotropic form, a mixed displacement-pressure formulation is discussed in terms of Cartesian tensors. The anisotropic equation parameters appearing in the differential equations are derived from material parameters which are possible to determine through experimental testing or micro-structural simulations of the fluid and the porous skeleton. Solutions are obtained by applying the finite element method to the proposed weak form and the results are verified against a weak displacement-based formulation for a foam and plate combination.

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