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  • 1.
    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.

  • 2. 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.

  • 3.
    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.

  • 4. 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.

  • 5.
    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.

  • 6. 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.

  • 7. 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.

  • 8.
    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.

  • 9. 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.

  • 10. 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.

  • 11.
    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.

  • 12. 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.

  • 13. 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.

  • 14.
    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.

  • 15. 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.

  • 16. 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.

  • 17.
    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.

  • 18. 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.

  • 19.
    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.

  • 20.
    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.

  • 21.
    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.

  • 22.
    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.

  • 23.
    Johnsson, Lennart
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Mathur, Kapil K
    Data Structures and Algorithms for the Finite Element Method on a Data Parallel Supercomputer1990In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 29, no 4, p. 881-908Article in journal (Refereed)
    Abstract [en]

    This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre-conditioner is used for the solution of the resulting linear system. Results from an implementation of the three-dimensional finite element method based on Lagrange elements are reported. For single-precision floating-point operations, the measured peak performance is approximately 2·4 G flops s−1 for evaluating the elemental stiffness matrices and approximately 850 M flops s−1 for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double-precision floating-point operations.

  • 24.
    Johnsson, Lennart
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Mathur, Kapil K
    Experience with the Conjugate Gradient Method for Stress Analysis on a Data Parallel Supercomputer1989In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 27, no 3, p. 523-546Article in journal (Refereed)
    Abstract [en]

    The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4–1·5 for the model problems.

  • 25.
    Kiousis, Dimitrios
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Gasser, Thomas
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Smooth contact strategies with emphasis on the modeling of balloon angioplasty with stenting2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 75, no 7, p. 826-855Article in journal (Refereed)
    Abstract [en]

    Critical to the simulation of balloon angioplasty is the modeling of the contact between the artery wall and the medical devices. In standard approaches, the 3D contact surfaces are described by means of C0-continuous facet-based techniques, which may lead to numerical problems. This work introduces a novel contact algorithm where the target surfaces are described by polynomial expressions with C2-continuity. On the basis of uniform cubic B-splines, two different parametrization techniques are presented and compared, while the related implementation of the algorithm into a finite element analysis program is described. Two numerical examples are selected to demonstrate the special merits of the proposed contact formulation. The first example is a benchmark contact problem selected to point out the special features of the proposed strategies. The second example is concerned with the simulation of balloon angioplasty and stenting, where the contact between the balloon, the stent and the artery wall is numerically modeled. A patient-specific 3D model of a stenotic femoral artery serves as a basis. The study concludes by identifying the changes in the mechanical environment of the artery in terms of contact forces and strains by considering two different stent designs.

  • 26. Nobile, F.
    et al.
    Tempone, Raúl
    Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients2009In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 80, no 6-7, p. 979-1006Article in journal (Refereed)
    Abstract [en]

    We consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forzing terms are Spatially correlated random fields The stochastic coefficients of the PDE are approximated by truncated Karhunen-Loeve expansions driven by a finite number of uncorrelated random variables. After approximating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE; of the same type, the dimension of the parameter set being equal to the number of random variables Introduced. After proving that the. solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based oil tensor product. total degree or sparse polynomial Spaces and constructed by either a Stochastic Galerkin or I Stochastic Collocation approach. We derive convergence rates for the different Cases and present numerical results that show how these approaches are a valid 'alternative to the more traditional Monte Carlo Method for this class of problems.

  • 27. Prot, V.
    et al.
    Skallerud, B.
    Holzapfel, Gerhard
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation2007In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 71, no 8, p. 987-1008Article in journal (Refereed)
    Abstract [en]

    The present study addresses constitutive modelling and implementation of transversely isotropic hyperelastic material models for the analysis of the mitral valve. This valve separates the left atrium and left ventricle in the heart. Two convex strain energy potentials are employed in derivation of stress tensors and elasticity tensors. The plane stress and incompressibility conditions are accounted for directly. The relationships are implemented in an implicit code (ABAQUS) via the user-defined interface. Numerical simulations of the valve motion during a part of the heart cycle are carried out and compared to ultrasound measurements of a healthy human valve. The significance of placement of chordae tendinae is illustrated. The implementation provides a tool for simulations of both healthy and pathological mitral valve conditions.

  • 28.
    Rumpler, Romain
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Pade approximants and the modal connection: Towards increased robustness for fast parametric sweeps2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 1, p. 65-81Article in journal (Refereed)
    Abstract [en]

    To increase the robustness of a Pade-based approximation of parametric solutions to finite element problems, an a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Pade-based expansion of the solution vector components, overcoming some of the current convergence and robustness limitations. In particular, this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of Pade approximants. The choice of these approximants, as shown in the present work, is theoretically supported by the Montessus de Ballore theorem, concerning the convergence of a series of approximants with fixed denominator degrees. Key features and originality of the proposed approach are (1) a component-wise expansion which allows to specifically target subsets of the solution field and (2) the a priori, simultaneous choice of the Pade approximants and their associated interval of convergence for an effective and more robust approximation. An academic acoustic case study, a structural-acoustic application, and a larger acoustic problem are presented to demonstrate the potential of the approach proposed.

  • 29.
    Rumpler, Romain
    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.
    Deü, J.-F
    Conservatoire National des Arts et Métiers, Paris France.
    A finite element approach combining a reduced-order system, Pade approximants, and an adaptive frequency windowing for fast multi-frequency solution of poro-acoustic problems2014In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 97, no 10, p. 759-784Article in journal (Refereed)
    Abstract [en]

    In this work, a solution strategy is investigated for the resolution of multi-frequency structural-acoustic problems including 3D modeling of poroelastic materials. The finite element method is used, together with a combination of a modal-based reduction of the poroelastic domain and a Pade-based reconstruction approach. It thus takes advantage of the reduced-size of the problem while further improving the computational efficiency by limiting the number of frequency resolutions of the full-sized problem. An adaptive procedure is proposed for the discretization of the frequency range into frequency intervals of reconstructed solution. The validation is presented on a 3D poro-acoustic example.

  • 30.
    Rumpler, Romain
    et al.
    Creo Dynam AB, Sweden.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Rice, H. J.
    Trinity College, Department of Mechanical and Manufacturing Engineering, Ireland.
    An adaptive strategy for the bivariate solution of finite element problems using multivariate nested Pade approximants2014In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 100, no 9, p. 689-710Article in journal (Refereed)
    Abstract [en]

    Most engineering applications involving solutions by numerical methods are dependent on several parameters, whose impact on the solution may significantly vary from one to the other. At times an evaluation of these multivariate solutions may be required at the expense of a prohibitively high computational cost. In the present paper, an adaptive approach is proposed as a way to estimate the solution of such multivariate finite element problems. It is based upon the integration of so-called nested Pade approximants within the finite element procedure. This procedure includes an effective control of the approximation error, which enables adaptive refinements of the converged intervals upon reconstruction of the solution. The main advantages lie in a potential reduction of the computational effort and the fact that the level of a priori knowledge required about the solution in order to have an accurate, efficient, and well-sampled estimate of the solution is low. The approach is introduced for bivariate problems, for which it is validated on elasto-poro-acoustic problems of both academic and more industrial scale. It is argued that the methodology in general holds for more than two variables, and a discussion is opened about the truncation refinements required in order to generalize the results accordingly.

  • 31.
    Sou, Kin Cheong
    et al.
    Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
    de Weck, Olivier
    Aeronautics and Astronautics, Massachusetts Institute of Technology.
    Fast time-domain simulation for large-order linear time-invariant state space systems2005In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 63, no 5, p. 681-708Article in journal (Refereed)
    Abstract [en]

    Time-domain simulation is essential for both analysis and design of complex systems. Unfortunately, high model fidelity leads to large system size and bandwidths, often causing excessive computation and memory saturation. In response we develop an efficient scheme for large-order linear time-invariant systems. First, the A matrix is block diagonalized. Then, subsystems of manageable dimensions and bandwidth are formed, allowing multiple sampling rates. Each subsystem is then discretized using a O(n(s)) scheme, where n(s) is the number of states. Subsequently, a sparse matrix O(n(s)) discrete-time system solver is employed to compute the history of the state and output. Finally, the response of the original system is obtained by superposition. In practical engineering applications, closing feedback loops and cascading filters can hinder the efficient use of the simulation scheme. Solutions to these problems are addressed in the paper. The simulation scheme, implemented as a MATLAB function fast1sim, is benchmarked against the standard LTI system simulator 1sim and is shown to be superior for medium to large systems. The algorithm scales close to O(n(s)(2)) for a set of benchmarked systems. Simulation of a high-fidelity model (n ≈ 2200) of the Space Interferometry Mission spacecraft illustrates real world application of the method.

  • 32. Stadler, M.
    et al.
    Holzapfel, Gerhard A.
    Subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3D2004In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 60, no 7, p. 1161-1195Article in journal (Refereed)
    Abstract [en]

    This paper presents a strategy to parameterize contact surfaces of arbitrary mesh topology in 3D with at least Cl-continuity for both quadrilateral and triangular meshes. In the regular mesh domain, four quadrilaterals or six triangles meet in one node, even C-2 -continuity is attained. Therefore, we use subdivision surfaces, for which non-physical pressure jumps are avoided for contact interactions. They are usually present when the contact kinematics is based on facet elements discretizing the interacting bodies. The properties of subdivision surfaces give rise to basically four different implementation strategies. Each strategy has specific features and requires more or less efforts for an implementation in a finite element program. One strategy is superior with respect to the others in the sense that it does not use nodal degrees of freedom of the finite element mesh at the contact surface. Instead, it directly uses the degrees of freedom of the smooth surface. Thereby, remarkably, it does not require an interpolation. We show how the proposed method can be used to parameterize adaptively refined meshes with hanging nodes. This is essential when dealing with finite element models whose geometry is generated by means of subdivision techniques. Three numerical 3D problems demonstrate the improved accuracy, robustness and performance of the proposed method over facet-based contact surfaces. In particular, the third problem, adopted from biomechanics, shows the advantages when designing complex contact surfaces by means of subdivision techniques.

  • 33. Stadler, M.
    et al.
    Holzapfel, Gerhard A.
    Korelc, J.
    C-n continuous modelling of smooth contact surfaces using NURBS and application to 2D problems2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 57, no 15, p. 2177-2203Article in journal (Refereed)
    Abstract [en]

    This paper presents a strategy for the finite-element implementation of C-n continuous contact surfaces for deformable bodies undergoing finite deformations, whereby n represents an arbitrary level of continuity. The proposed novel approach avoids the non-physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries. In particular, for certain problems, the level of continuity may influence the rate of convergence significantly within a non-linear solution scheme. A hierarchical tree data structure is proposed for an efficient search algorithm to find the neighbour elements on adaptively refined meshes, which are involved in the smoothing process of a particular finite element. The same data structure is used for the automatic detection of the contact surfaces of a body. Three representative numerical examples demonstrate the increased rate of convergence, the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method.

  • 34.
    Svanberg, Krister
    KTH, Superseded Departments, Mathematics.
    Modelling topology optimization problems as linear mixed 0-1 programs2003In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 57, no 5, p. 723-739Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of discretized continuum structures. It is shown that a large class of non-linear 0-1 topology optimization problems, including stress- and displacement-constrained minimum weight problems, can equivalently be modelled as linear mixed 0-1 programs. The modelling approach is applied to some test problems which are solved to global optimality.

  • 35.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Topology optimization by a neighbourhood search method based on efficient sensitivity calculations2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 67, no 12, p. 1670-1699Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of discretized load-carrying continuum structures, where the design of the structure is represented by binary design variables indicating material or void in the various finite elements. Efficient exact methods for discrete sensitivity calculations are developed. They utilize the fact that if just one or two binary variables are changed to their opposite binary values then the new stiffness matrix is essentially just a low-rank modification of the old stiffness matrix, even if some nodes in the structure may disappear or re-enter. As an application of these efficient sensitivity calculations, a new neighbourhood search method is presented, implemented, and applied on some test problems, one of them with 6912 nine-node finite elements where the von Mises stress in each non-void element is considered.

  • 36.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Using the sequential linear integer programming method as a post-processor for stress-constrained topology optimization problems2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 76, no 10, p. 1544-1567Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of load-carrying structures defined on discretized continuum design domains. In particular, the mininium compliance problem with stress constraints is considered. The finite element method is used to discretize the design domain into n finite elements and the design of a certain structure is represented by an n-dimensional binary design variable vector. In order to solve the problems, the binary constraints on the design variables are initially relaxed and the problems are solved with both the method of moving asymptotes and the sparse non-linear optimizer solvers for continuous optimization in order to compare the two solvers. By solving a sequence of problems with a sequentially lower limit on the amount of grey allowed, designs that are close to 'black-and-white' are obtained. In order to get locally optimal solutions that are purely {0, 1}(n). a sequential linear integer programming method is applied as a post-processor. Numerical results are presented for some different test problems.

  • 37.
    Zang, W.L.
    et al.
    KTH, Superseded Departments, Solid Mechanics.
    Gudmundson, Peter
    KTH, Superseded Departments, Solid Mechanics.
    Contact Problems Of Kinked Cracks Modeled By A Boundary Integral Method1990In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 29, no 4, p. 847-860Article in journal (Refereed)
    Abstract [en]

    Based on the integral equation for the resultant forces along a crack, a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account. The method is demonstrated by a consideration of an elastic half-plane containing a piece-wise straight line crack. Two numerical examples are presented and compared to finite element calculations. The numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact.

  • 38. Zang, W.L.
    et al.
    Gudmundson, Peter
    SICOMP, Swedish Institute of Compositie.
    Frictional Contact Problems Of Kinked Cracks Modeled By A Boundary Integral Method1991In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 31, no 3, p. 427-446Article in journal (Refereed)
    Abstract [en]

    A numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The method is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub-surface piece-wise straight line cracks in a half-plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.

  • 39.
    Östberg, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Hörlin, Nils
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Kari, Leif
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Weak forms for modelling of rotationally symmetric, multilayered structures, including anisotropic poro-elastic media2012In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 90, no 8, p. 1035-1052Article in journal (Refereed)
    Abstract [en]

    A weak form of the anisotropic Biot's equation represented in a cylindrical coordinate system using a spatial Fourier expansion in the circumferential direction is presented. The original three dimensional Cartesian anisotropic weak formulation is rewritten in an arbitrary orthogonal curvilinear basis. Introducing a cylindrical coordinate system and expanding the circumferential wave propagation in terms of orthogonal harmonic functions, the original, geometrically rotationally symmetric three dimensional boundary value problem, is decomposed into independent two-dimensional problems, one for each harmonic function. Using a minimum number of dependent variables, pore pressure and frame displacement, a computationally efficient procedure for vibro-acoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including anisotropic porous elastic materials is thus obtained. By numerical simulations, this method is compared with, and the correctness is verified against, a full three-dimensional Cartesian coordinate system finite element model.

  • 40.
    Östberg, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Hörlin, Nils-Erik
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Numerical acoustics. KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design.
    Göransson, Peter
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Numerical acoustics. KTH, School of Engineering Sciences (SCI), Centres, VinnExcellence Center for ECO2 Vehicle design.
    Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 81, no 11, p. 1439-1454Article in journal (Refereed)
    Abstract [en]

    A weak symmetric form of Biot's equation in cylindrical coordinates with a spatial Fourier expansion in the circumferential direction is presented. The solid phase displacement and the pore pressure are used as the dependent variables. The original three-dimensional boundary value problem is here, due to the orthogonality of the harmonic functions and the rotationally symmetric geometry, decomposed into independent two-dimensional problems, one for each harmonic function. This formulation provides a computationally efficient procedure for vibroacoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including porous elastic materials. By numerical Simulations, this method is compared with, and verified against, full three-dimensional Cartesian coordinate system finite element models.

1 - 40 of 40
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