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  • 1. Alsafadie, R.
    et al.
    Hjiaj, M.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Corotational mixed finite element formulation for thin-walled beams with generic cross-section2010In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 199, no 49-52, p. 3197-3212Article in journal (Refereed)
    Abstract [en]

    The corotational technique is adopted here for the analysis of three-dimensional beams. The technique exploits the technology that applies to a two-noded element, a coordinate system which continuously translates and rotates with the element. In this way, the rigid body motion is separated out from the deformational motion. In this paper, a mixed formulation are adopted for the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissner variational principle to permit elasto-plastic material behavior. The local beam kinematics is based on a low-order nonlinear strain expression using Bernoulli assumption. The present formulation captures both the Saint-Venant and warping torsional effects of thin-walled open cross-sections. Shape functions that satisfy the nonlinear local equilibrium equations are selected for the interpolation of the stress resultants. In particular, for the torsional forces and the twist rotation degree of freedom, a family of hyperbolic interpolation functions is adopted in lieu of conventional polynomials. Governing equations are expressed in a weak form, and the constitutive equations are enforced at each integration cross-section along the element length. A consistent state determination algorithm is proposed. This local element, together with the corotational framework, can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with generic cross-section. The present corotational mixed element solution is compared against the results obtained from a corotational displacement-based model having the same beam kinematics and corotational framework. The superiority of the mixed formulation is clearly demonstrated.

  • 2. Babuska, I.
    et al.
    Nobile, F.
    Tempone, Raul
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, p. 2517-2539Article in journal (Refereed)
    Abstract [en]

    This work describes a solution to the validation challenge problem posed at the SANDIA Validation Challenge Workshop, May 21-23, 2006, NM. It presents and applies a general methodology to it. The solution entails several standard steps, namely selecting and fitting several models to the available prior information and then sequentially rejecting those which do not perform satisfactorily in the validation and accreditation experiments. The rejection procedures are based on Bayesian updates, where the prior density is related to the current candidate model and the posterior density is obtained by conditioning on the validation and accreditation experiments. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.

  • 3. Babuska, I.
    et al.
    Nobile, F.
    Tempone, Raul
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Formulation of the static frame problem2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, p. 2496-2499Article in journal (Refereed)
    Abstract [en]

    This report describes a static framework validation challenge problem used in the SANDIA Validation Challenge Workshop, May 21-23, 2006. The challenge problem has clear engineering character, is simple to state and allows many different approaches to solve it. The regulatory assessment problem is to estimate the probability of a given vertical displacement to exceed a prescribed threshold.

  • 4. Babuska, I.
    et al.
    Tempone, Raul
    Zouraris, G. E.
    Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 16-dec, p. 1251-1294Article in journal (Refereed)
    Abstract [en]

    This work studies a linear elliptic problem with uncertainty. The introduction gives a survey of different formulations of the uncertainty and resulting numerical approximations. The major emphasis of this work is the probabilistic treatment of uncertainty, addressing the problem of solving linear elliptic boundary value problems with stochastic coefficients. If the stochastic coefficients are known functions of a random vector, then the stochastic elliptic boundary value problem is turned into a parametric deterministic one with solution u(y, x), y is an element of Gamma, x is an element of D, where D subset of R-d, d = 1, 2, 3, and Gamma is a high-dimensional cube. In addition, the function u is specified as the solution of a deterministic variational problem over Gamma x D. A tensor product finite element method, of h-version in D and k-, or, p-version in Gamma, is proposed for the approximation of it. A priori error estimates are given and an adaptive algorithm is also proposed. Due to the high dimension of Gamma, the Monte Carlo finite element method is also studied here. This work compares the asymptotic complexity of the numerical methods, and shows results from numerical experiments. Comments on the uncertainty in the probabilistic characterization of the coefficients in the stochastic formulation are included.

  • 5. Balzani, Daniel
    et al.
    Brinkhues, Sarah
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Constitutive framework for the modeling of damage in collagenous soft tissues with application to arterial walls2012In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 213, p. 139-151Article in journal (Refereed)
    Abstract [en]

    In this paper a new material model is proposed for the description of stress-softening observed in cyclic tension tests of collagenous soft tissues such as arterial walls, for applied loads beyond the physiological level. The modeling framework makes use of terms known from continuum damage mechanics and the concept of internal variables introducing a scalar-valued variable for the representation of fiber damage. A principle is given for the construction of damage models able to reflect remanent strains as a result of microscopic damage in the reinforcing collagen fiber families. Particular internal variables are defined able to capture the nature of arterial tissues that no damage occurs in the physiological loading domain. By application of this principle, specific models are derived and fitted to experimental data. Finally, their applicability in numerical simulations is shown by some representative examples where the damage distribution in arterial cross-sections is analyzed.

  • 6.
    Battini, Jean-Marc
    KTH, School of Engineering Sciences (SCI), Mechanics.
    A modified corotational framework for triangular shell elements2007In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 196, no 13-16, p. 1905-1914Article in journal (Refereed)
    Abstract [en]

    The corotational framework for triangular shell elements has been presented by different authors (see the Introduction). The purpose of this paper is to introduce three modifications in this approach. The first one is a simplified definition of the local rotations. The second one is a reduction of the number of local degrees of freedom from 18 to 15. The third and principal one concerns the parameterisation of the global finite rotations. A new approach based on Euler parameters (quaternion) is proposed. In particular, it is shown that only three parameters are required. The purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one. This aspect is illustrated in several numerical examples.

  • 7.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Co-rotational beam elements with warping effects in instability problems2002In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 17-18, p. 1755-1789Article in journal (Refereed)
    Abstract [en]

    The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and it is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed, This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements.

  • 8.
    Battini, Jean-Marc
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Pacoste, Costin
    On the choice of the linear element for corotational triangular shells2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 44-47, p. 6362-6377Article in journal (Refereed)
    Abstract [en]

    The corotational formulation for triangular thin shell elements presented in [A. Eriksson, C. Pacoste, Element formulation and numerical techniques for stability problems in shells, Comput. Methods Appl. Mech. Engrg. 191 (2002) 3775-3810] is further developed in order to incorporate elasto-plastic deformations. Several local formulations are implemented and tested. These local elements are geometrically linear and are obtained by the by superposition of a membrane and a plate part. Eleven elastic and elasto-plastic examples are presented. Both the incremental and deformation theories of plasticity are considered. The first objective is to assess the performance of the present formulation in modelling elasto-plastic instability problems. The second objective is to compare the different linear local formulations: it is shown that some of them give better results in instability problems.

  • 9.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Civil and Architectural Engineering.
    Plastic instability of beam structures using co-rotational elements2002In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 51-52, p. 5811-5831Article in journal (Refereed)
    Abstract [en]

    In a previous paper [Comput. Methods Appl. Mech. Engrg. 191 (2002) 1755], the authors have presented a 3D co-rotational elastic beam element including warping effects. This formulation is now further developed in order to incorporate elasto-plastic deformations. The element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross-sections. Thus, within the present approach, the centroid and shear center of the cross-section are not necessarily coincident. The main purpose of this element is to model elasto-plastic instability problems. In this context, two methods of branch-switching are tested and discussed. In the first one, the bifurcation point is isolated by successive bisections and the branch-switching is operated by using the eigenvector associated to the negative eigenvalue. In the second one, introduced by Petryk, an energy approach is used to select automatically the stable post-bifurcation path. Six examples, including large displacement and stability problems, are used in order to assess the performances of the element.

  • 10.
    Battini, Jean-Marc
    et al.
    KTH, Superseded Departments, Structural Engineering.
    Pacoste, Costin
    KTH, Superseded Departments, Structural Engineering.
    Eriksson, Anders
    KTH, Superseded Departments, Structural Engineering.
    Improved minimal augmentation procedure for the direct computation of critical points2003In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 16-18, p. 2169-2185Article in journal (Refereed)
    Abstract [en]

    This paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations. Compared to the approach described by Wriggers et al. [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 1551, two main modifications are introduced. First, following Eriksson [Comput. Methods Appl. Mech. Engrg. 114 (1994) 77; Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynam. l(l) (2001)], the condition of criticality is expressed by a scalar equation instead of a vectorial one. Next, the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition, but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control, Eight numerical examples, presenting bifurcation and limit points, are used in order to compare the performances of this new method and the one presented in [Comput. Methods Appl. Mech. Engrg. 70 (1988) 329; Int. J. Numer. Methods Engrg. 30 (1990) 155].

  • 11. Burman, E.
    et al.
    Hansbo, P.
    Larson, M. G.
    Massing, A.
    Zahedi, Sara
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Full gradient stabilized cut finite element methods for surface partial differential equations2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 310, p. 278-296Article in journal (Refereed)
    Abstract [en]

    We propose and analyze a new stabilized cut finite element method for the Laplace–Beltrami operator on a closed surface. The new stabilization term provides control of the full R3 gradient on the active mesh consisting of the elements that intersect the surface. Compared to face stabilization, based on controlling the jumps in the normal gradient across faces between elements in the active mesh, the full gradient stabilization is easier to implement and does not significantly increase the number of nonzero elements in the mass and stiffness matrices. The full gradient stabilization term may be combined with a variational formulation of the Laplace–Beltrami operator based on tangential or full gradients and we present a simple and unified analysis that covers both cases. The full gradient stabilization term gives rise to a consistency error which, however, is of optimal order for piecewise linear elements, and we obtain optimal order a priori error estimates in the energy and L2 norms as well as an optimal bound of the condition number. Finally, we present detailed numerical examples where we in particular study the sensitivity of the condition number and error on the stabilization parameter.

  • 12. Deckers, Elke
    et al.
    Hörlin, Nils-Erik
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Numerical acoustics.
    Vandepitte, Dirk
    Desmet, Wim
    A Wave Based Method for the efficient solution of the 2D poroelastic Biot equations2012In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 201, p. 245-262Article in journal (Refereed)
    Abstract [en]

    The vibro-acoustic behaviour of poroelastic materials is often formulated as boundary value problems based on the continuum mechanics Blot's theory expressed as two coupled partial differential equations. This paper presents an extension of the Wave Based Method (WBM), a numerical technique to solve these vibro-acoustic boundary value problems in a computationally efficient manner. At present, the Finite Element Method (FEM) is the most commonly used prediction technique to deal with these Biot equations, but suffers from the disadvantage that the system matrices have to be recalculated for each frequency of interest due to the frequency-dependent equation parameters. This harms the inherent effectiveness of the FEM. Additionally, due to the discretisation into a large number of small finite elements and the high number of unknowns per node, the computational efforts involved practically restrict the use of FEM to low-frequency applications. The method discussed in this paper is based on an indirect Trefftz approach. Exact solutions of the three coupled waves, supported by Biot's equations, are used as basis functions in a solution expansion to approximate the field variables in a poroelastic boundary value problem. This approach leads to smaller systems of equations, enabling an efficient solution at higher frequencies.

  • 13.
    Engquist, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Kreiss, H.O.
    Difference and finite element methods for hyperbolic differential equations1979In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 17-18, no 3, p. 581-596Article in journal (Refereed)
    Abstract [en]

    In recent years finite element methods have started to be applied to hyperbolic equations. Since modern finite element and finite difference methods for hyperbolic equations look very much alike, new results in the analysis of difference methods are also applicable to element methods. We shall discuss propagation of sharp signals, problems with different time scales and the effect of boundaries on stability and accuracy.

  • 14. Engwer, C.
    et al.
    Henning, Patrick
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Målqvist, A.
    Peterseim, D.
    Efficient implementation of the localized orthogonal decomposition method2019In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 350, p. 123-153Article in journal (Refereed)
    Abstract [en]

    In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of inseparable scales. We show how the method can be implemented in a fairly standard Finite Element framework and discuss its realization for different types of problems, such as linear elliptic problems with rough coefficients and linear eigenvalue problems.

  • 15. Eriksson, A.
    Equilibrium subsets for multi-parametric structural analysis1997In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 140, no 3-4, p. 305-327Article in journal (Refereed)
    Abstract [en]

    The paper discusses multi-parametric formulations for structural equilibrium problems. By seeking subsets of equilibrium states, which also fulfil extra conditions, more detailed information on structural behaviour can be obtained. These conditions can be related to analyses of, e.g. critical behaviour, imperfections or optimisation. The paper shows a general problem setting and some interesting augmentations. A solution method for the special case of one-dimensional equilibrium subsets is described. The algorithm is a generalisation of a path-following algorithm, where new methods are developed for the evaluation of the path tangent, and for the isolation of special solution points. Examples are used to show the properties and the possibilities of the ideas.

  • 16. Eriksson, A.
    Equilibrium subsets for multi-parametric structural analysis1997In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 140, no 3-4, p. 305-327Article in journal (Refereed)
    Abstract [en]

    The paper discusses multi-parametric formulations for structural equilibrium problems. By seeking subsets of equilibrium states, which also fulfil extra conditions, more detailed information on structural behaviour can be obtained. These conditions can be related to analyses of, e.g. critical behaviour, imperfections or optimisation. The paper shows a general problem setting and some interesting augmentations. A solution method for the special case of one-dimensional equilibrium subsets is described. The algorithm is a generalisation of a path-following algorithm, where new methods are developed for the evaluation of the path tangent, and for the isolation of special solution points. Examples are used to show the properties and the possibilities of the ideas.

  • 17. Eriksson, A.
    Fold lines for sensitivity analyses in structural instability1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 114, no 1-2, p. 77-101Article in journal (Refereed)
    Abstract [en]

    The paper describes how a two-parameter formulation of a structural equilibrium problem can be used for a more accurate description of the occurring critical states. A fold line concept is used to evaluate the dependence of these states on an added variable, describing a disturbing load case or a disturbed geometry. The concept describes the local behaviour for small disturbances, but can also be used for parameter dependence analyses, e.g. in connection with optimization algorithms. Two different augmentations of the equilibrium relations are discussed; they describe the criticality of a solution state in different ways. Numerical adoption for a general equilibrium path following algorithm is discussed. A postponed factorization method for solution of the augmented sets of equations is proposed. Two simple examples are used to show the properties and the possibilities of the fold line concept. It is concluded that the suggested numerical procedure can give a better description of critical structural behaviour, especially with respect to imperfections in the structure and idealizations in the model. © 1994.

  • 18. Eriksson, A.
    Fold lines for sensitivity analyses in structural instability1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 114, no 1-2, p. 77-101Article in journal (Refereed)
    Abstract [en]

    The paper describes how a two-parameter formulation of a structural equilibrium problem can be used for a more accurate description of the occurring critical states. A fold line concept is used to evaluate the dependence of these states on an added variable, describing a disturbing load case or a disturbed geometry. The concept describes the local behaviour for small disturbances, but can also be used for parameter dependence analyses, e.g. in connection with optimization algorithms. Two different augmentations of the equilibrium relations are discussed; they describe the criticality of a solution state in different ways. Numerical adoption for a general equilibrium path following algorithm is discussed. A postponed factorization method for solution of the augmented sets of equations is proposed. Two simple examples are used to show the properties and the possibilities of the fold line concept. It is concluded that the suggested numerical procedure can give a better description of critical structural behaviour, especially with respect to imperfections in the structure and idealizations in the model. © 1994.

  • 19. Eriksson, A.
    Structural instability analyses based on generalised path-following1998In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 156, no 1-4, p. 45-74Article in journal (Refereed)
    Abstract [en]

    This paper describes how quasi-static, conservative instability problems can be completely described, using generalised path-following procedures for augmented equilibrium formulations. In particular, methods for treatment of compound critical states are discussed. The numerical methods are seen as extensions to common equilibrium path methods, allowing the solution of subsets of equilibrium states, also fulfilling auxiliary relations, e.g. criticality. These formulations are in general used to describe the parameter dependence in structural response, in instability analyses and in optimisation. The paper describes the general setting of these generalised equilibrium problems, and discusses some details in their numerical treatment. Emphasis is given to the evaluation of path tangent vectors, in the presence of critical eigenvectors for the structural tangential stiffness matrix. Also, the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, is discussed. Numerical examples are used to show the possibilities and properties of the obtained solution paths, together with some aspects of the numerical procedures.

  • 20. Eriksson, A.
    et al.
    Pacoste, C.
    Zdunek, A.
    Numerical analysis of complex instability behaviour using incremental-iterative strategies1999In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 179, no 3-4, p. 265-305Article in journal (Refereed)
    Abstract [en]

    The paper describes how quasi-static, conservative instability problems can be analysed in a multi-parametric space, using generalised path-following procedures for augmented equilibrium problems. The general formulation of such augmented equilibrium problems is discussed in some detail. The focus is set on two classes of generalised 1D paths: basic equilibrium paths and fold lines, i.e. critical subset paths. The solution methods are seen as extensions to common incremental-iterative strategies, allowing the computation of subsets of equilibrium states which also fulfil some auxiliary conditions, e.g. criticality. In this context, some emphasis is also given to the evaluation of the properties of the problem, at a certain state; the tangential stiffness is here used to evaluate - possibly multidimensional - tangent spaces, and in the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, being important aspects of instability analyses. A set of carefully chosen numerical examples demonstrate on one hand the ability of the numerical procedures to deal with complex instability phenomena, including coincident or near coincident buckling modes, modal interaction, secondary bifurcations, and, on the other hand, their versatility in performing parameter sensitivity analyses. Finally, comparisons with alternative techniques, based on asymptotic strategies, are also put forth.

  • 21.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Fold lines for sensitivity analyses in structural instability1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 114, no 1-2, p. 77-101Article in journal (Refereed)
    Abstract [en]

    The paper describes how a two-parameter formulation of a structural equilibrium problem can be used for a more accurate description of the occurring critical states. A fold line concept is used to evaluate the dependence of these states on an added variable, describing a disturbing load case or a disturbed geometry. The concept describes the local behaviour for small disturbances, but can also be used for parameter dependence analyses, e.g. in connection with optimization algorithms. Two different augmentations of the equilibrium relations are discussed; they describe the criticality of a solution state in different ways. Numerical adoption for a general equilibrium path following algorithm is discussed. A postponed factorization method for solution of the augmented sets of equations is proposed. Two simple examples are used to show the properties and the possibilities of the fold line concept. It is concluded that the suggested numerical procedure can give a better description of critical structural behaviour, especially with respect to imperfections in the structure and idealizations in the model. © 1994.

  • 22.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimization in target movement simulations2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 49-50, p. 4207-4215Article in journal (Refereed)
    Abstract [en]

    This paper discusses a methodology for fixed-time simulations of optimal movements of a mechanical system, between specified initial and target configurations, without any a priori knowledge on the trajectory between those. It is primarily aimed at human movement simulations with muscular controls. The basic formulation considers both displacements and forces as unknowns during the movement, connects them, and utilizes a finite element time discretization for solving the whole fixed-time interval simultaneously. Through a consistent interpolation of all kinetic and kinematic variables, the formulation becomes general, needing only minimal input for description of a particular problem, but also eliminating errors inherent in many forms of time-integration. The same consistency allows systematic formulations of a large class of optimization cost functions, primarily focussing on the mechanical behavior of the system rather than on the matching of previously measured movements. It thereby allows the use of robust and efficient general optimization algorithms. Kinetic and kinematic constraints can restrict the movement. As an example of the general setting, a simplified human movement is studied, with different choices of controls (joint moments or muscular tensions), and with different optimization criteria. The example shows that the simulation results are strongly dependent on these choices, in particular that smoothness of movement demands forces considerably higher than the strictly minimum ones. A larger example shows that more complex constraints can be handled within the setting proposed, but also the effects from the fixed-time assumption.

  • 23.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Structural instability analyses based on generalised path-following1998In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 156, no 1-4, p. 45-74Article in journal (Refereed)
    Abstract [en]

    This paper describes how quasi-static, conservative instability problems can be completely described, using generalised path-following procedures for augmented equilibrium formulations. In particular, methods for treatment of compound critical states are discussed. The numerical methods are seen as extensions to common equilibrium path methods, allowing the solution of subsets of equilibrium states, also fulfilling auxiliary relations, e.g. criticality. These formulations are in general used to describe the parameter dependence in structural response, in instability analyses and in optimisation. The paper describes the general setting of these generalised equilibrium problems, and discusses some details in their numerical treatment. Emphasis is given to the evaluation of path tangent vectors, in the presence of critical eigenvectors for the structural tangential stiffness matrix. Also, the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, is discussed. Numerical examples are used to show the possibilities and properties of the obtained solution paths, together with some aspects of the numerical procedures.

  • 24.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Instability of hyper-elastic balloon-shaped space membranes under pressure loads2012In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 237, p. 118-129Article in journal (Refereed)
    Abstract [en]

    This paper discusses the evaluation of quasi-static equilibrium solutions for inflatable space membrane structures. A Mooney-Rivlin hyper-elastic material model, with variable constitutive constants, is considered. A compressible weightless medium is used to introduce within the membrane a one-parametric over-pressure loading compared to an ambient pressure. Analytical instability results are shown for a spherical and derived for a cylindrical case. These are compared to numerical simulations based on a flat linearly interpolated triangular space membrane element. Path-following procedures are used to find generalized equilibrium paths, with different parameterizations. Numerical examples show that the methods developed can give information on the stability of the membranes, but that the medium and means for introducing the internal pressure are of importance for the interpretation of stability.

  • 25.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Temporal finite element formulation of optimal control in mechanisms2010In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 199, no 25-28, p. 1783-1792Article in journal (Refereed)
    Abstract [en]

    A temporal finite element discretization of a boundary value problem has several advantages compared to a time-integrating evolution form for optimized target movement simulations. The paper gives some basic aspects on how such a finite element form can be stated, with both displacements and controls discretized and seen as unknowns. Aspects on the resulting formulations are discussed. Important issues are the order, continuity and fineness of the discretizations. When the formulation is seen in an optimization context, minimizing the effort for a prescribed movement, the discretization affects the results obtained in several manners, where some aspects of results are artifacts. The paper discusses these effects from basic principles, but also verifies them in numerical simulations.

  • 26.
    Eriksson, Anders
    et al.
    KTH, Superseded Departments, Structural Engineering.
    Pacoste, C.
    Element formulation and numerical techniques for stability problems in shells2002In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 191, no 35, p. 3775-3810Article in journal (Refereed)
    Abstract [en]

    In the context of instability problems in shells or shell like structures, the objective of the present paper is twofold. Primarily, the paper describes how quasi-static, conservative instability problems can be considered in a multi-parametric context, where generalized path-following procedures for augmented equilibrium problems are used as computational tools. These allow systematic treatment of the higher-dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem. The efficient implementation of the above mentioned procedures requires however, as an essential ingredient, a non-linear finite element which is not only accurate but also inexpensive. To this end, a systematic view on a corotational Total Lagrangian formulation is described. The TRIC element of Argyris and coworkers is slightly modified, and introduced as core element formulation. Special emphasis is given to the alternative methods for treatment of finite three-dimensional rotations, with reference to both the element definition and solution algorithms. Numerical examples verify the element capabilities, and the possibility to completely describe instability phenomena of large, discretized models.

  • 27.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Pacoste, C.
    Zdunek, A.
    Numerical analysis of complex instability behaviour using incremental-iterative strategies1999In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 179, no 3-4, p. 265-305Article in journal (Refereed)
    Abstract [en]

    The paper describes how quasi-static, conservative instability problems can be analysed in a multi-parametric space, using generalised path-following procedures for augmented equilibrium problems. The general formulation of such augmented equilibrium problems is discussed in some detail. The focus is set on two classes of generalised 1D paths: basic equilibrium paths and fold lines, i.e. critical subset paths. The solution methods are seen as extensions to common incremental-iterative strategies, allowing the computation of subsets of equilibrium states which also fulfil some auxiliary conditions, e.g. criticality. In this context, some emphasis is also given to the evaluation of the properties of the problem, at a certain state; the tangential stiffness is here used to evaluate - possibly multidimensional - tangent spaces, and in the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, being important aspects of instability analyses. A set of carefully chosen numerical examples demonstrate on one hand the ability of the numerical procedures to deal with complex instability phenomena, including coincident or near coincident buckling modes, modal interaction, secondary bifurcations, and, on the other hand, their versatility in performing parameter sensitivity analyses. Finally, comparisons with alternative techniques, based on asymptotic strategies, are also put forth. © 1999 Elsevier Science S.A.

  • 28.
    Eriksson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Redundant and force-differentiated systems in engineering and nature2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 41-43, p. 5437-5453Article in journal (Refereed)
    Abstract [en]

    Sophisticated load-carrying structures, in nature as well as man-made, share some common properties. A clear differentiation of tension, compression and shear is in nature primarily manifested in the properties of materials adapted to the efforts, whereas they in engineering are distributed on different components. For stability and failure safety, redundancy on different levels is also commonly used. The paper aims at collecting and expanding previous methods for the computational treatment of redundant and force-differentiated systems. A common notation is sought, giving and developing criteria for describing the diverse problems from a common structural mechanical viewpoint. From this, new criteria for the existence of solutions, and a method for treatment of targeted dynamic solutions are developed. Added aspects to previously described examples aim at emphasizing similarities and differences between engineering and nature, in the forms of a tension truss structure and the human musculoskeletal system.

  • 29.
    Gasser, Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Forsell, Caroline
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    The numerical implementation of invariant-based viscoelastic formulations at finite strains. An anisotropic model for the passive myocardium2011In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 200, no 49-52, p. 3637-3645Article in journal (Refereed)
    Abstract [en]

    The present study developed a conceptual framework for finite strain viscoelasticity thought to be suitable to capture the salient features of a class of passive soft biological tissues like the myocardium. A superposition of a Maxwell Body and an Elastic Body defines the viscoelastic continuum, and its deformation is related to two independent reference configurations. The reference configuration of the Maxwell Body moves in space as it is described (apart from rigid body rotation) by a rate equation in strain space, and stores the history of the deformation. At thermodynamic equilibrium the reference configuration of the Maxwell Body coincides with the current configuration of the continuum. The Helmholtz free energy is expressed as a function of two independent strain variables and entirely renders the constitution of the viscoelastic body. Although this view is to some extent different from reported viscoelastic concepts for finite strains, its linearization around the thermodynamic equilibrium coincides with earlier suggested viscoelastic models. The linearized viscoelastic model has been implemented for a particular anisotropic constitutive model for the passive myocardium. Non-negative dissipation of the model is guaranteed. Material parameters were estimated from in vitro testing of porcine myocardium and the response due to pushing a rigid punch into the myocardium was studied. Results between anisotropic and isotropic descriptions of the myocardium differed significantly, which justified the implementation of an anisotropic model for the myocardium.

  • 30.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    3D Crack propagation in unreinforced concrete. A two-step algorithm for tracking 3D crack paths2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 37-40, p. 5198-5219Article in journal (Refereed)
    Abstract [en]

    Tensile failure of unreinforced concrete involves progressive micro-cracking, and the related strain-softening can coalesce into geometrical discontinuities, which separate the material. Advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3D. In this paper we use the concept of strong discontinuities to model concrete failure. We introduce a cohesive fracture process zone, which is characterized by a transversely isotropic traction-separation law. We combine the cohesive crack concept with the partition of unity finite element method, where the finite element space is enhanced by the Heaviside function. The concept is implemented for tetrahedral elements and the failure initialization is based on the simple (non-local) Rankine criterion. For each element we assume the embedded discontinuity to be flat in the reference configuration, which leads to a non-smooth crack surfaces approximation in 3D, in general; different concepts for tracking non-planar cracks in 3D are reviewed. In addition, we propose a two-step algorithm for tracking the crack path, where a predictor step defines discontinuities according to the (non-local) failure criterion and a corrector step draws in non-local information of the existing discontinuities in order to predict a 'closed' 3D crack surface; implementation details are provided. The proposed framework is used to analyze the predictability of concrete failure by two benchmark examples, i.e. the Nooru-Moharned test, and the Brokenshire test. We compare our numerical results, which are mesh independent, with experimental data and numerical results adopted from the literature.

  • 31. Gasser, T. Christian
    et al.
    Holzapfel, Gerhard A.
    Geometrically non-linear and consistently linearized embedded strong discontinuity models for 3D problems with an application to the dissection analysis of soft biological tissues2003In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 47-48, p. 5059-5098Article in journal (Refereed)
    Abstract [en]

    Three different finite element formulations with embedded strong discontinuities are derived on the basis of the enhanced assumed strain method. According to the work by Jirasek and Zimmermann [Int. J. Numer. Methods Engrg. 50 (2001) 1269] they are referred to as statically optimal symmetric (SOS), kinematically optimal symmetric (KOS) and statically and kinematically optimal non-symmetric (SKON) formulations. The effect of the discontinuities are characterized by additional degrees of freedom on the element level. Modifications to the standard KOS and SKON formulations are proposed in order to achieve consistency with the employed type of a three-field Hu-Washizu principle under mode-I condition. Under this condition the formulation satisfies the internal compatibility at the discontinuity, i.e. the relation between the stress in the bulk material and the traction across the discontinuity surface, which is not the case for the classical KOS formulation. We propose a suitable explicit expression for a transversely isotropic traction law in form of a displacement-energy function and assume that softening phenomena in the cohesive zone are modeled by a damage law, which depends on the maximum gap displacement of the deformation path. A linearization of all quantities, which are related to the non-linear problem, leads to new closed form expressions. In particular, we focus attention on the linearization of the cohesive traction vector. The associated element residua and stiffness matrices are provided. Standard static condensation of the internal degree of freedom leads to a generalized displacement model. A comparative study of the modified formulations, carried out by means of two numerical examples, show the performance of the individual approach. We employ constant-strain tetrahedral elements with a single discontinuity embedded. Among the known stress locking phenomena associated with the SOS formulation, we recognized that the (non-symmetric) SKON formulation was not able to provide meaningful results for the dissection process of an arterial layer in three-dimensions on distorted meshes. For both numerical examples the (symmetric) KOS formulation seems to be most suitable for representing the embedded discontinuities.

  • 32. Gasser, T. Christian
    et al.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling 3D crack propagation in unreinforced concrete using PUFEM2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 25-26, p. 2859-2896Article in journal (Refereed)
    Abstract [en]

    Concrete is a quasi-brittle material, where tensile failure involves progressive micro-cracking, debounding and other complex irreversible processes of internal damage. Strain-softening is a dominate feature and advanced numerical schemes have to be applied in order to circumvent the ill-posdness of the Boundary-Value Problem to deal with. Throughout the paper we pursue the cohesive zone approach, where initialization and coalescence of micro-cracks is lumped into the cohesive fracture process zone in terms of accumulation of damage. We develop and employ a (discrete) constitutive description of the cohesive zone, which is based on a transversely isotropic traction separation law. The model reflects an exponential decreasing traction with respect to evolving opening displacement and is based on the theory of invariants. Non-negativeness of the damage dissipation is proven and the associated numerical embedded representation is based on the Partition of Unity Finite Element Method. A consistent linearization of the method is presented, where particular attention is paid to the (cohesive) traction terms. Based on the proposed concept three numerical examples are studied in detail, i.e. a double-notched specimen under tensile loading, a four point shear test and a pull-out test of unreinforced concrete. The computational results show mesh-independency and good correlation with experimental results. © 2004 Elsevier B.V. All rights reserved.

  • 33.
    Gärdsback, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics.
    A Comparison of Rotation-Free Triangular Shell Elements for Unstructured Meshes2007In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 196, no 49-52, p. 5001-5015Article in journal (Refereed)
    Abstract [en]

    Many engineering applications require accurate and rapidly computed thin-shell elements. Rotation-free (RF) shell elements include the bending behaviour of thin shells without introducing any additional degrees of freedom compared to a membrane element. Instead, constant curvatures are approximated from the out-of-plane displacements of a patch of usually four triangular elements. A consequence of this is that the accuracy for irregular meshes has been unsatisfactory. The aim of this study is to find an RF shell element which is accurate also for unstructured meshes. The main difference between existing elements is whether they assume two-dimensional constant curvatures over the patch or use superposition of one-dimensional constant curvatures for the three pairs of triangles. The first assumption fulfils constant curvatures for a Kirchhoff plate exactly, whereas the second and most common assumption only approximates constant curvatures. The first assumption is significantly more resistant to element shape distortions, whereas the second assumption is slightly faster to compute and more appropriate on boundaries where one or more elements are missing or several neighbouring elements share a side. The combination is significantly more accurate for irregular meshes than other comparable RF elements for linear benchmark tests.

  • 34. Hansbo, P
    et al.
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A velocity pressure streamline diffusion finite element method for Navier-Stokes equations1990In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 84, no 2, p. 175-192Article in journal (Refereed)
    Abstract [en]

    A streamline diffusion finite-element method is introduced for the time-dependent incompressible Navier-Stokes equations in a bounded domain in R squared and R cubed in the case of a flow with a high Reynolds number. An error estimate is proved and numerical results are given. The method is based on a mixed velocity-pressure formulation using the same finite-element discretization of space-time for the velocity and the pressure spaces, which consist of piecewise linear functions, together with certain least-squares modifications of the Galerkin variational formulation giving added stability without sacrificing accuracy.

  • 35. Hansbo, Peter
    et al.
    Larson, Mats G.
    Zahedi, Sara
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    A Cut Finite Element Method for Coupled Bulk-Surface Problems on Time-Dependent Domains2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 307, p. 96-116Article in journal (Refereed)
    Abstract [en]

    In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space–time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh. The domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems. In the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set, essentially using the restrictions of the piecewise linear functions to the computational domain. In addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step. We show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh.

  • 36. Hansbo, Peter
    et al.
    Larson, Mats G.
    Zahedi, Sara
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Characteristic cut finite element methods for convection-diffusion problems on time dependent surfaces2015In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 293, p. 431-461Article in journal (Refereed)
    Abstract [en]

    We develop a finite element method for convection-diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant. The method is based on a characteristic-Galerkin formulation combined with a piecewise linear cut finite element method in space. The cut finite element method is constructed by embedding the surface in a background grid and then using the restriction to the surface of a finite element space defined on the background grid. The surface is allowed to cut through the background grid in an arbitrary fashion. To ensure stability and well posedness of the resulting algebraic systems of equations, independent of the position of the surface in the background grid, we add a consistent stabilization term. We prove error estimates and present confirming numerical results. (C) 2015 Elsevier B.V. All rights reserved.

  • 37. Hansbo, Peter
    et al.
    Szepessy, Anders
    A velocity pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations1990In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 84, no 2, p. 175-192Article in journal (Refereed)
  • 38.
    Henning, Patrick
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Persson, A.
    A multiscale method for linear elasticity reducing Poisson locking2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 310, p. 156-171Article in journal (Refereed)
    Abstract [en]

    We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by Målqvist and Peterseim (2014). Assuming only L∞-coefficients we prove linear convergence in the H1-norm, also for materials with large Lamé parameter λ. The theoretical a priori error estimate is confirmed by numerical examples.

  • 39. Hills, Richard G.
    et al.
    Pilch, Martin
    Dowding, Kevin J.
    Redhorse, John
    Paez, Thomas L.
    Babuska, Ivo
    Tempone, Raúl
    Validation Challenge Workshop2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, p. 2375-2380Article in journal (Refereed)
    Abstract [en]

    This special issue presents the results of the Sandia organized Model Validation Challenge Workshop, held May 2006. The workshop brought together researchers from different fields to present various approaches to model validation, and focused on the methodological elements of model validation rather than on model building. Three problems were defined in the disciplines of structural statics, structural dynamics, and heat transfer, all with a uniform structure. The workshop was specifically designed to investigate the relative merits of different approaches to hierarchal model validation through application to these problems. This paper describes a hierarchal approach in the challenge problems, presents the uniform conceptual framework that was used for the challenge problem definitions, and provides an overview of the organization of this special issue.

  • 40.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    De Abreu, Rodrigo Vilela
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation2011In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 200, no 37-40, p. 2758-2767Article in journal (Refereed)
    Abstract [en]

    In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier-Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size.

  • 41.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). Basque Ctr Appl Math, Spain.
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). Basque Ctr Appl Math, Spain.
    Jansson, Niclas
    RIKEN Advanced Institute for Computational Science, Kobe, Japan.
    De Abreu, Rodrigo Vilela
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation2015In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 288, p. 60-74Article in journal (Refereed)
    Abstract [en]

    We present work towards a parameter-free method for turbulent flow simulation based on adaptive finite element approximation of the Navier-Stokes equations at high Reynolds numbers. In this model, viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimised based on solution features, in particular no bounder layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated. 

  • 42.
    Hoffman, Johan
    et al.
    Courant Institute, New York University.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A new approach to computational turbulence modeling2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 23-24, p. 2865-2880Article in journal (Refereed)
    Abstract [en]

    We present a new approach to computational fluid dynamics (CFD) using adaptive stabilized Galerkin finite element methods with duality based a posteriori error control for chosen output quantities of interest. We address the basic question of computability in CFD: For a given flow, what quantity is computable to what tolerance to what cost? We focus on incompressible Newtonian flow with medium to large Reynolds numbers involving both laminar and turbulent flow features. We estimate a posteriori the output of the computed solution with the output based on the exact solution to the Navier–Stokes equations, thus circumventing introducing and modeling Reynolds stresses in averaged Navier–Stokes equations. Our basic tool is a representation formula for the error in the quantity of interest in terms of a space–time integral of the residual of a computed solution multiplied by weights related to derivatives of the solution of an associated dual problem with data connected to the output. We use the error representation formula to derive an a posteriori error estimate combining residuals with computed dual weights, which is used for mesh adaptivity in space–time with the objective of satisfying a given error tolerance with minimal computational effort. We show in a concrete example that outputs such as a mean value in time of drag of a turbulent flow around a bluff body are computable on a PC with a tolerance of a few percent using a few hundred thousand mesh points in space. We refer to our methodology as adaptive DNS/LES, where automatically by adaptivity certain features of the flow are resolved in a direct numerical simulation (DNS), while certain other small scale turbulent features are left unresolved in a large eddy simulation (LES). The stabilization of the Galerkin method giving a weighted least square control of the residual acts as the subgrid model in the LES. The a posteriori error estimate takes into account both the error from discretization and the error from the subgrid model. We pay particular attention to the stability of the dual solution from (i) perturbations replacing the exact convection velocity by a computed velocity, and (ii) computational solution of the dual problem, which are the crucial aspects entering by avoiding using averaged Navier–Stokes equations including Reynolds stresses. A crucial observation is that the contribution from subgrid modeling in the a posteriori error estimation is small, making it possible to simulate aspects of turbulent flow without accurate modeling of Reynolds stresses.

  • 43.
    Hoffman, Johan
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Johnson, Claes
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Stability of the dual Navier-Stokes equations and efficient computation of mean output in turbulent flow using adaptive DNS/LES2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 13-16, p. 1709-1721Article in journal (Refereed)
    Abstract [en]

    We discuss aspects of adaptive DNS/LES, where adaptive finite element methods are used to accurately compute chosen output from a turbulent flow with the computational power of a PC. The key to this break-through is: (i) application of the general approach to adaptive error control in Galerkin methods based on duality.. coupled with (ii) crucial properties of turbulent flow allowing accurate computation of mean value quantities such as drag and lift without full resolution of all scales.

  • 44.
    Hoffman, Johan
    et al.
    Mathematics, Chalmers.
    Johnson, Claes
    Bertoluzza, S.
    Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar Multiresolution analysis2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 1, p. 19-44Article in journal (Refereed)
    Abstract [en]

    In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.

  • 45. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications2001In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 190, no 34, p. 4379-4403Article in journal (Refereed)
    Abstract [en]

    This paper presents a viscoelastic model for the fully three-dimensional stress and deformation response of fiber-reinforced composites that experience finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical properties of the composites depend on two fiber directions. The relaxation and/or creep response of each compound of the composite is modeled separately and the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tenser (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite strains with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting 'stretch inversion phenomenon' in the low pressure domain. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response with satisfying accuracy. A third numerical example is designed to illustrate the anisotropic stretching process of a fiber-reinforced rubber bar and the subsequent relaxation behavior at finite strains. The material parameters are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state.

  • 46. Johan, Zdenek
    et al.
    Hughes, Tom
    Mathur, Kapil K
    Johnsson, Lennart
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    A Data Parallel Finite Element Method for Computational Fluid Dynamics on the Connection Machine Systems1992In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 99, no 1, p. 113-134Article in journal (Refereed)
    Abstract [en]

     A finite element method for computational fluid dynamics has been implemented on the Connection Machine systems CM-2 and CM-200. An implicit iterative solution strategy, based on the pre-conditioned matrix-free GMRES algorithm, is employed. Parallel data structures built on both nodal and elemental sets are used to achieve maximum parallelization. Communication primitives provided through the Connection Machine Scientific Software Library substantially improved the overall performance of the program. Computations of three-dimensional compressible flows using unstructured meshes having close to one million elements, such as a complete airplane, demonstrate that the Connection Machine systems are suitable for these applications. Performance comparisons are also carried out with the vector computers Cray Y-MP and Convex C-1.

  • 47. Johan, Zdenek
    et al.
    Mathul, Kapil K
    Johnsson, Lennart
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Hughes, Thomas J.R.
    Scalability of Finite Element Applications on Distributed–Memory Parallel Computers1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 119, no 1-2, p. 61-72Article in journal (Refereed)
    Abstract [en]

    This paper demonstrates that scalability and competitive efficiency can be achieved for unstructured grid finite element applications on distributed memory machines, such as the Connection Machine CM-5 system. The efficiency of finite element solvers is analyzed through two applications: an implicit computational aerodynamics application and an explicit solid mechanics application. Scalability of mesh decomposition and of data mapping strategies is also discussed. Numerical examples that support the claims for problems with an excess of fourteen million variables are presented.

  • 48. Johan, Zdenek
    et al.
    Mathur, Kapil K
    Johnsson, Lennart
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Hughes, Tomas J.R.
    An Efficient Communication Strategy for Finite Element Methods on the Connection Machine CM-5 System1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 113, no 3-4, p. 363-387Article in journal (Refereed)
    Abstract [en]

    The objective of this paper is to propose communication procedures suitable for unstructured finite element solvers implemented on distributed-memory parallel computers such as the Connection Machine CM-5 system. First, a data-parallel implementation of the recursive spectral bisection (RSB) algorithm proposed by Pothen et al. is presented. The RSB algorithm is associated with a node renumbering scheme which improves data locality of reference. Two-step gather and scatter operations taking advantage of this data locality are then designed. These communication primitives make use of the indirect addressing capability of the CM-5 vector units to achieve high gather and scatter bandwidths. The performance of the proposed communication strategy is illustrated on large-scale three-dimensional fluid dynamics problems

  • 49.
    Kroon, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Elastic properties of anisotropic vascular membranes examined by inverse analysis2009In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 198, no 45-46, p. 3622-3632Article in journal (Refereed)
    Abstract [en]

    An inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic vascular membranes such as cerebral aneurysms is proposed. The material description of the membrane is based on a versatile structural model able to represent multiple collagen layers and the passive response of the vascular wall. Each individual layer is assumed to behave transversely isotropic following exponential stiffening with increasing loading. The model includes four parameters to be explainable physically: two initial stiffnesses of the collagen fabric, a parameter related to the nonlinearity of the collagen fabric, angle between the principal directions of the collagen fabric and a reference coordinate system. For this finite deformation problem a finite element framework for membranous structures considering pressure boundary loading is outlined. i.e. the principle of virtual work, its linearisation and the related spatial discretisation. The estimation procedure consists of the following three steps: (i) in vivo or in vitro approaches record the mechanical responses of membranous structures whose properties are to be determined; (ii) define a corresponding finite element model; (iii) minimise an error function (regarding the unknown parameters) that quantifies the deviation of the numerical prediction from the recorded data. To achieve a robust parameter estimation, an element partition method is employed. The outcome of the procedure is affected by the number of nodes defined on the membrane surface and the number of load steps. In a numerical example, the proposed procedure is assessed by reestablishing given reference distributions in a reference membrane. The deviations of the estimated material parameter distributions from the related reference fields are within just a few percent. In most of the investigated cases the standard deviation for the resulting maximum principal stress was even below 1%, which is accurate enough for rupture risk assessment of vascular membranes.

  • 50.
    Le, Thanh Nam
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures2014In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 269, p. 538-565Article in journal (Refereed)
    Abstract [en]

    The purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3D flexible frames. The novelty of the formulation lies in the use of the corotational framework (i.e., the decomposition into rigid body motion and pure deformation) to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. As a consequence, cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. To enhance the efficiency of the iterative procedure, an approximate expression of the tangent dynamic matrix is adopted. Four numerical examples are considered to assess the performance of the new formulation against the one suggested by Simo and Vu-Quoc (1988) [48]. It was observed that the proposed formulation proves to combine accuracy with efficiency. In particular, the present approach achieves the same level of accuracy as the formulation of Simo and Vu-Quoc but with a significantly smaller number of elements.

12 1 - 50 of 62
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