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Set Strategy (set + strategy)

Distribution by Scientific Domains
Engineering83%

Kinds of Set Strategy

  • active set strategy
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    Selected Abstracts

    An augmented Lagrange multiplier approach to continuum multislip single crystal thermo,elasto,viscoplasticity

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2005
    C. C. Celigoj
    Abstract The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of ,generalized standard materials (gsm)' is used to set up the equations for finite deformation multislip single crystal thermo,elasto,viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an ,augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust ,active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)/p0(pressure)/j0(jacobian)-finite elements and in an isogeometric thermal phase via q1(temperatures)-finite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0/45/30 in Euler angles) fcc-crystals under tension and plane strain conditions are given. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    A dual mortar approach for 3D finite deformation contact with consistent linearization

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010
    Alexander Popp
    Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    An online active set strategy to overcome the limitations of explicit MPC

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2008
    H. J. Ferreau
    Abstract Nearly all algorithms for linear model predictive control (MPC) either rely on the solution of convex quadratic programs (QPs) in real time, or on an explicit precalculation of this solution for all possible problem instances. In this paper, we present an online active set strategy for the fast solution of parametric QPs arising in MPC. This strategy exploits solution information of the previous QP under the assumption that the active set does not change much from one QP to the next. Furthermore, we present a modification where the CPU time is limited in order to make it suitable for strict real-time applications. Its performance is demonstrated with a challenging test example comprising 240 variables and 1191 inequalities, which depends on 57 parameters and is prohibitive for explicit MPC approaches. In this example, our strategy allows CPU times of well below 100 ms per QP and was about one order of magnitude faster than a standard active set QP solver. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Similarities and differences between the concepts of operability and flexibility: The steady-state case

    AICHE JOURNAL, Issue 3 2010
    Fernando V. Lima
    Abstract This article presents a comparative review on the operability and flexibility concepts and their application to process design and control. First, the operability and flexibility methodologies are summarized. Then the application of the operability framework to steady-state and dynamic systems is illustrated through the examination of several example categories such as linear and nonlinear, square and non-square systems. The flexibility approach based on the active set strategy is used to study the same examples from the flexibility point of view. The discussed results show that the operability and flexibility approaches examine a process from different perspectives and provide valuable complementary information. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

    Non-linear dynamic contact of thin-walled structures

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
    Thomas Cichosz
    In many areas of mechanical engineering contact problems of thin,walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment,rotation characteristics of a bolted beam,column joint, contact occurs. Effective simulation of these and other contact problems, especially in three,dimensional non,linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin,walled character and dynamic effects into account. We use a segment,to,segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized-, Method and the Generalized Energy,Momentum Method. Using the "Velocity,Update" Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]