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Multiplier Method (multiplier + method)

Distribution by Scientific Domains
Engineering88%

Kinds of Multiplier Method

  • lagrange multiplier method
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    Selected Abstracts

    Solution to shape identification problem of unsteady heat-conduction fields

    HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2003
    Eiji Katamine
    Abstract This paper presents a numerical analysis method for shape determination problems of unsteady heat-conduction fields in which time histories of temperature distributions on prescribed subboundaries or time histories of gradient distributions of temperature in prescribed subdomains have prescribed distributions. The square error integrals between the actual distributions and the prescribed distributions on the prescribed subboundaries or in the prescribed subdomains during the specified period of time are used as objective functionals. Reshaping is accomplished by the traction method that was proposed as a solution to shape optimization problems of domains in which boundary value problems are defined. The shape gradient functions of these shape determination problems are derived theoretically using the Lagrange multiplier method and the formulation of material derivative. The time histories of temperature distributions are evaluated using the finite-element method for a space integral and the Crank,Nicolson method for a time integral. Numerical analyses of nozzle and coolant flow passage in a wing are demonstrated to confirm the validity of this method. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 212,226, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10086 [source]

    Modelling of contaminant transport through landfill liners using EFGM

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010
    R. Praveen Kumar
    Abstract Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection-dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Simulation of special loading conditions by means of non-linear constraints imposed through Lagrange multipliers

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002
    M. A. Gutiérrez
    Abstract This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton,Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A modified node-to-segment algorithm passing the contact patch test

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
    Giorgio Zavarise
    Abstract Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Essential boundary condition enforcement in meshless methods: boundary flux collocation method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002
    Cheng-Kong C. Wu
    Abstract Element-free Galerkin (EFG) methods are based on a moving least-squares (MLS) approximation, which has the property that shape functions do not satisfy the Kronecker delta function at nodal locations, and for this reason imposition of essential boundary conditions is difficult. In this paper, the relationship between corrected collocation and Lagrange multiplier method is revealed, and a new strategy that is accurate and very simple for enforcement of essential boundary conditions is presented. The accuracy and implementation of this new technique is illustrated for one-dimensional elasticity and two-dimensional potential field problems. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Optimal flow control for Navier,Stokes equations: drag minimization

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007
    L. Dedè
    Abstract Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier,Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier,Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Robust force control of a flexible arm with a nonsymmetric rigid tip body

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 5 2001
    Yoshifumi Morita
    In this article, we discuss modeling and robust control of bending and torsional vibrations and contact force of a flexible arm with a nonsymmetric rigid tip body. By using Hamilton's principle and the Lagrange multiplier method, dynamic equations of the constrained flexible arm are derived. Since the flexible arm has the nonsymmetric tip body, the bending and torsional vibrations are coupled. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. By using the eigenvalues and the correpsonding eigenfunctions related to the distributed parameter system, we derive a finite-dimensional modal model. To compensate for the spillover instability, we construct robust controllers of an optimal controller with a low-pass property and an H, controller. Some experiments have been carried out to show the effectiveness of the proposed robust controllers. © 2001 John Wiley & Sons, Inc. [source]

    General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2009
    Aissa Guesmia
    Abstract In this paper we consider the following Timoshenko system: with Dirichlet boundary conditions and initial data where a, b, g and h are specific functions and ,1, ,2, k1, k2 and L are given positive constants. We establish a general stability estimate using the multiplier method and some properties of convex functions. Without imposing any growth condition on h at the origin, we show that the energy of the system is bounded above by a quantity, depending on g and h, which tends to zero as time goes to infinity. Our estimate allows us to consider a large class of functions h with general growth at the origin. We use some examples (known in the case of wave equations and Maxwell system) to show how to derive from our general estimate the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize some existing results in the literature and generate some interesting open problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    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]