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Lagrangian Method (lagrangian + method)

Distribution by Scientific Domains
Engineering83%

Selected Abstracts

An operator-split ALE model for large deformation analysis of geomaterials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2007
Y. Di
Abstract Analysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian,Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid,fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Augmented Lagrangian coordination for distributed optimal design in MDO

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2008
S. Tosserams
Abstract Quite a number of coordination methods have been proposed for the distributed optimal design of large-scale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for so-called quasi-separable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper, we present a new coordination approach for multidisciplinary design optimization problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented, offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush,Kuhn,Tucker points of the original problem by using the existing convergence results. We illustrate the flexibility of the proposed approach by showing that the analytical target cascading method of Kim et al. (J. Mech. Design-ASME 2003; 125(3):475,480) and the augmented Lagrangian method for quasi-separable problems of Tosserams et al. (Struct. Multidisciplinary Opt. 2007, to appear) are subclasses of the proposed formulations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Simulation of high velocity concrete fragmentation using SPH/MLSPH

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003
T. Rabczuk
Abstract The simulation of concrete fragmentation under explosive loading by a meshfree Lagrangian method, the smooth particle hydrodynamics method (SPH) is described. Two improvements regarding the completeness of the SPH-method are examined, first a normalization developed by Johnson and Beissel (NSPH) and second a moving least square (MLS) approach as modified by Scheffer (MLSPH). The SPH-Code is implemented in FORTRAN 90 and parallelized with MPI. A macroscopic constitutive law with isotropic damage for fracture and fragmentation for concrete is implemented in the SPH-Code. It is shown that the SPH-method is able to simulate the fracture and fragmentation of concrete slabs under contact detonation. The numerical results from the different SPH-methods are compared with the data from tests. The good agreement between calculation and experiment suggests that the SPH-program can predict the correct maximum pressure as well as the damage of the concrete slabs. Finally the fragment distributions of the tests and the numerical calculations are compared. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Fixed-order H, control design via a partially augmented Lagrangian method

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003
Pierre Apkarian
Abstract In this paper we develop an augmented Lagrangian method to determine local optimal solutions of the reduced- and fixed-order H, synthesis problems. We cast these synthesis problems as optimization programs with a linear cost subject to linear matrix inequality (LMI) constraints along with nonlinear equality constraints representing a matrix inversion condition. The special feature of our algorithm is that only equality constraints are included in the augmented Lagrangian, while LMI constraints are kept explicitly in order to exploit currently available semi definite programming (SDP) codes. The step computation in the tangent problem is based on a Gauss,Newton model, and a specific line search and a first-order Lagrange multiplier update rule are used to enhance efficiency. A number of computational results are reported and underline the strong practical performance of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Computational Simulation of the Blood Separation Process

ARTIFICIAL ORGANS, Issue 8 2005
Sandro De Gruttola
Abstract:, The aim of this work is to construct a computational fluid dynamics model capable of simulating the quasitransient process of apheresis. To this end a Lagrangian,Eulerian model has been developed which tracks the blood particles within a delineated two-dimensional flow domain. Within the Eulerian method, the fluid flow conservation equations within the separator are solved. Taking the calculated values of the flow field and using a Lagrangian method, the displacement of the blood particles is calculated. Thus, the local blood density within the separator at a given time step is known. Subsequently, the flow field in the separator is recalculated. This process continues until a quasisteady behavior is reached. The simulations show good agreement with experimental results. They shows a complete separation of plasma and red blood cells, as well as nearly complete separation of red blood cells and platelets. The white blood cells build clusters in the low concentrate cell bed. [source]