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Eulerian Formulation (eulerian + formulation)
Selected AbstractsStabilized updated Lagrangian corrected SPH for explicit dynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Y. Vidal Abstract Smooth particle hydrodynamics with a total Lagrangian formulation are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may still be necessary in some problems involving extremely large distortions. However, as discussed here, a standard updated formulation suffers the presence of zero-energy modes that are activated and may completely spoil the solution. It is important to note that, unlike an Eulerian formulation, the updated Lagrangian does not present tension instability but only zero-energy modes. Here a stabilization technique is incorporated to the updated formulation to obtain an improved method without any mechanisms and which is capable to solve problems with extremely large distortions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Optimization of thermo-elasto-plastic processes using Eulerian sensitivity analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003S. Paul Abstract A computational scheme for the analysis and optimization of quasi-static thermo-mechanical processes is presented in this paper. In order to obtain desirable mechanical transformations in a workpiece using a thermal treatment process, the optimal control parameters need to be determined. The problem is addressed by posing the process as a decoupled thermo-mechanical finite element problem and performing an optimization using gradient methods. The forward problem is solved using the Eulerian formulation since it is computationally more efficient compared to an equivalent Lagrangian formulation. The design sensitivities required for the optimization are developed analytically using direct differentiation. This systematic design approach is applied to optimize a laser forming process. The objective is to maximize the angular distortion of a specimen subject to the constraint that the phase transition temperature is not exceeded at any point in the model. Copyright © 2003 John Wiley & Sons, Ltd. [source] Flow-induced vibrations of non-linear cables.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002Part 1: Models, algorithms Abstract In this paper, we develop governing equations for non-linear cables as well as a formulation for the coupled flow-structure problem. The structure is discretized with second-order accuracy while the flow is discretized using spectral/hp elements in the context of the arbitrary Lagrangian,Eulerian formulation (ALE). Several benchmark problems are considered and the computational implementation is detailed. In the second part of this work large-scale simulation examples are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006Martin Engel Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||