scholarly journals An Annular Plate Model in Arbitrary Lagrangian-Eulerian Description for the DLR FlexibleBodies Library

2011 ◽  
Author(s):  
Andreas Heckmann ◽  
Stefan Hartweg ◽  
Ingo Kaiser
Keyword(s):  
Annular Plate ◽  
Plate Model ◽  
Arbitrary Lagrangian Eulerian ◽  
Eulerian Description

Variational Principles for Non-Material Systems Within an Arbitrary Lagrangian Eulerian Description of Motion

2020 ◽  
Author(s):  
Giuseppe Pennisi ◽  
Olivier Bauchau
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Variational Principles ◽  
Material System ◽  
Arbitrary Lagrangian Eulerian ◽  
Complex Dynamic ◽  
Eulerian Description ◽  
Material Systems ◽  
Axially Moving ◽  
Dynamic Description

Abstract Dynamics of axially moving continua, such as beams, cables and strings, can be modeled by use of an Arbitrary La-grangian Eulerian (ALE) approach. Within a Finite Element framework, an ALE element is indeed a non-material system, i.e. a mass flow occurs at its boundaries. This article presents the dynamic description of such systems and highlights the peculiarities that arise when applying standard mechanical principles to non-material systems. Starting from D’Alembert’s principle, Hamilton’s principle and Lagrange’s equations for a non-material system are derived and the significance of the additional transport terms discussed. Subsequently, the numerical example of a length-changing beam is illustrated. Energetic considerations show the complex dynamic behavior non-material systems might exhibit.

Optimization Using Arbitrary Lagrangian–Eulerian Formulation of the Navier–Stokes Equations

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Eysteinn Helgason ◽  
Siniša Krajnović
Keyword(s):  
Stokes Equations ◽  
Optimization Method ◽  
Navier Stokes ◽  
Lagrangian Description ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Mesh Motion ◽  
Eulerian Description ◽  
Eulerian Formulation

In this paper, we present a new shape optimization method by using sensitivities obtained from the Arbitrary Lagrangian–Eulerian (ALE) form of the Navier–Stokes equations. In the ALE description, the nodes of the computational domain may be moved with the fluid as in the Lagrangian description, held fixed in space as in the Eulerian description, or moved in some arbitrary way in between. Applying the adjoint method with respect to mesh motion allows the whole sensitivity field for the shape changes to be calculated using only two solver calls, a primal solver call and an adjoint solver call. We show that the sensitivities with respect to the mesh motion can be calculated in a postprocessing step to the primal and adjoint flow simulations. The resulting ALE sensitivities are compared to sensitivities obtained using a finite difference approach. Finally, the sensitivities are coupled to a mesh motion smoothing algorithm, and a duct is optimized with respect to the total pressure drop using the proposed method.

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

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