Simulation of 3D metal-forming using an arbitrary Lagrangian–Eulerian finite element method

Aymone, José Luf́s Farinatti; Bittencourt, Eduardo; Creus, Guillermo J.

doi:10.1016/s0924-0136(00)00886-4

Cited by 50 publications

(37 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Often-used methods include the weighted average method [25], the transfinite mapping method [26], the method based on the solution of a linear elastic equation to define the new positions of nodes [8], the method based on the solution of Laplace's equation to find the velocity of mesh [27] and so forth.…”

Section: Mesh Moving In Qale-femmentioning

confidence: 99%

Quasi ALE finite element method for nonlinear water waves

W.¹,

Yan²

2006

Journal of Computational Physics

100

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link: AbstractThis paper presents a newly developed quasi arbitrary Lagrangian-Eulerian finite element method (QALE-FEM) for simulating water waves based on fully nonlinear potential theory. The main difference of this method from the conventional finite element method developed by one of authors of this paper and others (see, e.g., [11] and [22]) is that the complex mesh is generated only once at the beginning and is moved at all other time steps in order to conform to the motion of the free surface and structures. This feature allows one to use an unstructured mesh with any degree of complexity without the need of regenerating it every time step, which is generally inevitable and very costly. Due to this feature, the QALE-FEM has high potential in enhancing computational efficiency when applied to problems associated with the complex interaction between large steep waves and structures since the use of an unstructured mesh in such a case is likely to be necessary. To achieve overall high efficiency, the numerical techniques involved in the QALE-FEM are developed, including the method to move interior nodes, technique to re-distribute the nodes on the free surface, scheme to calculate velocities and so on. The model is validated by water waves generated by a wavemaker in a tank and the interaction between water waves and periodic bars on the bed of tank. Satisfactory agreement is achieved with analytical solutions, experimental data and numerical results from other methods.

show abstract

Section: Mesh Moving In Qale-femmentioning

confidence: 99%

Quasi ALE finite element method for nonlinear water waves

W.¹,

Yan²

2006

Journal of Computational Physics

100

View full text Add to dashboard Cite

show abstract

“…The majority of ALE methods on unstructured meshes employs smoothing algorithms which are not governed by quality evolution, including heuristic procedures [27,12,31] and physically-based smoothing [32,9]. Even though these methods are computationally attractive, they cannot ensure that any mesh processed is not worse than before.…”

Section: Mesh Motion Stepmentioning

confidence: 99%

“…The heuristic averaging algorithm of Aymone et al [27] efficiently smoothes mesh boundaries on a local level. Compared to the boundary mesh, smoothing of the internal mesh is much more complicated and can be stated as an optimization problem [37]:…”

Section: Mesh Motion Stepmentioning

confidence: 99%

“…The first is based on weighted averaging and is applied in the ALE method of Aymone et al [27]. The second algorithm has been developed by Giuliani [31] and is based on the analytical expression of the minimizer of a function describing the mesh distortion.…”

Section: Comparison Of Mesh Smoothing Algorithmsmentioning

confidence: 99%

“…In contrast to that, running the ALE method in the purely Lagrangian mode causes the calculation to terminate just after a few time steps. We also tested other smoothing algorithms for internal meshes relying on heuristic approaches [27,31], but only our new optimization-based algorithm led to a convergent solution for this example. The other two algorithms could not prevent elements to invert along with penetration, particularly at the indented mesh corner [28].…”

Section: Shallow Penetration Into Sandmentioning

confidence: 99%

See 2 more Smart Citations

An ALE method for penetration into sand utilizing optimization-based mesh motion

Aubram

Rackwitz

Wriggers

et al. 2015

Computers and Geotechnics

View full text Add to dashboard Cite

ArbitraryLagrangian–Eulerian Methods

Donéa

Huerta

Ponthot

et al. 2004

Encyclopedia of Computational Mechanics

580

441

View full text Add to dashboard Cite

The aim of the present chapter is to provide an in‐depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh‐update strategy is underlined, and various automatic mesh‐displacement prescription algorithms are reviewed. This includes mesh‐regularization methods essentially based on geometrical concepts, as well as mesh‐adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress‐update procedures for materials with history‐dependent constitutive behavior.

show abstract

Simulation of 3D metal-forming using an arbitrary Lagrangian–Eulerian finite element method

Cited by 50 publications

References 34 publications

Quasi ALE finite element method for nonlinear water waves

Quasi ALE finite element method for nonlinear water waves

An ALE method for penetration into sand utilizing optimization-based mesh motion

ArbitraryLagrangian–Eulerian Methods

Contact Info

Product

Resources

About