Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation

Scheidl, Jakob; Vetyukov, Yury; Schmidrathner, Christian; Schulmeister, Klemens G.; Proschek, Michael

doi:10.1016/j.ijmecsci.2021.106572

Cited by 12 publications

(6 citation statements)

References 57 publications

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“…We observe by comparison to (18) and (22) with constants according to (27) that for pure bending the Crisfield yield surface exactly captures the initial yield surface; χ p = 0 and γ = 1 as well as the limit yield surface; χ p → ∞ and γ = 3/2. Instead of γ, the newly proposed model makes use of the isotropic hardening function of the dissipative work k M (A p ) introduced for the plate srp-model developed in [16], which was identified for the uniaxial bending continuum reference solution.…”

Section: Stress Resultant Model Of Elastic-plasticmentioning

confidence: 71%

“…An elegant way to mitigate these drawbacks is the use of the Arbitrary Lagrangian Eulerian (ALE) methods [9], where a Lagrangian step is succeeded by a Eulerian step within a time step, see [8] in the context of roll forming. In this respect, we adopt the efficient mixed Euerlian-Lagrangian (MEL) kinematic description, see [17,21,22], whichin contrast to more traditional variants of ALE -allows for a solution scheme that limits the Eulerian update step to the transport of plastic variables.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

Kocbay

Scheidl²,

Schwarzinger³

et al. 2023

Preprint

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The proposed Kirchhoff–Love shell stress resultant plasticity model extends a previously reported model for plates by complementing the constitutive law of elastoplasticity with membrane effects. This enhanced model is designed for bending dominant settings with small to moderate membrane forces. It is thus implemented in a purpose-built nonlinear mixed Eulerian–Lagrangian finite element scheme for the simulation of sheet metal roll forming. Numerical experiments by imposing artificial strain histories on a through-the thickness element are conducted to test the model against previously reported stress resultant plasticity models and to validate it against the traditional continuum plasticity approach that features an integration of relations of elastoplasticity in a set of grid points distributed over the thickness. Results of actual roll forming simulations demonstrate the practicality in comparison to the computationally more expensive continuum plasticity approach.

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Section: Stress Resultant Model Of Elastic-plasticmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

Kocbay

Scheidl²,

Schwarzinger³

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…[40][41][42] This method combines the Lagrangian approach, which follows the displacement of the fin by mobile grids, and the Eulerian approach, which follows the movement of the fluid by fixed grids, which ensures good numerical stability. The research 43,44 describes an extensive proof of this method. The governing equations are transformed into weak forms and discretized using the Galerkin finite element method.…”

Section: Numerical Simulationmentioning

confidence: 99%

Fluid‐structure interaction study of an oscillating heat source effect on the natural convection flow

Tarek,

Elhadj,

Mohammad

et al. 2024

Heat Trans

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The objective of this paper is to investigate fluid‐structure interaction (FSI) within conjugate natural convection. An oscillating fin, featuring a heat source placed at different locations, is examined using the Arbitrary Lagrangian–Eulerian formulation. The Galerkin finite element method is utilized to solve nonlinear dimensionless equations. Verification of grid independence is conducted and the model undergoes validation. Simulation outcomes for three fin positions (left, center, and right) and three heat source locations (bottom, middle, and top) are presented, illustrating streamlines, isotherms, and the average Nusselt number. The governing equations and boundary conditions are addressed using the finite element method. Temperature profiles in four scenarios are analyzed, along with horizontal velocities at different levels (0, D/2, D from the bottom wall). Dimensionless time (10−5 ≤ t ≤ 3), Ra = 106, Kr = 10, E = 1011 are used as parameters. The impact of the heat source position on vibratory motion is evaluated through Nusselt number variation, affecting heat exchange in different cases. The results show that heat transfer is minimal for a source location at the center of the fin (c). These findings also offer insights into FSI applications in economics and industry, guiding practical design considerations. Additionally, coupling the vibratory motion of the heat source with the flexible oscillating fin at the same frequency enhances understanding of the system.

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“…Alternatively, nodes can follow an arbitrary movement pattern. Comprehensive validation of this method is elaborated [47,48]. The computational fluid dynamics (CFD) framework draws upon diverse numerical solvers to execute the weighted residual Galerkin finite element method (FEM) [49,50].…”

Section: Numerical Simulationmentioning

confidence: 99%

Numerical Simulation of Fluid-Structure Interaction in Undulated Cavity

Tarek,

Elhadj,

Mohammed

et al. 2023

IJHT

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This study presents a numerical exploration into the phenomenon of natural convection within a cavity, characterized by a straight (cold) right wall and a wavy (hot) left wall. The focus lies in the dynamic interaction between the working fluid (air) and a sinusoidally moving solid structure (the fin). The Arbitrary Lagrangian-Eulerian (ALE) methodology is employed to handle the moving mesh, and the Galerkin weighted residual finite element method is utilized to solve the nonlinear equations and boundary conditions. A mesh validation test is undertaken, and a comparative analysis against numerical reference is included. In a novel approach, a mathematical formulation incorporating the geometric aspect ratio Ar (defined as the fundamental wavelength relative to its wavy width) is introduced into the fundamental equations. Numerical results, including isotherms, streamlines, temperature profiles, horizontal velocity, and local heat flux coefficient, are presented under specific conditions: a geometry ratio Ar=0.3, a Rayleigh number spanning from 10 3 to 10 7 , and a dimensionless time t ranging from 10 -5 to 3. These results are based on three distinct positions of the oscillating elastic. The findings elucidate the combined effect of convection and the vibration of the flexible oscillating fin, particularly at high Rayleigh numbers. This study contributes novel insights into the complex interplay between fluid dynamics and vibrating structures in the context of natural convection.

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Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation

Cited by 12 publications

References 57 publications

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

Fluid‐structure interaction study of an oscillating heat source effect on the natural convection flow

Numerical Simulation of Fluid-Structure Interaction in Undulated Cavity

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