Implementation of Mini-Element for Solving Navier-Lame System with a New Boundary Condition

Koubaiti, Ouadie; El-Mekkaoui, Jaouad; Elkhalfi, Ahmed

doi:10.36478/jeasci.2019.6575.6586

Cited by 7 publications

(6 citation statements)

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“…According to reference [ 9 , 13 , 22 , 23 ], all the defects detected during fatigue testing or during operation of the lower control arm appear at the end of the part show in Figure 6 . To complete these studies by these cited researchers, we will propose that the defect resulting from the manufacturing process be reproduced in the same area.…”

Section: Computational Modellingmentioning

confidence: 99%

“…The geometry that we will study is characterized by thickness (t), width, and length, as detailed in Table 1 and Figure 5 below. According to reference [9,13,22,23], all the defects detected during fatigue testing or during operation of the lower control arm appear at the end of the part show in Figure 6.…”

Section: Designmentioning

confidence: 99%

“…Because the enrichment functions at the edge of the crack take a role in modeling the discontinuous region, it is the power of this method compared to the classical finite element method which requires a specific mesh at the crack tip (Figure 7). According to reference [9,13,22,23], all the defects detected during fatigue testing or during operation of the lower control arm appear at the end of the part show in Figure 6. To complete these studies by these cited researchers, we will propose that the defect resulting from the manufacturing process be reproduced in the same area.…”

Section: Meshing Loadings and Boundary Conditionmentioning

confidence: 99%

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Predicting Stress Intensity Factor for Aluminum 6062 T6 Material in L-Shaped Lower Control Arm (LCA) Design Using Extended Finite Element Analysis

El Fakkoussi,

Vlase,

Marin

et al. 2023

Materials

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The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm’s attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm.

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Section: Computational Modellingmentioning

confidence: 99%

Section: Designmentioning

confidence: 99%

Section: Meshing Loadings and Boundary Conditionmentioning

confidence: 99%

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Predicting Stress Intensity Factor for Aluminum 6062 T6 Material in L-Shaped Lower Control Arm (LCA) Design Using Extended Finite Element Analysis

El Fakkoussi,

Vlase,

Marin

et al. 2023

Materials

Self Cite

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“…Among the different enrichment methods, we find nodal enrichment where the enrichment degrees of freedom were added [ 19 ]. The methods based on the concept of unit partition [ 20 ] are called the nodal enrichment method, the Generalized Finite Element Method (GFEM) [ 21 ], and the XFEM [ 22 , 23 , 24 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Crack Prediction and Growth in Automotive Wheel Rims

Montassir,

Moustabchir,

El Khalfi

et al. 2024

Materials

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Finite element analysis has become an essential tool for simulating and understanding crack growth. This technique holds significant importance in the field of mechanical engineering, where it finds wide application in the design and optimization of structural components and material properties. This work began with the identification of critical zones and estimated the number of load life repeats through fatigue analysis, specifically applied to automotive rims utilizing innovative finite element methods. To investigate crack behavior, we are used the Extended Finite Element Method (XFEM) with the volumetric approach to compute the Stress Intensity Factor (SIF). The results obtained by our study align closely with experimental tests in terms of detecting the critical zone where a crack can appear. Our findings contribute to the understanding of fatigue behavior in automotive rims, offering new insights into their structural integrity and performance under various load conditions.

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“…The variational multiscale method, as discussed in [11], was explored as an effective approach to tackle the computational challenges posed by Navier-Stokes equations. Additionally, the mini-element method, presented in [12], is crucial for solving the Navier-Lame equation with a new boundary condition.…”

Section: Introductionmentioning

confidence: 99%

A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition

El Moutea,

Nakbi,

El Akkad

et al. 2023

Symmetry

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In this paper, we present a numerical scheme for addressing the unsteady asymmetric flows governed by the incompressible Navier–Stokes equations under a general boundary condition. We utilized the Finite Element Method (FEM) for spatial discretization and the fully implicit Euler scheme for time discretization. In addition to the theoretical analysis of the error in our numerical scheme, we introduced two types of a posteriori error indicators: one for time discretization and another for spatial discretization, aimed at effectively controlling the error. We established the equivalence between these estimators and the actual error. Furthermore, we conducted numerical simulations in two dimensions to assess the accuracy and effectiveness of our scheme.

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Implementation of Mini-Element for Solving Navier-Lame System with a New Boundary Condition

Cited by 7 publications

References 0 publications

Predicting Stress Intensity Factor for Aluminum 6062 T6 Material in L-Shaped Lower Control Arm (LCA) Design Using Extended Finite Element Analysis

Predicting Stress Intensity Factor for Aluminum 6062 T6 Material in L-Shaped Lower Control Arm (LCA) Design Using Extended Finite Element Analysis

Numerical Study of Crack Prediction and Growth in Automotive Wheel Rims

A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition

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