A coupled Meshless-FEM method based on strong form of Radial Point Interpolation Method (RPIM)

Kadmiri, Redouane El; Belaasilia, Youssef; Timesli, Abdelaziz; Kadiri, Moulay S.

doi:10.1088/1742-6596/1743/1/012039

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…The objective in the future is to apply this approach on other type of shells, such as FGM cylindrical Shells [15,19]. In addition, we will try to develop meshless models [20][21][22][23][24][25][26][27] based on TSDT theory for the analysis of FGM plates. Comparison of natural frequencies between a laminated P-FGM plate and a simple P-FGM plate using the power law.…”

Section: Discussionmentioning

confidence: 99%

TSDT theory for free vibration of functionally graded plates with various material properties

Allah¹,

Belaasilia²,

Timesli³

et al. 2021

Math. Model. Comput.

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In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

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Section: Discussionmentioning

confidence: 99%

TSDT theory for free vibration of functionally graded plates with various material properties

Allah¹,

Belaasilia²,

Timesli³

et al. 2021

Math. Model. Comput.

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“…The accuracy of meshless methods in capturing fine details and gradients is crucial for modeling the precise thermal effects and material removal processes in laser drilling. So, meshless methods offer significant advantages over the FEM in terms of flexibility, accuracy, and efficiency, particularly for problems with large deformations, and moving boundaries [66]. These features make meshless methods an attractive choice for modeling and simulating processes like laser drilling, where high precision and adaptability are critical.…”

Section: Numerical Discretization 31 Spatial Approximationmentioning

confidence: 99%

Fractional non-Fourier modeling of laser drilling process

Hassan,

Abidou,

Elsaid

et al. 2024

Phys. Scr.

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In this paper, a novel fractional non-Fourier model is employed to simulate the laser drilling process, addressing limitations inherent in classical heat conduction equations, including the well-known heat equation paradox associated with infinite heat propagation velocity. This model approach combines spatial approximation via the Meshless Local Petrov-Galerkin method with temporal approximation using the Grünwald-Letnikov finite difference scheme. The study assesses the impact of employing fractional orders, both constant and variable over time, on numerical results, and validates the model using experimental data.

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Optimal variable support size for mesh-free approaches using genetic algorithm

Hassouna¹,

Timesli²

2021

Math. Model. Comput.

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The main difficulty of the meshless methods is related to the support of shape functions. These methods become stable when sufficiently large support is used. Rather larger support size leads to higher calculation costs and greatly degraded quality. The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem. In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with high order mesh-free algorithms which the optimal value depends on the accuracy and stability of the results. The proposed strategy provides guarantees about the growth of approximation errors, monitor the level of error, and adapt the evaluation strategy to reach the required level of accuracy. This allows the adaptation of the proposed algorithm with problem complexity. This new strategy in meshless approaches are tested on some examples of structural analysis.

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A coupled Meshless-FEM method based on strong form of Radial Point Interpolation Method (RPIM)

Cited by 3 publications

References 21 publications

TSDT theory for free vibration of functionally graded plates with various material properties

TSDT theory for free vibration of functionally graded plates with various material properties

Fractional non-Fourier modeling of laser drilling process

Optimal variable support size for mesh-free approaches using genetic algorithm

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