Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM

Vinh, Pham Van; Chính, Nguyễn Văn; Tounsi, Abdelouahed

doi:10.1016/j.euromechsol.2022.104743

Cited by 172 publications

(27 citation statements)

References 37 publications

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“…For more articles in this direction, we refer the interesting readers to [16][17][18][19] and references cited therein. On the other hand, it is important here to mention that we can also apply the theory of the discrete dynamical system to other recent published works [20][21][22][23][24][25][26][27][28] to explore the possibilities of bifurcation and chaos. Motivated from aforementioned studies, the purpose of present studies is to investigate the dynamics of a discrete chemostat model (14).…”

Section: Chemostat Parameters Corresponding Dimensions Biological Int...mentioning

confidence: 99%

Bifurcation Analysis of a Discrete‐Time Chemostat Model

Al-Basyouni

Khan

2023

Mathematical Problems in Engineering

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In this article, a discretized two-dimensional chemostat model is investigated. By using the algebraic technique, it is proved that the discrete chemostat model has semitrivial equilibrium solution for all involved parametric values, but it has an interior equilibrium solution under certain parametric conditions. We have studied the local dynamics with topological classifications about the semitrivial and interior equilibrium solution on the basis of the theory of the discrete dynamical system. By bifurcation theory, we studied the existence of bifurcations for the understudied discrete chemostat model and proved that at a semitrivial equilibrium solution, it did not undergo flip bifurcation, but it undergoes flip bifurcation at interior equilibrium solution, and no other bifurcation occurs at this point. It has also explored the existence of periodic points and chaos control by the state feedback method. Finally, with the help of MATLAB software, flip bifurcation diagrams and corresponding maximum Lyapunov exponents were also presented. These numerical simulations not only show the correctness of theoretical results but also reveal the complex dynamics such as the orbits of period − 7 , − 8 , − 13 , and − 16 .

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Section: Chemostat Parameters Corresponding Dimensions Biological Int...mentioning

confidence: 99%

Bifurcation Analysis of a Discrete‐Time Chemostat Model

Al-Basyouni

Khan

2023

Mathematical Problems in Engineering

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“…There are currently no reference curves that represent a data set as large as the one presented within this paper. The design curve may be implemented in FEM by engineers and scientists in order to calculate the fatigue life in a reliable way, especially for simple objects that have been printed, e.g., plates with the dimensions reported by Van Vihn et al [21].…”

Section: Introductionmentioning

confidence: 99%

General Reference and Design S–N Curves Obtained for 1.2709 Tool Steel

et al. 2023

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At present, due to advanced fatigue calculation models, it is becoming more crucial to find a reliable source for design S–N curves, especially in the case of new 3D-printed materials. Such obtained steel components are becoming very popular and are often used for important parts of dynamically loaded structures. One of the commonly used printing steels is EN 1.2709 tool steel, which has good strength properties and high abrasion resistance, and can be hardened. The research shows, however, that its fatigue strength may differ depending on the printing method, and may be characterized by a wide scatter of the fatigue life. This paper presents selected S–N curves for EN 1.2709 steel after printing with the selective laser melting method. The characteristics are compared, and conclusions are presented regarding the resistance of this material to fatigue loading, especially in the tension–compression state. A combined general mean reference and design fatigue curve is presented, which incorporates our own experimental results as well as those from the literature for the tension–compression loading state. The design curve may be implemented in the finite element method by engineers and scientists in order to calculate the fatigue life.

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“…Moreover, there is still a lack of verification methods for SFEM with random field. In most cases, the Monte-Carlo method is used for such a purpose, but it definitely and inevitably has the disadvantage of absolute dependence on the amount of samples [ 37 , 38 , 39 , 40 ]. Hence, it is very crucial and urgent to build an effective analysis model of free vibration for the structure with random field and to develop a new verification method regarding the presented model.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Dynamic Characteristic Analysis for Structures with Spatially Dependent Random System Parameters

Zhou

et al. 2023

Materials

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This work presents a robust non-deterministic free vibration analysis for engineering structures with random field parameters in the frame of stochastic finite element method. For this, considering the randomness and spatial correlation of structural physical parameters, a parameter setting model based on random field theory is proposed to represent the random uncertainty of parameters, and the stochastic dynamic characteristics of different structural systems are then analyzed by incorporating the presented parameter setting model with finite element method. First, Gauss random field theory is used to describe the uncertainty of structural material parameters, the random parameters are then characterized as the standard deviation and correlation length of the random field, and the random field parameters are then discretized with the Karhunen–Loeve expansion method. Moreover, based on the discretized random parameters and finite element method, structural dynamic characteristics analysis is addressed, and the probability distribution density function of the random natural frequency is estimated based on multi-dimensional kernel density estimation method. Finally, the random field parameters of the structures are quantified by using the maximum likelihood estimation method to verify the effectiveness of the proposed method and the applicability of the constructed model. The results indicate that (1) for the perspective of maximum likelihood estimation, the parameter setting at the maximum value point is highly similar to the input parameters; (2) the random field considering more parameters reflects a more realistic structure.

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Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM

Cited by 172 publications

References 37 publications

Bifurcation Analysis of a Discrete‐Time Chemostat Model

Bifurcation Analysis of a Discrete‐Time Chemostat Model

General Reference and Design S–N Curves Obtained for 1.2709 Tool Steel

Uncertain Dynamic Characteristic Analysis for Structures with Spatially Dependent Random System Parameters

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