Simulation of plane elastostatic equations of anisotropic functionally graded materials by integrated radial basis function based on finite difference approach

Ebrahimijahan, Ali; Dehghan, Mehdi; Abbaszadeh, Mostafa

doi:10.1016/j.enganabound.2021.10.011

Cited by 12 publications

(3 citation statements)

References 32 publications

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“…These improvements can be in the shape of higher accuracy, less computation time, etc. [1], [2], [3]. The radial basis function (RBF) method is a powerful method for solving differential equations related to many physical problems [4], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Talebirostami,

Najafabadi,

Ganji

2024

Int. J. Appl. Comput. Math

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This study introduces a semi-analytical New Trigonometric Radial Basis Function (NTRBF) method for solving strongly nonlinear differential equations in vibration problems. The method uses a particular trigonometric function to deal with differential equations in an extraordinary and original approach. It was compared to four different problems, including the Global Residue Harmonic Balance Method (GRHBM) in solving circular sector oscillator problem, the Continuous Piecewise Linearization method (CPLM) in solving strong nonlinear differential equation of a tapered beam, the Differential Transform Method (DTM) to solve centrifugal rotating frame motion, and Akbari-Ganji's Method (AGM) to solve Duffing-type nonlinear oscillator. These problems were solved in different conditions. The plots and tables represent both cumulative and maximum errors between the NTRBF and other methods, which use the numerical 4th-order Runge-Kutta method as a benchmark for accuracy. The outcomes prove the high accuracy and efficiency of the innovative technique and its unique capability in solving various nonlinear vibration problems.

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Section: Introductionmentioning

confidence: 99%

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Talebirostami,

Najafabadi,

Ganji

2024

Int. J. Appl. Comput. Math

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“…However, when thick plates are considered or when complex materials with non-homogeneous or anisotropic characteristics are considered, the plate theories (classical and higher order) suffer from low accuracy. Therefore, the most general approach to consider all strains is using the continuum theory of elasticity [ 5 , 6 ]. The traditional computational techniques such as the finite element method are costly in 3D elasticity analysis of plate structures.…”

Section: Introductionmentioning

confidence: 99%

Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach

2023

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In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.

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“…For fulfilling specific industrial applications, FGMs have been widely used in structural elements such as beams, plates, and shells [14,15]. The preparation technology of FGMs is continually being improved [16][17][18], and the research on the microstructure [19][20][21], fracture [22][23][24], and mechanical properties [24][25][26][27] of functionally graded materials is gradually catching up.…”

Section: Introductionmentioning

confidence: 99%

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

Yan

2022

Crystals

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This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material.

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Simulation of plane elastostatic equations of anisotropic functionally graded materials by integrated radial basis function based on finite difference approach

Cited by 12 publications

References 32 publications

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

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