A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping

Rad, Mohammad Hossein Ghadiri; Shahabian, Farzad; Hosseini, Seyed Mahmoud

doi:10.1007/s00707-014-1266-2

Cited by 25 publications

(4 citation statements)

References 19 publications

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“…The boundary conditions are on deflections 'W', slope 'θ=dW/dx', moment 'M=EI(d 2 W/dx 2 )', and shear force 'V= -EI(d 3 W/dx 3 )' . Instead of solving this differential equation, the weak form of Equation ( 10) is minimized over a local subdomain of each node 'Ω' [45]:…”

Section: Mlpg Methods For Buckling Analysis Of the Columnmentioning

confidence: 99%

“…By using the RBF, the lateral displacement function of the column 'W' over the support domain of an arbitrary point can be estimated in terms of its nodal values at all points located in the support domain [45,46]:…”

Section: Radial Basis Function (Rbf)mentioning

confidence: 99%

“…The constant coefficients vector of Equation ( 25) can be determined by satisfying this equation in all nodes placed in the support domain [45,46].…”

Section: Radial Basis Function (Rbf)mentioning

confidence: 99%

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Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

Elahihamezanlui

Kazemi

Rad

2022

NMCE

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The spread of different material processing technologies has led to novel methods developed for reinforcing structural members. One of these approaches is to add carbon nanotubes (CNTs) with different distributions through the matrix phase of composite materials to improve their properties. Due to their superior properties such as lightweight and high values of elastic modulus, elastic strain, and failure strain, CNTs can be used to reinforce structures and elements. The present paper aims to investigate the effect of adding CNTs as reinforcement of matrix on the buckling capacity of columns by applying the meshless local Petrov-Galerkin (MLPG) method for buckling analysis. Since the MLPG method uses some scattered nodes through the domain and boundaries for discretization (rather than the meshing), the functionally graded (FG) variation of material properties can be conveniently modeled under the influence of reinforcing elements (CNTs). Four types of volume fraction exponent functions are considered for modeling the FG variation of the CNT volume fraction to examine the effect of CNTs distribution on the buckling capacity of the column and determine the most optimal distribution of CNTs. Effective mechanical properties of the CNT-reinforced column are estimated based on the extended rule of mixture. Results show that reinforcing the polymer matrix with a low volume fraction of CNTs with appropriate distribution can significantly increase its buckling capacity. Using the obtained results, one can determine the best distribution pattern of CNTs in the longitudinal direction of the column at various boundary conditions.

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Section: Mlpg Methods For Buckling Analysis Of the Columnmentioning

confidence: 99%

Section: Radial Basis Function (Rbf)mentioning

confidence: 99%

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Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

Elahihamezanlui

Kazemi

Rad

2022

NMCE

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“…Ghadiri Rad et al [37] analyzed the large deflection analysis of a functionally graded thick hollow cylinder with Rayleigh damping using MLPG method. They considered the hyper-elastic neo-Hookean model for the cylinder.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear dynamic analysis of functionally graded thick hollow cylinders using total Lagrangian MLPG method

2015

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In this article, geometrically nonlinear transient analysis based on the meshless local Petrov-Galerkin method (MLPG) is presented for functionally graded material thick hollow cylinders with infinite length subjected to a mechanical shock loading. The cylinder is assumed to be axisymmetric and in plane strain conditions. The mechanical properties of functionally graded cylinder are assumed to vary across the thickness. In MLPG analysis, the total Lagrangian formulation, radial base function, and Heaviside test function are used for approximation of displacement field in the weak form of the equation of motion. The system nonlinear equations are solved by Newmark finite difference and Newton-Raphson iteration methods. The time history of the radial displacement and stress for various values of the power law exponents, radii and thicknesses are investigated. The effects of different loading types and also the duration of loading on the dynamic behaviors of displacement and stress fields are obtained and discussed in details. Moreover, the obtained results from nonlinear analysis are compared with those obtained from linear analysis.

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Direct meshless local Petrov–Galerkin method for elastodynamic analysis

Mirzaei

Hasanpour

2015

Acta Mech

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A meshless local Petrov–Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping

Cited by 25 publications

References 19 publications

Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

Geometrically nonlinear dynamic analysis of functionally graded thick hollow cylinders using total Lagrangian MLPG method

Direct meshless local Petrov–Galerkin method for elastodynamic analysis

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