Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method

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

doi:10.1016/j.enganabound.2014.08.002

Cited by 14 publications

(3 citation statements)

References 21 publications

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“…They considered the hyper-elastic neo-Hookean model for the cylinder. Also in another research [38], they obtained the displacements and stresses in hyper-elastic FG thick hollow cylinder using MLPG method.…”

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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Section: Introductionmentioning

confidence: 99%

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

2015

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“…Ghoohestani et al [39] studied the dynamic behavior of structures made of CNTreinforced multi-layer composite materials under impact loading. Rad et al [40] evaluated the geometrically nonlinear dynamic behavior of hollow cylindrical structures made of FGM with variable properties along the radius direction using the MLPG method. Hosseini and Zhang [41] utilized the meshless finite difference method to analyze the time history of FG graphene platelet-reinforced (FG-GPLTR) cylindrical structures with variable properties in the radial direction.…”

Section: Introductionmentioning

confidence: 99%

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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“…They assumed radial variation of material properties by power law function and used classical theory (PET) and Gausshypergeometric function to derive and solve equations, respectively. Geometrically nonlinear dynamic behavior of FG thick hollow cylinder under axisymmetric mechanical shock loading is investigated using meshless local Petrov-Galerkin (MLPG) method by Ghadiri Rad et al (2015). The FG cylinder is assumed to be made of large deformable neo-Hookean materials such as carbon-based polymers.…”

Section: Introductionmentioning

confidence: 99%

New nonlinear solution of nearly incompressible hyperelastic FGM cylindrical shells with arbitrary variable thickness and non-uniform pressure based on perturbation theory

Gharooni

Ghannad

2019

Lat. Am. j. solids struct.

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In this paper, nonlinear analysis of thick cylindrical shells with arbitrary variable thickness made of hyperelastic FGM with radially variation of material properties in nearly incompressible state under non-uniform pressure loading is presented. Thickness and pressure of the shell vary in axial direction by linear and/or nonlinear functions. The governing equilibrium equations are derived based on shear deformation theory (SDT). The Mooney-Rivlin type material is considered which is a suitable hyperelastic model for rubbers. Boundary Layer Method of the perturbation theory which is known as Matched Asymptotic Expansion (MAE) is used for solving the governing equations. A new ingenious solution and formulation have been defined during current study to simplify and abbreviate the representation of inner and outer equations components in MAE. In order to validate the results of the current analytical solution, a numerical modeling based on Finite Element Method (FEM) have been investigated. Afterwards, for different rubber case studies, the effect of material constants, inhomogeneity index, geometry and pressure profiles on displacements, stresses and hydrostatic pressure distributions resulting from MAE and FEM solution have been illustrated. This approach enables insight into the nature of the deformation and stress distribution across the wall of rubber vessels and offers the potential for investigating the mechanical functionality of blood vessels such as arteries in physiological pressure range. The results prove the effectiveness of SDT and MAE combination to derive and solve the governing equations of nonlinear problems such as nearly incompressible hyperelastic FG shells.

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Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method

Cited by 14 publications

References 21 publications

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

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

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

New nonlinear solution of nearly incompressible hyperelastic FGM cylindrical shells with arbitrary variable thickness and non-uniform pressure based on perturbation theory

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