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ARTICLE

Large Deformation Hyper-Elastic Modeling for Nonlinear Dynamic Analysis of Two Dimensional Functionally Graded Domains Using the Meshless Local Petrov-Galerkin (MLPG) Method

Mohammad Hossein Ghadiri Rad¹, Farzad Shahabian^1,2, Seyed Mahmoud Hosseini³

1 Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2 Corresponding author: Farzad Shahabian, Tel: +98 513 38805047, Fax: +98 513 38763301, E-mails: fshahabianm@yahoo.com & shahabf@um.ac.ir
3 Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Computer Modeling in Engineering & Sciences 2015, 108(3), 135-157. https://doi.org/10.3970/cmes.2015.108.135

Abstract

A meshless method based on the local Petrov-Galerkin approach is developed for elasto-dynamic analysis of geometrically nonlinear two dimensional (2D) problems in hyper-elastic functionally graded materials. The radial point interpolation method (RPIM) is utilized to build the shape functions and the Heaviside step function is used as the test function. The mechanical properties of functionally graded material are considered to continuously vary in a certain direction and are simulated using a nonlinear power function in volume fraction form. Considering the large deformations, it is assumed that the domain be made of large deformable neo-Hookean hyperelastic materials. Rayleigh damping is employed to model energy dissipation in analyses. The Newmark finite difference method is used to treat the time dependence of the variables. At any time step of Newmark method, the Newton-Raphson iteration technique is employed to solve the nonlinear governing equations. Accuracy of the proposed method is verified using the results available in the literature. It is shown that the present MLPG method is a suitable meshless method for large deformation problems. The nonlinear time histories and wave propagations of displacement field for various FG distributions and damping ratios are studied in detail.

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