scholarly journals Numerical simulation of two-dimensional wave propagation in functionally graded materials

2003 ◽  
Vol 22 (2) ◽  
pp. 257-265 ◽  
Author(s):  
Arkadi Berezovski ◽  
Juri Engelbrecht ◽  
G.A Maugin
Keyword(s):  
Numerical Simulation ◽  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Graded Materials ◽  
Dimensional Wave

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

2020 ◽  
Vol 234 (10) ◽  
pp. 2012-2023
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

P Wave Propagation in the Functionally Graded Materials

2013 ◽  
Vol 706-708 ◽  
pp. 1685-1688
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Lin Yuan
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Wave Motion ◽  
Mass Density ◽  
Functionally Graded ◽  
P Wave ◽  
Exponential Form ◽  
Graded Materials ◽  
P Wave Velocity

The P wave propagation in the functionally graded materials (FGM) is studied. The differential equation with varied-coefficient of wave motion in the FGM is established. By using of the WKBJ approximation method, the differential equation with varied-coefficient is solved, and the closed-analytical solutions of displacement in the FGM are obtained. The properties of the FGM whose shear modulus and mass density are gradually varying in exponential form are calculated; the curves of P wave velocity and amplitude, and the general properties of the P wave in the FGM are analyzed.

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