Shock-induced two dimensional coupled non-Fickian diffusion-elasticity analysis using meshless generalized finite difference (GFD) method. (English) Zbl 1403.74278
Summary: In this work, the application of a meshfree method based on the generalized finite differences (GFD) method is developed for two dimensional analysis of coupled non-Fickian diffusion-elasticity. The two dimensional analyzed domain is subjected to shock loading in the problem. The equations of motion are transferred to Laplace domain by Laplace-transform technique and descritized using the presented meshfree method. The obtained results in Laplace domain are transferred to time domain using Talbot Laplace inversion technique for studying on the dynamic behaviors of displacements and molar concentration. It is found that the molar concentration diffuses through 2D domain with a finite speed similar to elastic wave. The propagation of mass diffusion and elastic waves are obtained and discussed at various time intervals. The distribution of molar concentration and displacements along “\(x\)” and “\(y\)” directions are illustrated at various time intervals for certain points on both axes.
MSC:
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 74F15 | Electromagnetic effects in solid mechanics |
Keywords:
non-Fickian diffusion; coupled problem; wave propagation; generalized finite differences (GFD) method; molar concentrationReferences:
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