Application of meshless local integral equations to two dimensional analysis of coupled non-Fick diffusion–elasticity

This work presents the application of meshless local Petrov–Galerkin (MLPG) method to two dimensional coupled non-Fick diffusion–elasticity analysis. A unit step function is used as the test functions in the local weak-form. It leads to local integral equations (LIEs). The analyzed domain is divided into small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized. Several numerical examples are given to verify the accuracy and the efficiency of the proposed method. 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 instants. The MLPG method has a high capability to track the diffusion and elastic wave fronts at arbitrary time instants in 2D domain. The profiles of molar concentration and displacements in two orthogonal directions are illustrated at various time instants.