A novel stabilized node-based smoothed radial point interpolation method (SNS-RPIM) for coupling analysis of magneto-electro-elastic structures in hygrothermal environment

Abstract

In this article, a stabilized node-based smoothed radial point interpolation method (SNS-RPIM) was proposed to simulate the magneto-electro-elastic (MEE) structures in hygrothermal environment. The node-based smoothing domains were constructed based on triangular background elements, and the approximate strain, electric field intensity and magnetic flux density were derived using node-based strain smoothing operation. In the present formulation, the stabilization term related to the gradient variance of the field variables was used to obtain the system stiffness matrices. Then, by using the smoothed Galerkin weak form, discrete equations of the system were established to solve the generalized displacement of the structure. The numerical experiments validated the feasibility of SNS-RPIM for solving hygrothermo-magneto-electro-elastic (HMEE) coupling problems with different hygrothermal loadings and boundary conditions. Results proved that the introduction of the stabilization term made the SNS-RPIM had a ‘close-to-exact’ stiffness, thereby solving the ‘overly-soft’ in the traditional node-based smoothed radial point interpolation method (NS-RPIM). SNS-RPIM was in good agreement with the reference solution when using the same fewer nodes as finite element method (FEM), and the errors were much smaller than those of FEM. Moreover, SNS-RPIM performed better than NS-RPIM and FEM when processing distorted meshes. Therefore, the developed method showed great potential in simulating MEE structure in hygrothermal environment.