Stable node-based smoothed radial point interpolation method for the dynamic analysis of the hygro-thermo-magneto-electro-elastic coupling problem

In the current work, the stable node-based smoothed radial point interpolation method (SNS-RPIM) was used to investigate the dynamic responses of magneto-electro-elastic (MEE) beams under hygrothermal environment with the generalized Newmark method. Based on the generalized smoothed Galerkin weak form and the gradient smoothing technique, the basic equations for hygro-thermo-magneto-electro-elastic (HTMEE) coupling problems were derived. The stable item of SNS-RPIM made the stiffness ‘close-to-exact’ and cured the ‘over-soft’ of the model. Through the numerical examples, the effect of empirical constants, temperature variation and moisture concentration on the elastic stiffness coefficients and generalized displacement was investigated. Besides, numerical results verified the accuracy, convergence and correctness of the present method compared with the traditional finite element method when analyzing the HTMEE coupling problems. Moreover, SNS-RPIM was very stable and accurate for extremely distributed meshes, which can have an excellent application for future studies of the coupled multi-physical problems.