Dynamic analysis of magneto-electro-elastic nanostructures using node-based smoothed radial point interpolation method combined with micromechanics-based asymptotic homogenization technique

The node-based smoothed radial point interpolation method combined with the asymptotic homogenization method was proposed, as an addition to the finite element method, to address the static and dynamic reactions of magneto-electro-elastic coupling micromechanical problems. First, several basic equations for relevant problems were derived. Second, asymptotic homogenization method was utilized to determine the material properties of magneto-electro-elastic nanomaterials. Third, node-based smoothed radial point interpolation method was applied to obtain the discrete equations of magneto-electro-elastic nanostructures. Then, the Newmark method was introduced to solve the response of microcosmic problems. Finally, several numerical examples were calculated to prove the accuracy, convergence, and reliability of node-based smoothed radial point interpolation method by comparing the results of node-based smoothed radial point interpolation method with those of finite element method.