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.

中文翻译：

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基于节点的平滑径向点插值法结合基于微力学的渐近均匀化技术对磁电弹性纳米结构进行动力学分析

提出了基于节点的平滑径向点插值方法结合渐近均匀化方法，作为有限元方法的补充，以解决磁-电-弹性耦合微机械问题的静态和动态反应。首先，推导出相关问题的几个基本方程。其次，利用渐近均质化方法确定磁电弹性纳米材料的材料特性。第三，应用基于节点的平滑径向点插值方法获得磁电弹性纳米结构的离散方程。然后，引入Newmark方法来解决微观问题的响应。最后，计算了几个数值例子来证明准确性，收敛性，