Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates
Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates
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叠层磁电弹性板静态和动态响应的半解析分析
DOI：
10.1016/j.compstruct.2019.110933
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发表时间：
2019-08
影响因子：
6.3
通讯作者：
Huang Yesheng
中科院分区：
文献类型：
--
作者：
Zhang Pengchong;Qi Chengzhi;Fang Hongyuan;Ma Chao;Huang Yesheng
将比例边界有限元法（SBFEM）与精细积分技术（PIT）相结合，对磁电弹性复合材料层合板的静态弯曲和自由振动特性进行了半解析分析。它适用于薄和厚的多层磁电弹性板。基本方程仅用二维模型来表示，这有助于确保计算效率。离散化是根据谱元素进行的。仅选取位移分量、电势和磁势三个分量作为基本变量。利用SBFEM的重要特性，可以解析地求解沿厚度方向的弹性位移、电磁势和沿着方向的电势。与大多数板模型对力、电、磁变量的分布进行先验假设不同，SBFEM控制方程的推导严格遵循三维电磁弹性材料理论，而不引入任何多物理场假设。利用比例边界坐标和虚功原理，将关键的偏微分方程简化为控制常微分矩阵方程。为了提高SBFEM控制方程的精度，利用PIT，这确保了可以达到任何期望的结果精度。静态和动态数值算例表明，该方法预测的机械、电场、磁场和固有频率的变化与其他方法的弹性解非常一致。因此，充分验证了本技术的通用性和完美的准确性。进一步讨论了纵横比、边界条件和叠层顺序对多层磁电弹性板中位移、应力、电势、电位移、磁势、磁感应强度和振动频率沿厚度方向分布的影响。
The scaled boundary finite element method (SBFEM) incorporated with the precise integration technique (PIT) is further extended to present the semi-analytical analysis of static bending and free vibration behaviors of laminated magneto-electro-elastic composite plates. It is applicable to thin and thick multilayered magneto-electro-elastic plates. The basic equations are formulated by only using the two dimensional model, which helps to make sure that the computation is efficient. The discretization is carried out in terms of spectral elements. Only three displacement components, electric and magnetic potentials are selected as the basic variables. Characterized by the important features of the SBFEM, the elastic displacements, electric and magnetic potentials along the thickness direction can be solved analytically. Differing from most plate models taking a priori assumptions on distributions of the mechanical, electric and magnetic variables, the derivation of governing SBFEM equations strictly follows the 3D theory of magneto-electro-elastic materials without introducing any assumptions on multiphysics fields. By virtue of the scaled boundary coordinates and the principle of virtual work, the key partial differential equations are simplified into the governing ordinary differential matrix equation. To increase the accuracy of the SBFEM governing equation, the PIT is utilized, which ensures that any desired accuracy of the results can be reached. Static and dynamic numerical examples show that variations of mechanical, electric, magnetic fields and natural frequencies predicted by the proposed approach are in excellent agreement with the elastic solutions of other methods. Therefore, the versatility and perfect accuracy of the present technique is fully validated. Furthermore, the influences of aspect ratios, boundary conditions and stacking sequences on the cross-thickness distributions of displacements, stresses, electric potential, electric displacements, magnetic potential, magnetic induction and vibration frequencies in the multilayered magneto-electro-elastic plate are discussed.
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影响因子：
4.7
作者：
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通讯作者：
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影响因子：
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