This article investigates the bending response performances of the magneto–electro–elastic (MEE) laminated plates resting on the Winkler foundation or the elastic half-space subjected to a transverse mechanical loading .By assuming that the foundation is not electrically and magnetically conductive, the scaled boundary finite element method (SBFEM) based on the three-dimensional (3D) theory of elasticity is applied for both the simulation of the MEE laminated plate and the elastic half-space. The SBFEM model considers the generalized displacement involving the elastic displacement, electric potential and magnetic potential as the nodal degree of freedom for the MEE laminated plates, and only the in-plane of the MEE laminated plate or the boundary of the elastic half-space needs to be discretized leading to reduce the spatial dimension by one. Furthermore, in the SBFEM, the governing equations can be solved by using an analytical approach in the radial direction of the scaled coordinate system, so that it is particularly suitable for the simulation of the elastic half-space. For the Winkler foundation–plate system, the global stiffness coupling governing equation that includes the interaction between the MEE laminated plate and the Winkler foundation is derived directly from the 3D elasticity equations of the MEE laminated plate by assuming that the foundation reactions are proportional to the transverse displacements of the plate structure. While for the MEE laminated plate-half-space system, the whole domain is divided into three sub-domains including the MEE laminated plate structure, the near and semi-infinite far foundation systems based on the sub-structure method, and then the stiffness matrix of each sub-domain can be determined by means of the SBFEM. As a result, the global stiffness equation of the plate-half-space system can be assembled according to the principle of the degree of freedom matching at the same nodes. The numerical results obtained for limiting cases by using the proposed method were compared with the published works and showed excellent agreements with the solutions based on the analytical and numerical approaches, so that the accuracy and applicability of the proposed formulations for the analysis of the interaction problems between the MEE laminated plate and the Winkler foundation or elastic half-space can be verified. Moreover, several numerical examples with various material properties, geometries, stacking sequences, aspect ratios, and supported boundary conditions were presented to show the effects of which on the responses of the plate–foundation system.

本文研究了放置在Winkler基础上或承受横向机械载荷的弹性半空间上的磁电弹性（MEE）层压板的弯曲响应性能。假定基础不导电和不导电，则基于三维（3D）弹性理论的比例边界有限元法（SBFEM）被用于MEE层压板和弹性半空间的模拟。SBFEM模型将涉及弹性位移，电势和磁势的广义位移视为MEE叠层板的节点自由度，仅需要MEE叠层板的平面内或弹性半空间的边界离散化导致空间尺寸减小一倍。此外，在SBFEM中，可以使用解析方法在比例坐标系的径向上求解控制方程，因此它特别适合于弹性半空间的模拟。对于Winkler地基-板系统，假定基础反作用力与MEE层压板的3D弹性方程式直接相关，则包括MEE层压板和Winkler地基之间相互作用的整体刚度耦合控制方程式。板结构的横向位移。对于MEE叠层板半空间系统，整个域分为三个子域，包括MEE叠层板结构，基于子结构方法的近无限和半无限远基础系统，然后可以通过SBFEM确定每个子域的刚度矩阵。结果，可以根据在相同节点处的自由度匹配的原理来组装板半空间系统的整体刚度方程。通过使用所提出的方法获得的有限情况下的数值结果与已发表的作品进行了比较，并显示出与基于解析和数值方法的解决方案的极好的一致性，从而所提出的公式对于相互作用问题的分析的准确性和适用性可以验证MEE层压板与Winkler基础之间的距离或弹性半空间。此外，还有一些具有各种材料特性，几何形状，堆叠顺序，长宽比的数值示例，