均布荷载作用下悬臂磁电弹性梁的解析解

对磁电弹性平面问题进行了研究，给出了用拟调和位移函数表达的通解，进而以试凑法按平面应力问题推导出了均布荷载作用下悬臂磁电弹性粱的解析解，所得解有易于理解、便于校对、形式统一简洁的特点。本文还将计算结果与压电材料和弹性材料相应结果进行了分析、比较，为验证各种数值计算方法提供了参考依据。

Analytical Solution to Magneto-electro-elastic Cantilever Beam Under Uniform Load

On the basis of two-dimensional constitutive relationships of magneto-electro-elastic materials, the general solution to the problem of plane stress is derived and expressed in terms of four displacement functions (weighted harmonic functions). The analytical solution to a magneto-electro-elastic cantilever beam is obtained with the method of trial-and-error, which is clearly understood, conveniently proofread and concisely expressed. And the numerical results are given and compared with those of a piezoelectric cantilever beam and an orthotropic elastic beam, which possess the same elastic, piezoelectric and dielectric constants, and boundary conditions as the magneto-electro-elastic cantilever beam. It is obvious that the displacements and electric potential caused by uniform load on the upper surface are different, whereas the electric displacement exhibits no noticeable difference. The solutions can serve as benchmarks for numerical methods, such as the finite element method, the boundary element method, etc.