压电弹性层合梁的电场作用下的二维解析解

由压电弹性介质的二维本构关系，通过假设电势分布和利用应力边界条件，得到其应力函数，由此假设弹性体的应力函数，利用几何方程分别得到弹性和压电体的位移，最后利用应力边界条件、应力和位移连续条件以及位移边界条件，推导出一端固支带压电层的弹性梁在电场作用下的位移、应力分布的解析表达式，并给出了算例。

Analytical Solution to the Piezoelastic Laminated Beam Subjected to Electric Field

Based on the two dimensional constitutive relationship of piezoelastic material, an analytical solution to a cantilever beam with piezoelectric layers subjected to electric field was derived together with an example. The stress function of the piezoelectric layer was obtained through the assumed electric potential and using the stress boundary condition, thereby the stress function of the elastic beam was assumed. The displacements of the piezoelectric layers and the elastic beam can be obtained using the stress boundary, the stress and displacement continuity condition and the displacement boundary conditions.