Buckling of a Reissner–Mindlin plate of piezoelectric semiconductors

We study the buckling of a Reissner–Mindlin plate of piezoelectric semiconductors. A set of two-dimensional equations is established. The pre-buckling state is determined by the zero-order plate equations for in-plane extension/compression. The buckling state is governed by the first-order plate equations for bending with shear deformation. A rectangular plate is analyzed using bi-sinusoidal trigonometric series. The buckling loads and modes are obtained. It is shown that piezoelectric coupling exhibits a stiffening effect and raises the buckling load. At the same time semiconduction reduces the piezoelectric stiffening effect because of the screening effect of the mobile charges. The mobile charges assume various in-plane distributions in different buckling modes. Buckling loads and modes of circular plates are also presented.