板面为各向异性面的横观各向同性拉伸板的精化理论

Refinrd theory of a transversely isotropic stretching plate with anisotropic plane

基于板面为各向异性面的横观各向同性弯曲板的精化理论,对板面为各向异性面的横观各向同性拉伸板进行了分析和研究。不作任何预先假设,利用横观各向同性弹性理论和Elliott-Lodge通解,获得了由板中面上的位移和横向正应变表示的位移场和应力场。根据Lur’e方法和边界条件获得了板面受横向载荷的精化方程,略去高阶项后获得了板的近似控制微分方程。将各向同性材料常数代入到方程中,得到的精化理论与各向同性拉伸板的精化理论一致。

In this paper,based on the refined theory of a transversely isotropic bending plate with the anisotropic plane,the transversely isotropic stretching plate with the anisotropic plane is studied and analysed. By using Elliott- Lodge solution and transversely isotropic elastic theory,the displacement and stress components were obtained in terms of the mid-plane displacements and transverse normal strain without any pre-assumptions. The refined equation for the plate with transverse surface loadings is obtained using Lur’e method and boundary conditions and then omitting the high orders. Also, the approximate governing differential equation is obtained. The result is consistent with the refined theory of isotropic plates for extensional deformation by substituting isotropic material constants into the equation.