基于高阶变形理论的硬夹芯夹层板横向载荷条件下的弯曲

Bending of Sandwich Plates With Hard Cores Under Transverse Loading Based on the High-Order Deformation Theory

考虑面板和夹芯的面内刚度及抗弯刚度,基于高阶变形理论考虑各层的横向抗剪刚度,并根据横向剪应变分布情况给出应力函数,基于广义虚位移原理推导了夹层板的基本方程.详细研究了四边简支受横向载荷条件下的夹层板的弯曲,对比计算了面板与芯层厚度变化对计算结果的影响,并与一阶变形理论计算结果进行对比.研究了厚度方向的剪应变分布情况以及中面法线变形后的形态,给出了横向剪应变引起的附加转角在面内的分布情况.

Based on the high-order deformation theory,the in-plane stiffness and bending stiffness of both surface layer and core layer of the sandwich plate were considered to derive the transverse shearing stiffnesses of all the layers. The transverse stress function was given according to the transverse strain distribution,and the differential equations for the sandwich plate were deduced with the generalized principle of virtual displacement. The bending deformation of simply supported rectangular sandwich plates with different core-to-surface thickness ratios were detailedly studied under transverse loading,and the calculation results were compared with those from the 1st-order deformation theory to give a bigger relative deformation difference at a smaller thickness ratio. The distribution of transverse strain along the thickness direction makes a half sine curve,and the center-plane normal line distortion culminates at the surface height.