基于Reissner理论的硬夹心夹层板的弯曲研究

传统的夹层板理论都是将夹心视为软夹心,不考虑其面内应力分量和抗弯刚度.本文在修正了Reissner理论的基础上,研究了硬夹心夹层板的弯曲问题,根据最小势能原理得到了具有3个广义位移的弯曲基本方程和边界条件,并对其进行了简化.同时还研究了硬夹心夹层板弯曲问题的有限元格式,推导了4节点四边形等参单元单元刚度矩阵和等效节点载荷列阵,并给出了矩形填充多孔夹层板的ANSYS实体模型解,计算结果表明位移的有限元解收敛于解析解且具有足够的精度,与ANSYS实体模型解也有较好的一致性.

Study on bending of hard core sandwich plates based on Reissner＇s sandwich theory

In the traditional theories of sandwich plates the core is soft so the in-plane stress components and bending stiffness are neglected. This paper explores the bending problem of hard core sandwich plates based on the revised Reissner＇s hypothesis. The basic equations and boundary conditions expressed with three generalized displacements are established and simplified according to the principle of minimum potential energy. In addition this paper presents the finite element model for the bending problem of hard core sandwich plates. Based on this model a four-node quadrilateral isoparametric element is constructed, the element stiffness matrix and equivalent nodal load vector are derived. It is built the solid model for ANSYS. According to the numerical analysis the finite element solutions converge to the analytical solutions with sufficient accuracy and also consistent with solutions of ANSYS.