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研究了四边简支具有功能梯度芯材的夹层板在分布载荷作用下的弯曲问题。基于Reissner假设,根据功能梯度材料的本构方程得出了应力、位移及内力的表达式,得到功能梯度夹层板的平衡方程;针对四边简支的边界条件,通过将挠度w与横向剪力Qx、Qy用双三角级数展开的方法,求解平衡方程。采用本文方法分别求解了均布载荷作用下、芯材弹性模量线性变化的功能梯度夹层板与芯材为均质各向同性材料的夹层板的弯曲挠度,并通过与经典解及有限元解进行比较,证明了本文方法的正确性。
The bending problem of sandwich plate with functionally graded core with four edges simply under distributed load is studied. Based on the Reissner assumption, the expressions of stress, displacement and internal force are obtained according to the constitutive equations of functionally graded material. The equilibrium equations of the functionally graded sandwich plate are obtained. For the boundary conditions of four-sided simple support, the deflection w and the transverse shear force Qx , Qy uses the double trigonometric series expansion method to solve the equilibrium equation. In this paper, the bending deflection of the sandwich panel with a linear gradient of the elastic modulus of the core under uniformly distributed loads and the sandwich with the core of the isotropic isotropic material were solved respectively. By using the proposed method, Compared to prove the correctness of the method in this paper.