Bending analysis of the simply supported functionally graded sandwich plate under distributed load
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摘要: 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。Abstract: The bending analysis was presented for simply supported sandwich plate with a functionally graded core subjected to distributed load. Based on the Reissner assumptions, the expressions of the stress, displacements and internal force were presented according to the constitutive relations of functionally graded materials, and the equilibrium equations of functionally graded sandwich plate were given. Finally, the solutions of the equilibrium equations were derived by expanding the deflection w, transverse shearing force Qx and Qy with double trigonometric series which satisfied the simply supported boundary conditions. In the example, the proposed solution was validated by comparing the degenerated results for sandwich plates with a homogeneous isotropic core subjected to uniform pressure to the classical elastic solution, and comparing the result for sandwich plate with a functionally graded core to FEM (Finite element method), whose Young’s modulus obey a linear distribution in the thickness.
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