基于分层一阶剪切理论的夹层梁弯曲特性

为了构建夹层梁的弯曲位移模型，提出了一种基于二变量的分层一阶剪切理论，该理论满足于Timoshenko梁平均切应变要求.然后，利用最小势能原理建立弯曲控制方程并用Rayleigh Ritz法求解.结果表明:由于考虑了上下表板抵抗剪力的能力，分层一阶剪切理论预测的跨中挠度比传统夹层梁一阶剪切理论较为保守，用其计算的芯层切应变与切应力比传统一阶剪切理论低，但随着芯层厚度的增加，两种理论的计算差异逐渐减小，通过分层一阶剪切理论反推出的剪力满足于静力平衡条件.

Bending Property of Sandwich Beam Based on Layer Wise First Order Theory

A new simple layer wise first order theory(LFOT) with two variables was proposed, in which the shear strain was piecewise first order function and integration of it through the laminate thickness could fulfill Timoshenko shear strain theory. The equilibrium equation was derived by minimum energy principle and solved by Rayleigh Ritz method. After comparison with classical first order theory(CFOT) and test results, it has been shown that the predicted value by LFOT is relatively more conservative than CFOT because of considering skin resistance to shear force. Generally, the core shear strain and stress calculated by LFOT is lower than that of CFOT with the same construction and loading level. But difference between the two theories becomes smaller with the increasing core thickness. Furthermore, the shear resultant derived by LFOT fulfils the static equilibrium.