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A trigonometric plate theory with 5-unknowns and stretching effect for advanced composite plates

机译：具有未知数和拉伸效应的5级三角板理论用于高级复合板

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摘要

A simple but accurate trigonometric plate theory (TPT) for the bending analysis of functionally graded single-layer and sandwich plates is presented. The significant feature of this formulation is that, in addition to including the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 as in the well-known TPT. The TPT possesses in-plane and transverse shear strain shape functions (sin(z/m) and cos(z)) containing the parameters "m" and "n" that should be properly selected. The governing equations and boundary conditions are derived by employing the principle of virtual work. A Navier-type closed-form solution is obtained for functionally graded single-layer and sandwich plates subjected to bi-sinusoidal load for simply supported boundary conditions. Numerical results of the present TPT are compared with the FSDT, other quasi-3D higher order shear deformation theories (HSDTs), and 3D solutions. The important conclusions that emerge from the present numerical results suggest that: (a) for powerly graded plates the present TPT produces as good results as refined quasi-3D HSDTs, however (b) for exponentially graded plates the present TPT yields improved results; and (c) it is possible to gain accuracy keeping the unknowns' number constant but by selecting properly the parameter "m" and "n".
机译：提出了一种简单而精确的三角板理论（TPT），用于功能梯度的单层和夹心板的弯曲分析。该公式的显着特征是，除了包括厚度拉伸效果外，它还处理5个未知数作为一阶剪切变形理论（FSDT），而不是众所周知的TPT中的6个未知数。 TPT具有面内和横向剪切应变形状函数（sin（z / m）和cos（z / n）），其中应适当选择参数“ m”和“ n”。利用虚功原理推导了控制方程和边界条件。对于功能分级的单层和夹层板，在简单支持的边界条件下承受双正弦载荷，可获得Navier型封闭形式的解决方案。将本TPT的数值结果与FSDT，其他准3D高阶剪切变形理论（HSDT）和3D解决方案进行了比较。从当前数值结果得出的重要结论表明：（a）对于强梯度板，本发明的TPT产生与精制准3D HSDT一样好的结果，但是（b）对于指数级板，本发明的TPT产生改进的结果； （c）通过适当选择参数“ m”和“ n”，可以使未知数保持恒定，从而获得精度。

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