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Five-unknowns generalized hybrid-type quasi-3D HSDT for advanced composite plates

机译：用于高级复合板的五种未知的广义混合型准3D HSDT

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摘要

In this paper a 5-unknowns generalized hybrid-type quasi-3D HSDT for the static analysis of functionally graded single and sandwich plates is presented. Generalized hybrid-type modeling can adopted with any kind of shear strain shape functions for the inplane and transverse displacement, and therefore infinite hybrid-type (non-polynomial, polynomial, mixed type) displacement based shear deformation theory complying with the free surface boundary condition can be obtained. The key feature of this theory is that, in addition to including stretching, it has only 5 unknowns in the displacement field modeling as the first order shear deformation theory (FSDT). The generalized hybrid-type theory is also quasi-3D because the 3D Hooke's law equation is utilized, i.e. σ_(zz) ≠ 0. The generalized governing equations and boundary conditions are derived by employing the principle of virtual works. A generalized Navier-type closed-form solution is obtained for functionally graded single and sandwich plates subjected to transverse load for simply supported boundary conditions. Analytical results from the new generalized hybrid-type quasi-3D higher order shear deformation theory (HSDT) are compared with the FSDT, other quasi-3D HSDTs, and refined HSDTs. The fundamental conclusions that emerge from the present numerical results suggest that: (a) infinite shears strain shape function can be evaluated by using the present theory; (b) polynomial shear strain functions appear to be a good choice for the implementing of a quasi-3D HSDT based on this generalized quasi-3D hybrid type HSDT; (c) this generalized theory can be as accurate as the 6-unknown generalized hybrid-type quasi-3D HSDT; (d) the best HSDT with stretching effect and 5-unknows can be obtained from the present generalized theory, this can be done by optimizing a theory that for example has a given non-polynomial inplane and transverse shears strain shape functions.
机译：本文提出了一种5种未知的广义混合型准3D HSDT，用于对功能梯度单板和夹心板进行静态分析。平面和横向位移可以采用具有任何剪切应变形状函数的广义混合类型建模，因此符合自由表面边界条件的基于无限混合类型（非多项式，多项式，混合类型）的位移变形理论可以获得。该理论的关键特征在于，除了包括拉伸之外，它在位移场建模中仅具有5个未知数（作为一阶剪切变形理论（FSDT））。广义混合类型理论也是准3D的，因为利用了3D虎克定律方程，即σ_（zz）≠0。广义控制方程和边界条件是通过虚构原理导出的。对于在简单支撑边界条件下承受横向载荷的功能梯度单板和夹心板，可以获得广义的Navier型封闭形式解。将新的广义混合型准3D高阶剪切变形理论（HSDT）的分析结果与FSDT，其他准3D HSDT和改进的HSDT进行了比较。从目前的数值结果得出的基本结论表明：（a）可以通过使用本理论来评估无限剪力应变形状函数； （b）基于这种准3D混合类型HSDT，多项式剪应变函数似乎是实现准3D HSDT的好选择； （c）这种广义理论可以和6种未知的广义混合型准3D HSDT一样准确； （d）可以从当前的广义理论中获得具有拉伸效果和5个未知数的最佳HSDT，这可以通过优化例如具有给定的非多项式面内和横向剪切应变形状函数的理论来完成。

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