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A three variable refined shear deformation theory for porous functionally graded doubly curved shell analysis

机译：多孔功能梯度双曲壳分析的三变量精细剪切变形理论

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摘要

This study develops a three variable refined shear deformation theory to analyze the free vibration and bending behavior of porous functionally graded doubly curved shallow shells subjected to uniform and sinusoidal pressure. Shell displacements are assumed to be caused by extensional, bending, and shear effects. The in-plane displacements produced by bending effects are considered taking the form of the classical plate theory. The in-plane displacements produced by shear effects satisfy the stress-free and strain-free condition at the top and bottom surfaces, eliminating the usage of the shear correction factor in the present study. Two porosity types influence material properties and structure behaviors in different aspects. Hamilton's principle is used to derive Euler-Lagrange equations. Spatial solutions for the differential equation are assumed satisfying boundary conditions and their time-dependent amplitude equations are obtained by applying the Bubnov-Galerkin technique. Natural frequencies and transverse deflections of the shell in different geometry configurations and different porosity types and degrees are obtained and compared. The proposed theory is proved feasible to be applied in the analysis of functionally graded plates and shells with porosity. (C) 2019 Elsevier Masson SAS. All rights reserved.
机译：这项研究提出了一种三变量精制剪切变形理论，以分析多孔功能梯度双曲浅壳在均匀和正弦压力下的自由振动和弯曲行为。假定壳位移是由拉伸，弯曲和剪切效应引起的。由弯曲效应产生的平面内位移被视为采用经典板理论的形式。由剪切作用产生的面内位移满足上下表面无应力和无应变的条件，从而消除了本研究中使用的剪切校正因子。两种孔隙率类型在不同方面影响材料特性和结构行为。汉密尔顿原理用于推导欧拉-拉格朗日方程。假定微分方程的空间解满足边界条件，并且通过应用Bubnov-Galerkin技术获得其随时间变化的振幅方程。得到并比较了不同几何结构，不同孔隙率类型和程度的壳的固有频率和横向挠度。该理论被证明是可行的，可用于功能梯度板和壳的分析。 （C）2019 Elsevier Masson SAS。版权所有。

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