Abstract

The main aim of this study is to establish a hybrid quasi-3D theory for the deflections, stresses and free vibration analysis of bi-functionally graded sandwich plates resting on Pasternak’s elastic foundations. In the proposed hybrid quasi-3D theory, the polynomial function is used to describe the distribution of transverse shear strains through the thickness direction while the trigonometric function is used to describe the thickness stretching effects. The bi-functionally graded sandwich plates are made of one homogeneous core and two different functionally graded face sheets. The governing equations of motion of the plates are established using Hamilton’s principle and they are solved by a closed-form solution via Navier’s technique. The present numerical results are compared with the published results using different higher-order and normal shear deformation theories to show the accuracy and efficiency of the proposed theory. And then the proposed theory was applied to examine the bending and free vibration behavior of the bi-functionally graded sandwich plates. A comprehensive study about the effects of some parameters such as side-to-thickness ratio, aspect ratio, skin-core-skin thicknesses, power-law index and elastic foundation parameters on the bending and free vibration behavior of the bi-functionally graded plates is carried out. The results of the deflections, stresses and frequency of the functionally graded sandwich with two different material face sheets can serve as benchmark solutions for engineering and future works.

摘要

本研究的主要目的是建立一种混合准三维理论，用于基于帕斯捷尔纳克弹性地基的双功能梯度夹层板的挠度、应力和自由振动分析。在所提出的混合准三维理论中，多项式函数用于描述横向剪切应变在厚度方向上的分布，而三角函数用于描述厚度拉伸效应。双功能梯度夹层板由一个均质芯和两个不同的功能梯度面板制成。板块运动的控制方程是使用哈密顿原理建立的，并通过 Navier 技术通过封闭形式的解来求解。将目前的数值结果与使用不同的高阶和法向剪切变形理论发表的结果进行比较，以显示所提出理论的准确性和效率。然后将所提出的理论应用于检验双功能梯度夹层板的弯曲和自由振动行为。综合研究边厚比、纵横比、皮-芯-皮厚度、幂律指数和弹性地基参数等参数对双功能梯度板弯曲和自由振动行为的影响完成了。具有两种不同材料面板的功能分级夹层的挠度、应力和频率的结果可以作为工程和未来工作的基准解决方案。