A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUS™ code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.

中文翻译：

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具有三维有限元功能梯度夹层板的自由振动和静力分析

提出了功能梯度材料 (FGM) 夹层板的自由振动和静态响应的三维建模。固有频率和相关的振型以及位移和应力是通过使用 ABAQUS™ 代码中的有限元方法确定的。通过用户定义的材料子程序 UMAT 对三维 (3-D) 砖分级有限元进行编程并合并到代码中。模态和静态分析的结果证明了方形金属陶瓷功能梯度简支板，其陶瓷成分的体积分数随厚度变化的幂律变化。基于 Mori-Tanaka 方案定义点处有效材料属性的全厚度分布。首先，位移的精确值，文献中 FGM 夹层板可用的应力和固有频率用于验证性能并估计开发的 3-D 梯度有限元的准确性。然后，通过改变陶瓷体积分数的体积分数分布和值，对频率分析进行参数研究。