Purpose

The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Design/methodology/approach

Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.

Findings

The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.

Originality/value

Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

中文翻译：

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利用反三角剪切变形理论分析FGM板的自由振动和屈曲

目的

本文的目的是对功能梯度材料（FGM）板进行自由振动和屈曲分析。

设计/方法/方法

利用基于有限元方法的反三角剪切变形理论（ITSDT），推导了不同边界条件下FGM矩形板的平衡和稳定方程。本分析使用在每个节点处具有七个自由度的八节点矩形板单元。已经考虑了幂律分布方法，以便在功能梯度板的整个厚度范围内对陶瓷和金属相的成分进行连续梯度变化。

发现

结合ITSDT的有限元公式和FGM板本构模型的规定已通过数字代码实现，从而获得了单轴和双轴压缩载荷下的固有频率和临界屈曲载荷。研究了材料梯度，体积分数指数，跨度与厚度之比以及边界约束对自由振动和屈曲响应的影响。

创意/价值

开发和验证了使用ITSDT预测FGM板在不同载荷，几何和边界条件下的结构响应的有限元方法。