Large deflection analysis of functionally graded circular microplates with modified couple stress effect

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• 作者：Yong-Gang Wang ; Hui-Fang Song ; Wen-Hui Lin…
• 关键词：Functionally graded materials ; Circular microplate ; Small scale effect ; Modified couple stress theory ; Axisymmetric large deformation ; Von Kármán nonlinear theory
• 刊名：Journal of the Brazilian Society of Mechanical Sciences and Engineering
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：39
• 期：3
• 页码：981-991
• 全文大小：
• 刊物主题：Mechanical Engineering;
• 出版者：Springer Berlin Heidelberg
• ISSN：1806-3691
• 卷排序：39

文摘

This paper addresses the microstructure dependent axisymmetric large deflection bending of pressure loaded circular microplates made of functionally graded materials in two cases of boundary conditions. The modulus of elasticity is assumed to vary across the thickness direction so the power-law distribution is used to describe the constituent components, while Poisson’s ratio depends weakly on position and is assumed to be a constant. The underlying higher order continuum theory behind the proposed approach is the modified couple stress theory, which can take into account the small size effects through using one scale parameter. The governing differential equations with nonlinearity and coupling between the deflection and radial membrane force are developed following the von Kármán assumption. By employing the orthogonal collocation point technique, the governing equations are transformed into systems of algebraic equations. The numerical solutions are generated through the Newton–Raphson method. Selected results are presented for the bending deflection of FGM circular microplates and influences played by the important parameters including length scale parameter, functionally graded variation, boundary conditions and the symmetrical transverse loadings are discussed.