Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

doi:10.1007/s10483-014-1871-7

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (11): 1467-1478.doi: https://doi.org/10.1007/s10483-014-1871-7

• • 上一篇

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

张鹤, 蒋吉清, 张治成

1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P.R. China;
2. School of Civil Engineering, Zhejiang University City College, Hangzhou 310058, P.R. China;
3. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P.R. China

收稿日期:2013-11-29 修回日期:2014-04-30 出版日期:2014-11-01 发布日期:2014-11-01
通讯作者: Zhi-cheng ZHANG, Associate Professor, Ph.D., E-mail: cezhangzc@gmail.com E-mail:cezhangzc@gmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 51108412, 11472244, and 11202186), the National Basic Research Program of China (973 Program) (No. 2013CB035901), the Fundamental Research Funds for the Central Universities (No. 2014QNA4017), and the Zhejiang Provincial Natural Science Foundation of China (No. LR13A020001)

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

He ZHANG, Ji-qing JIANG, Zhi-cheng ZHANG

1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P.R. China;
2. School of Civil Engineering, Zhejiang University City College, Hangzhou 310058, P.R. China;
3. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P.R. China

Received:2013-11-29 Revised:2014-04-30 Online:2014-11-01 Published:2014-11-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 51108412, 11472244, and 11202186), the National Basic Research Program of China (973 Program) (No. 2013CB035901), the Fundamental Research Funds for the Central Universities (No. 2014QNA4017), and the Zhejiang Provincial Natural Science Foundation of China (No. LR13A020001)

摘要/Abstract

摘要： Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model (ALM) is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.

关键词: semianalytical approach, three-dimensional solution, thick plate, functionally grade material

Abstract: Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model (ALM) is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.

Key words: functionally grade material, thick plate, three-dimensional solution, semianalytical approach

中图分类号:

O343

张鹤;蒋吉清;张治成. Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1467-1478.

He ZHANG;Ji-qing JIANG;Zhi-cheng ZHANG. Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1467-1478.

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Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

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