文献类型：期刊文献

英文题名：On a consistent finite-strain plate theory of growth

作者：Wang, Jiong[1];Steigmann, David[2];Wang, Fan-Fan[3];Dai, Hui-Hui[4]

机构：[1]South China Univ Technol, Sch Civil Engn & Transportat, Guangzhou 510640, Guangdong, Peoples R China;[2]Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USA;[3]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[4]City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon Tong, Hong Kong, Peoples R China

年份：2018

卷号：111

起止页码：184

外文期刊名：JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

收录：;EI(收录号：20174604392060);WOS:【SCI-EXPANDED(收录号:WOS:000424178500010)】；

基金：This paper was supported by a GRF grant (Project No.: CityU 11303015) from the Research Grants Council of Hong Kong SAR, China. Jiong Wang is supported by a grant from the National Nature Science Foundation of China (Project No.: 11602086) and the Guangdong Nature Science Funds for Distinguished Young Scholar (Project No.: 2015A030306009). David Steigmann gratefully acknowledges the support of the US NSF through grant CMMI 1538228.

语种：英文

外文关键词：Finite elasticity; Growth; Consistent plate theory; Bifurcation analysis; Analytical solutions

摘要：In this paper, a consistent finite-strain plate theory for growth-induced large deformations is developed. The three-dimensional (3D) governing system of the plate model is formulated through the variational approach, which is composed of the mechanical equilibrium equation and the constraint equation of incompressibility. Then, series expansions of the unknown functions in terms of the thickness variable are adopted. By using the 3D equilibrium equations and the surface boundary conditions, recursion relations for the expansion coefficients are successfully established. As a result, a 2D vector plate equation with three unknowns is obtained and the associated edge boundary conditions are proposed. It can be verified that the plate equation ensures the required asymptotic order for all the terms in the variations of the total energy functional. The weak formulation of the plate equation has also been derived for future numerical calculations. As applications of the plate theory, two examples regarding the growth-induced deformations and instabilities in thin hyper-elastic plates are studied. Some analytical results are obtained in these examples, which can be used to describe the large deformations and reveal the bifurcation properties of the thin plates. Furthermore, the results obtained from the current plate theory are compared with those obtained from the classical Foppl-von karman plate theory, from which the efficiencies and advantages of the current plate theory can be demonstrated. (C) 2017 Elsevier Ltd. All rights reserved.