文献类型：期刊文献

英文题名：A uniformly-valid asymptotic plate theory of growth with numerical implementation

作者：Du, Ping[1];Wang, Fan-Fan[2];Wang, Jiong[1,3]

机构：[1]South China Univ Technol, Sch Civil Engn & Transportat, Guangzhou 510640, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[3]South China Univ Technol, State Key Lab Subtrop Bldg Sci, Guangzhou 510640, Peoples R China

年份：2023

卷号：239

外文期刊名：INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES

收录：;EI(收录号：20230213352305);WOS:【SCI-EXPANDED(收录号:WOS:000906650700001)】；

基金：Acknowledgments This work is supported by the National Natural Science Foundation of China (Project No.: 11872184) .

语种：英文

外文关键词：Growth-induced deformation; Finite-strain plate theory; Asymptotic analysis; Weak formulation; Numerical simulation

摘要：In this paper, we aim to develop a simplified and uniformly-valid finite-strain plate theory of growth. First, starting from a consistent finite-strain plate theory of growth proposed in our previous work, we specify the magnitudes of growth functions in five different cases and conduct systematic asymptotic analyses, from which the original plate theory can be reduced to some classical plate and membrane theories. Based on the asymptotic analyses, it is found that some terms in the original plate equations (which contain the high-order stress tensor S(2)) always have higher asymptotic orders. By dropping these terms, the plate equations can be simplified significantly. Then, a reduced finite-strain plate theory of growth is established, which is valid in a wide range of growth and mechanical loading conditions. The associated weak form of this uniformly-valid plate theory has also been derived for numerical implementation. To demonstrate the efficiency of this plate theory, it is implemented into a finite element software and applied to study four typical examples. To verify the accuracy of the 2D plate models, the corresponding 3D volume models have also been constructed for these examples. Through some comparisons, it is found that the numerical results obtained from the 2D and 3D models can fit each other quite well. Furthermore, the numerical calculations based on the plate models show obvious advantages in the aspects of computational efficiency, convergence rate and stability. In our opinion, the uniformly-valid asymptotic plate theory of growth proposed in the current work is adequate for studying the complex growth behaviors of thin hyperelastic plates.