On a consistent finite-strain plate theory of growth
On a consistent finite-strain plate theory of growth
复制标题
一致的有限应变板生长理论
DOI：
10.1016/j.jmps.2017.10.017
复制
发表时间：
2018-02
影响因子：
5.3
通讯作者：
Dai Hui Hui
中科院分区：
文献类型：
--
作者：
Wang Jiong;Steigmann David;Wang Fan Fan;Dai Hui Hui
本文建立了一致的生长诱发大变形有限应变板理论。用变分方法建立了由力学平衡方程和不可压缩约束方程组成的板模型的三维控制系统。然后对未知函数进行关于厚度变量的级数展开。利用三维平衡方程和表面边界条件，成功地建立了膨胀系数的递推关系。由此得到了三维矢量板方程，并给出了相应的边界条件。结果表明，板方程保证了总能量泛函变分中所有项的渐近级数。文中还推导了板方程的弱形式，为以后的数值计算提供了依据。作为板理论的应用，给出了两个超弹性薄板生长引起的变形和不稳定性的算例。在这些算例中得到了一些解析结果，可以用来描述大变形和揭示薄板的分叉特性。并将现行板理论的结果与经典的Föppl-von Kármán板理论的结果进行了比较，从而说明了现行板理论的有效性和优越性。
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 hyperelastic 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 Föppl-von Kármán plate theory, from which the efficiencies and advantages of the current plate theory can be demonstrated.
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影响因子：
5.3
作者：
Budday S;Steinmann P;Kuhl E
通讯作者：
Kuhl E
DOI：
10.1201/9780849384165
发表时间：
2006-11
期刊：
--
影响因子：
--
作者：
J. Reddy
通讯作者：
J. Reddy
DOI：
10.5860/choice.28-2130
发表时间：
1990-06
期刊：
--
影响因子：
--
作者：
Y. Fung;S. Cowin
通讯作者：
Y. Fung;S. Cowin
DOI：
10.1016/s0020-7683(02)00352-9
发表时间：
2002-09-01
影响因子：
3.6
作者：
Lubarda, VA;Hoger, A
通讯作者：
Hoger, A
影响因子：
1.6
作者：
Newell, AC;Shipman, PD
通讯作者：
Shipman, PD