In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations.

在本文中，我们从一致有效的渐近板理论推导出由不可压缩的新胡克材料组成的夹紧板的弱形式。利用有限元软件COMSOL，我们研究了弱形式的数值解。我们通过比较二维弱形式和三维模型的数值结果来展示弱形式的准确性和效率。作为比较的基础，我们选择位移、第二 Piola-Kirchhoff 应力和底部的 Green-Lagrange 应变的数值。数值模拟针对三种不同的厚度-跨度比情况进行，包括（1）非常薄的板，（2）薄板，和（3）中厚板。