A formulation of the asymptotically exact first-order shear deformation theory for linear-elastic homogeneous plates in the rescaled coordinates and angles of rotation is considered. This allows the development of its asymptotically accurate and shear-locking-free finite element implementation. As applications, numerical simulations are performed for circular and rectangular plates, showing complete agreement between the analytical solution and the numerical solutions based on two-dimensional theory and three-dimensional elasticity theory.

翻译：考虑在重缩放坐标和旋转角下，针对线弹性均质板提出渐近精确的一阶剪切变形理论公式。该公式允许开发具有渐近准确性和无剪切闭锁特征的有限元实现。作为应用，对圆形板和矩形板进行了数值模拟，结果表明基于二维理论和三维弹性理论的分析解与数值解完全吻合。