A formulation of the 2D refined shell theory incorporating transverse shear in the rescaled coordinates and angles of rotation is considered. This novel approach provides the first asymptotically accurate and inherently locking-free finite element implementation. Numerical simulations of semi-cylindrical shells demonstrate excellent agreement between the analytical solution, the 2D refined shell theory, and three-dimensional elasticity theory, validating the effectiveness and accuracy of the method.

翻译：本文提出了一种在重标度坐标和旋转角中考虑横向剪切的二维精细化壳理论公式。这一创新方法首次实现了渐近精确且本质上无闭锁的有限元实施。通过对半圆柱壳的数值模拟，解析解、二维精细化壳理论与三维弹性理论之间展现出高度一致性，验证了该方法的有效性与精确性。