An Improved Method Based on the Total Updated Lagrange Formulation for Shell Element

The finite element method plays a critical role in engineering analysis, where balancing precision and efficiency is essential. Although the traditional Total Updated Lagrange (T.U.L.) formulation substantially shortens the simulating time with acceptable accuracy, it lacks a quantitative equation to confirm the updating step-size. In this paper, an improved variable step-size T.U.L. formulation is proposed, which automatically adjusts the step-size according to the incremental displacement of each element. Unlike the traditional method, the proposed formulation allows the elements in the same system to have various updating intervals. To alleviate the shear locking phenomenon, the interpolations of the classical MITC4 element formulation are adopted for explicit dynamic analysis of shells. Finite element matrices are derived in detail based on the virtual work principle. Several dynamic examples involving large deflection are presented, and the predicted results are in good agreement with those in ANSYS. Compared with the traditional T.U.L formulation, the proposed formulation shows higher efficiency, which is significant for the dynamic simulation of complex structures.