Motion State Factor Driven for Doubly-Curved Shallow Shell Deformation Reconstruction

The conventional shape sensing method, based on C0 continuity, is recognized for its computational efficiency. However, it is prone to shear locking due to low-order polynomial interpolation in shell analysis, introducing two primary challenges. Firstly, it lacks consideration for C1 continuity. Secondly, existing high-order polynomial interpolation methods significantly increase the number of degrees of freedom (DOF), reducing computational efficiency. Therefore, a brand-new real-time structural health monitoring (SHM) method driven by motion state factor instead of nodal factors is proposed. This method accommodates all deformation modes of shallow shells with C1 continuity and improves the shape function's order without additional DOF. It begins with deriving motion states from compatibility equations, leading to a polynomial shape function expression. Subsequently, conversion equations for real constants and DOF are developed, establishing a least-squares model for theoretical strains and measured values. Following that, the higher-order element formula, optimized for minimal DOF, is then inferred from varied displacement data. Finally, simulations and experiments demonstrate this method's effectiveness, accuracy, and reliability in analyzing shallow shell elements.