An improved Vector Form Intrinsic Finite Element (VFIFE) method with S–R decomposition from thin to thick shell analysis

This paper presents an improved Vector Form Intrinsic Finite Element (VFIFE) method for the unified analysis of thin and thick shell structures. The proposed formulation integrates the Strain–Rotation (S–R) decomposition theorem and the Mixed Interpolation of Tensorial Components (MITC) technique into the VFIFE framework. Specifically, the S–R decomposition is incorporated into VFIFE to provide a unique and mechanically consistent separation of strain and rigid-body rotation, eliminating the arbitrariness associated with fictitious reverse motion in conventional formulations. A three-node flat-shell element based on the Reissner–Mindlin theory and the MITC3+ technique is formulated within VFIFE to effectively alleviate transverse shear locking, enabling accurate analysis across a wide range of thickness ratios. The proposed formulation is validated through fundamental patch tests and a series of benchmark problems involving thin and thick shells under static, dynamic, and geometrically nonlinear conditions. The patch tests demonstrate its effectiveness in capturing large rigid-body motions and large-deflection behaviors, while subsequent benchmarks confirm high accuracy, robust convergence, and reliable performance for general shell-structure analysis.