An efficient nonuniform ALE formulation for dynamic analysis of variant-direction sliding plates/shells

Variant-direction sliding shell structures exhibit superior engineering adaptability compared to conventional single-direction configurations. While the Arbitrary Lagrangian-Eulerian (ALE) framework has become a standard tool for modeling sliding shells, two critical limitations persist: (1) excessive computational overhead due to complex 2D mesh-material mapping relationships, and (2) inability of some 1D mapping-based ALE formulations to capture variant-directional sliding behaviors. This study presents an efficient ALE shell formulation specifically tailored for the simulation of variant-direction sliding mechanics. The proposed method distinguishes mass flow from spatial motion using mesh and material nodes, and decomposes the virtual displacement on the Euler boundaries. A novel nonuniform mesh-material mapping formula is derived by simplifying the 2D bilinear mapping to reduce complexity. The generalized elastic forces are simplified using the Reynolds transport theorem, the sliding constraints are simplified using differential-algebraic equations (DAEs), and d'Alembert's Principle is adopted on the mesh domain to derive the final governing equation. The proposed ALE shells based on nonuniform mesh-material mappings achieve comparable modeling accuracy and numerical convergence to conventional 2D mesh-material mapping-based ALE shells, yet demonstrate computational efficiency orders of magnitude higher. This advancement stems from the capability of nonuniform mappings to support ALE shell modeling of variant-direction sliding shells. Besides, nonuniform ALE shells are particularly adept at resolving sliding shell problems involving contact clearances, showcasing remarkable potential for broad engineering applications.