Configurational forces and ALE formulation for geometrically exact, sliding shells in non-material domains

Abstract

The paper presents a novel Arbitrary Lagrangian–Eulerian formulation for dynamic problems of geometrically exact, sliding shells. In contrast to previous researches where the sliding motions are prescribed at sliding boundaries and the existence of configurational forces is not identified, the configurational momentum equation that governs the evolution of sliding motions is derived in a consistent variational framework in the present paper. To this end, the time-varying material domain due to the presence of sliding motion is mapped onto a time-invariant mesh domain, variations at fixed material and at fixed mesh coordinates are introduced, and their relationship with variation of material coordinates at fixed mesh coordinates are derived. Hamilton’s principle of variation of action is employed to derive the strong form of mechanical and configurational momentum equations together with natural boundary conditions at the sliding boundaries. In the finite element formulation, transfinite interpolation is employed to relate material coordinates of nodes inside the domain to the values at the sliding boundaries. The discrete form of Hamilton’s variational principle leads to discrete governing equations of the proposed ALE formulation. The generalized-α scheme is adjusted to integration the resulting mechanical and configurational momentum equations. Numerical examples are presented to validate correctness and efficiency of the proposed formulation.