Civil Engineering Association

A new energy and momentum conserving algorithm for the non-linear dynamics of shells

A numerical time-integration scheme for the dynamics of non-linear elastic shells is presented that simultaneously and independent of the time-step size inherits exactly the conservation laws of total linear, total angular momentum as well as total energy. The proposed technique generalizes to non-linear shells recent work of the authors on non-linear elastodynamics and is ideally suited for long-term/large-scale simulations. The algorithm is second-order accurate and can be immediately extended with no modification to a fourth-order accurate scheme. The property of exact energy conservation induces a strong notion of non-linear numerical stability which manifests itself in actual simulations. The superior performance of the proposed scheme method relative to conventional time-integrators is demonstrated in numerical simulations exhibiting large strains coupled with a large overall rigid motion. These numerical experiments show that symplectic schemes often regarded as unconditionally stable, such as the mid-point rule, can exhibit a dramatic blow-up in finite time while the present method remains perfectly stable.