A mixed stress model for linear elastodynamics of arbitrarily curved beams

This work presents a mixed stress finite element for linear elastodynamics of arbitrarily curved beams based on a modified Hellinger–Reissner functional. A rational approach to choose the stress approximation is proposed. In particular, the self-equilibrated stress is augmented by some stress modes obtained from the lower-order displacement approximation using the equilibrium equations, in such a way that the total number of stress modes is equal to the number of strain modes. The rationale is to preserve all the interactions among the stresses, proper of a curved structure without compromising the flexibility of the element. An arbitrarily curved geometry is described using a parametric Hermitian interpolation scheme tuned by minimizing the initial curvature of the arch. The effectiveness of the present approach is numerically demonstrated.