A Unified Approach for the Nonlinear Dynamics of Rods and Shells Using an Exact Conserving Integration Algorithm

A unified formulation is presented in this work for the nonlinear dynamics analysis of rods and shells undergoing arbitrarily large deformations and rigid body motions. Based on our previous works, we develop a special notation and describe both rod and shell kinematics with the same set of expressions. Differences are observed only at the constitutive equation. Important aspects of the above-mentioned works are preserved, such as the special paramete-rization of the rotation field, the concept of stress resultants and the ability to handle nonlinear hyperelastic materials in a totally conserving way. The time integration algorithm developed for the equations of motion follows an energy-momentum approach and results in a fully conserving scheme. The formulation is well-suited for (but not restricted to) finite element approximations and its unified character leads to a straightforward simultaneous implementation of both rod and shell dynamics models within a finite element code. Assessment is made by means of numerical simulations.