A family of total Lagrangian Petrov–Galerkin Cosserat rod finite element formulations

The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where test functions arise from a consistent variation of ansatz functions. This approach becomes increasingly complex when highly nonlinear are chosen to approximate rod's centerline and cross-section orientations. Using Petrov–Galerkin we propose whole family nodal generalized virtual displacements velocities interpolated instead using variations time derivatives leads significant simplification expressions discrete work functionals. In addition, independent strategies can be for interpolating points We discuss three objective interpolation give an in-depth analysis concerning locking convergence behavior formulations.