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

DOI10.1002/GAMM.202300008arXiv2304.05036OpenAlexW4382238798MaRDI QIDQ6432713

Publication date: 11 April 2023

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

Full work available at URL: https://doi.org/10.1002/gamm.202300008

Mathematics Subject Classification ID

Thin bodies, structures (74Kxx) Numerical and other methods in solid mechanics (74Sxx) Numerical methods for ordinary differential equations (65Lxx)