Large Rotation Finite Element Analysis of 3D Beams Based on Incremental Rotation Vector and Exact Strain Measures

Abstract

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing beams undergoing large rotations. The interpolation of the total rotation vector is path independent but also singular at the full angle and non objective. The interpolation of the incremental rotation vector avoids the singularity but is also non objective and leads to path dependence. In this work, we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations, which are then interpolated for the evaluation of the nonlinear strains. This choice makes the approach singularity-free, allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation: rotational variables, objectivity, exact strain measure, path independence and symmetric stiffness matrix for conservative loads.