Three-dimensional finite rotations treatment based on a minimal set parameterization and vector space operations in beam elements

Aminimal set vectorial parameterization involving vector space operations is proposed for finite 3D rotations in structural analysis. In this approach, based on the updated Lagrangian description, complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. In particular, slopes are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. This approach is applied to a geometrically nonlinear formulation for 3D beam elements in the hypotheses of large rotations and small strains. Numerical tests have been carried out to validate the developed technique in the frame structures context.