A finite element analysis is performed for large elastic deformations of a beam using cross-section integrated 3-dimensional beam element. It is assumed that deformations of a beam undergoes a small elastic strains with possibly large rotations or large displacements, and that plane cross-section remains plane when a small distortion of cross-section due to warping, which has the magnitude of order of strains, is ignored. Deformations of a beam is represented by independent interpolation functions for displacement and rotational degree of freedoms. Rotation of cross-section is objectively updated with the aid of orthogonal transformation defined by rotational degree of freedom at nodes to treat finite rotations. the updated Langrangian procedure for finite element analysis, derived from virtual work principle in continuum mechanics, is used for programming.
Solutions for several examples of elastic deformations with small strains but with possibly large rotations are obtained and confirmed through comparison to elasticity solutions, which are accurate to first order in strains.
