A three-dimensional beam element undergoing finite rotations based on slopes and distance measures

A geometrically nonlinear formulation for three-dimensional beam elements in the hypotheses of large rotations and small strains is presented. In this formulation, based on the total Lagrangian description, the use of the rotation parameters is bypassed. Complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. In particular, slopes and distances are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. Numerical tests have been carried out to validate the developed technique in the frame structures context.