Large deformations of in-plane beam

A theory of large deformations of straight slender in-plane beam is presented, based on the assumption of uniaxiality of the strain tensor. The integration of the compatibility conditions gives the parabolic variation of the axial component of the strain tensor over the cross-section of the beam. The integration of the kinematic equations gives linear variation of the displacement components over the cross-section. The equilibrium equations are written on a deformed configuration and numerically solved for linear elastic cantilever, subjected to concentrated or distributed conservative and nonconservative loads.