Nurbs-based Timoshenko formulation of a geometrically nonlinear planar beam

This paper investigates the nonlinear analysis of planar beams based on the total Lagrangian Timoshenko theory. The isogeometric analysis (IGA) is adopted as the numerical solution technique. Nurbs functions are used to discretize the unknown kinematics, including displacements and rotation, as well as the linearized governing equations. The virtual work principle is employed to derive the nonlinear governing equations and boundary conditions, which are then solved using the Newton-Raphson algorithm. The results of the proposed formulation have been validated by analytical results, as well as through assessments against available numerical results reported in the relevant literature, demonstrating the efficiency and accuracy of the proposed formulation.