LAUSR

Abstract Based on the geometrically exact beam theory, a novel force-based beam finite element formulation is proposed in this paper for geometrically nonlinear analysis of functional graded (FG) curved beams with discontinuous stiffness. In this formulation, the distributions of stress resultants including axial force, shear force and bending moment along the beam’s axis are treated as the unknown fields of the beam, and the specific forms of these unknown fields are predefined according to the equilibrium differential equations of geometrically exact beam. The element equation system and its linearization are detailed for implementation of incremental/iterative solution scheme. Numerical examples are presented to validate the formulation proposed in this study. As revealed by the numerical results, the proposed element has excellent performance and can achieve high solution accuracy in geometrically nonlinear analysis of curved beams, especially for those with discontinuous stiffness. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of the FG circular arch, and the impact of FG material parameters on the level of nonlinear stability is discussed.