Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.

基于几何精确梁理论，开发了一阶剪切可变形弯曲梁单元，用于功能梯度（FG）弯曲梁的几何非线性分析。为了准确预测横向剪应力的分布，采用位移和内力为独立场的混合有限元方法，将应力平衡条件引入单元公式中。通过进行一致的线性化程序，获得了用于非线性迭代解的单元节点力矢量和一致的切线刚度矩阵。给出了数值示例，以验证当前的公式。如数值结果所示，所提出的元素证明了高水平的求解精度和良好的适用性。此外，使用建议的元素，