Next-generation civil aircraft and atmospheric satellites will have high-aspect-ratio wings. Such a design necessitates successive analysis of static, frequency, and time-domain dynamic responses based on a three-dimensional nonlinear beam model. In this study, a new successive-analysis framework based on an absolute nodal coordinate formulation with mean artificial strains (ANCF-MAS) is developed. While retaining the advantages of other three-dimensional (3D) ANCF approaches, such as constancy of the mass matrix and absence of velocity-dependent terms, ANCF-MAS uses the elastic force of the mean artificial strains to remove cross-sectional deformations that cause locking problems. The equation becomes a differential equation with an easily linearized elastic force that enables not only static and dynamic analyses but also frequency analysis using standard eigenvalue solvers. The solutions converge to the analytical frequencies without suffering from locking problems. A proposed successive-analysis method with model-order reduction reveals that the frequencies vary with the nonlinear static deformation because of the 3D deformation coupling. This reduced-order model agrees well with nonlinear models even when the wing experiences a large nonlinear dynamic deformation.