Geometrically nonlinear analysis of non-prismatic beam structures using strong Unified Formulation

Geometrically nonlinear analysis is essential for characterizing the behavior of non-prismatic beam structures including wings, rotor blades and space antennas that undergo large deflections and rotations in service. Due to inherent flexibility of its kinematics representation, the Unified Formulation (UF) shows excellent capability for efficient design of structural components. However, the classical isoparametric description of UF limits the application to prismatic structures. In the present work, we propose a geometrically nonlinear anisoparametric UF based on 1D strong-form equilibrium equations to investigate large deflection of non-prismatic structures. A detailed derivation of the 1D strong UF (SUF) combined with Serendipity Lagrange-based cross-sectional finite element is presented. In the context of SUF, Gauss operations are restricted to the variable cross-sections of non-prismatic structures in a discrete sense while the differential quadrature method is used along the axial direction of the beam leading to efficient computation of the stiffness matrix. Numerical examples of cantilevered non-prismatic beam structures under different loading conditions analyzed by the SUF show accurate predictions for global and local structural responses and demonstrate excellent computational efficiency over ABAQUS FE models.