Continuum Modeling for Deployable Space Trusses with Collapsible Tubular Masts

An equivalent continuum model is developed for 2D and 3D square deployable space trusses consisting of composite Collapsible Tubular Mast (CTM) members. The repetitive nature of these structures allow for the utilization of single unit cell geometries in deriving effective stiffness and mass properties through energy equivalence, which are then compatible with continuous structural analysis such as standard beam theory. This provides an efficient method of approximating the global structural performance over a large parameter space for design optimization. Finite element analysis (FEA) in Abaqus/Standard models the CTM members as beam elements with direction dependent stiffnesses. End moment releases on the beam elements simulate how the CTM members are joined together by bonding the ends in a flattened state. FEA is used validate the analytical natural frequencies of 2D and 3D square truss configurations including bending, longitudinal, torsional, and warping-shear vibration modes. It also characterizes how the 3D square face arrangement influences the vibration modes based on whether the diagonal members from adjacent faces share common joints. An FEA validated parametric analysis is then conducted to examine how variations in unit cell geometries and truss patterns influence the equivalent continuum vibration modes for 2D and 3D square trusses.