The simulation of deployable composite longerons is not trivial. An appropriate mathematical model should account for large rotations/displacements and an accurate (eventually layer-wise) description of strains and stresses in the far nonlinear regime. In this context, the present work proposes a novel modelling technique for the nonlinear analysis of thin-walled composite booms based on the well-established Carrera unified formulation. Refined beam models are obtained as degenerated cases from 3D elasticity by using a recursive index notation. Then, the nonlinear governing equations are expressed in terms of a few fundamental nuclei, which are invariant of the theory approximation order. Attention is focussed on the simulation of composite Triangular Rollable And Collapsible (TRAC) longerons, with particular emphasis given to the comparison of the numerical results against the experiments carried out at the Space Structures Laboratory at Caltech