This work deals with the analysis of highly flexible composite booms subjected to large displacements and rotations. The governing nonlinear equations of lower- to higher-order ID structural theories for laminated flexible beams are expressed as degenerated cases of the three-dimensional elasticity equilibrium via an appropriate index notation and by employing the Carrera unified formulation. Although the provided equations are valid for any one-dimensional structural theory in a unified sense, mostly layer-wise kinematics are employed here through the use of Lagrange polynomial expansions of the primary mechanical variables. The principle of virtual work and a finite element approximation are, thus, used to formulate the governing equations in a total Lagrangian manner, whereas a Newton-Raphson linearization scheme along with a path-following method based on the arc-length constraint is exploited to solve the geometrically nonlinear problem. It is demonstrated that the proposed method is accurate and efficient. It can provide the correct 3D strain/stress fields in any equilibrium regime and with limited computational efforts.
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