Implicit Folding Simulation of Ultrathin Shells Using Refined One-Dimensional Finite Elements

The focus of this study is the numerical simulation of the folding of ultrathin shells, focusing on slender deployable longerons. The proposed solution leverages the finite element method, specifically within the framework of the Carrera unified formulation, to develop one-dimensional finite elements with enhanced three-dimensional capabilities. Refined one-dimensional beam finite elements are used to model the longerons, and the three-dimensional displacement field is computed as a general expansion of the nodal displacements along the axis. The folding of these deployable structures is simulated with an implicit approach, and quasi-static simulation is performed. Moreover, a novel node-to-surface contact is introduced, where nonlinear springs act upon predefined node pairs. Simulations of a 400-mm-long longeron are conducted to fine-tune the parameters of the nonlinear spring stiffness. A deployable structure comprising two 400-mm-long longerons connected by transverse straight battens is analyzed. The results are compared with reference results obtained with the Abaqus software, revealing a noteworthy degree of agreement. The proposed method is also employed to simulate the folding of longer strips (1 and 5 m in length), where elements are not strictly constrained by aspect ratios, and it efficiently handles these structures.