Modal rotations: A modal-based method for large structural deformations

The study presents the derivation and application of the Modal Rotation Method (MRM), a novel modeling framework for the computation of large deformations of complex structures using a modal approach. The method targets static analyses of slender structures, accounting for large-deformation nonlinearity. The input for the analysis is linear modal data that is typically obtained from a finite element (FE) modal analysis. However, the MRM uses modal rotation data, rather than deformation modes. The modal rotations are used for the solution of the nonlinear kinematic problem along with an iterative load correction procedure that accounts for the change in the load distribution in the deformed structure. The method is suitable for structures that cannot be explicitly modeled as a beam, such as structures of multiple different sections, structures having abrupt geometrical changes, and lattice structures. The MRM is verified with three test cases. The first test case is of a simple geometry, two-dimensional beam under tip and distributed loads. Deformations computed with the MRM are shown to be in very good agreement with those computed by a nonlinear FE software while the computational time required for MRM analysis is about two orders of magnitude lower than that of nonlinear FE analysis. In the second test case, the deformations of a complex slender structure, with multiple holes and abrupt geometry changes, under tip loads are computed using the MRM with three-dimensional FE-based modal data. The third test case is a composite wing-like structure with varying sweep angles, camber, and a strongly non-isotropic stack-up, acted by a distributed load. The second and third test cases were specifically designed to challenge the MRM with their complex geometries. In both cases, the deformation errors are less than 2% compared to nonlinear FE analysis, and the computational time is about two orders of magnitude lower. A parametric study presents the dependency of the results on different computational parameters and the load magnitude. It is shown that the method can handle very large loads, and yields accurate results with reasonable selection of the computational parameters. For some extreme loading cases, the MRM converged to a solution while the nonlinear FE analysis did not, demonstrating its numerical stability.