Modal Rotations: A Modal-Based Method for Large Structural Deformations of Slender Bodies

Abstract

This study presents the derivation and application of the modal rotations method (MRM), a novel framework for the computation of large deformations of complex wing-like 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 finite-element-based data. 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 geometric stiffening. The method is suitable for cases where the generation of an equivalent beam model is impossible or requires considerable effort, 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 is a simple geometry, a one-dimensional symmetric beam loaded in one plane. The second and third test cases are three-dimensional built-up structures aimed to challenge the method with abrupt geometric changes, orthotropic material coupling, and nontrivial geometries. All test cases yield accurate results compared with nonlinear finite element analyses. Parametric studies present the dependency of the results on different computational parameters and the load magnitude.