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

The study presents a novel method for static analysis of slender structures accounting for large deformations. The Modal Rotations Method (MRM) formulation describes the rotation-change over a structure and the structural deformation as a combination of curvature mode shapes. An iterative procedure is used to update the location and orientation of the external forces acting on the structure and their effect on the internal loads. The method is very simple to implement, even for complex structures, since it only requires linear modes. These can be computed by linear modal analysis, typically in a finite-element software, with no modeling restrictions, enabling the use of detailed finite-element models. The method is derived and demonstrated on a beam acted by a large tip force and distributed load. The MRM yields accurate results compared to those from nonlinear FE codes. It is shown to be robust even for extremely nonlinear cases of a beam undergoing large deformations, far above those of real aircraft wings. The MRM is shown to be highly computationally efficient. For the test case presented, the MRM analysis time is two orders of magnitude shorter than that of the FE analysis. The paper presents a parametric study of the convergence error as a function of the computational parameters used in the modeling process.