Direct Computation of Higher Order Mode Components from Successively Linearized Geometrically Nonlinear Beam Theory

Kurzfassung

The extended modal approach is a simplified nonlinear method for the steady and unsteady computation of geometrically nonlinear structural deflections that was developed for loads and flight dynamics analyses of highly flexible aircraft. Compared to the classical modal approach, which is based on the superposition of normal modes, the extensions include higher order stiffness terms and higher order mode components to account for nonlinearities both in the load displacement relationships (cubic stiffness terms) as well as in the geometrically nonlinear displacement field (large deflections and rotations of structural components). These extensions make the method particularly suitable for aeroelastic applications involving highly flexible structures and nonlinearities due to nonconservative loads. In this work, a new approach for the calculation of the higher order mode components is proposed which uses the nonlinear relationships between strains (or curvatures) and displacements from a geometrically nonlinear beam theory. The idea is to take the curvatures of a particular structural mode and to integrate them using successively linearized compatibility equations to compute the higher order mode components. In his way, the higher order mode components are directly obtained, and the costly pre-processing step with a series of nonlinear static simulations is circumvented.