Condensation of large finite-element models for wing load analysis with geometrically-nonlinear effects

This paper describes a procedure to construct 1-D geometrically-nonlinear structural dynamics models from built-up 3-D linear finite-element solutions. The nonlinear 1-D model is based on an intrinsic form of the equations of motion, which uses sectional inertial velocities and stress resultants as primary degrees of freedom. It is further written in modal coordinates, which yields an finite-dimensional approximation of the geometrically-exact beam dynamics through ordinary differential equations with quadratic nonlinearities. We show that the evaluation of the coefficients in the resulting equations of motion does not actually require the generation of a finite-element model with beam elements. Instead, they are directly identified in the 3-D model through a process of static condensation on nodes defined along spanwise stations, as it is typically done in aircraft dynamic load analysis. In fact, the method exploits the multi-point constraints of linear load models that are normally used to obtain sectional loads. We illustrate the approach on simple aircraft-type structures modelled using shell elements