Numerical Aspects of Nonlinear Flexible Aircraft Flight Dynamics Modeling

A critical review of the numerical approximations made in flexible aircraft dynamics modeling is presented. The baseline model is a geometrically-exact. composite beam model describing the flexible-body dynamics which are subject to aerodynamic forces predicted using the unsteady vortex-lattice method (UVLM). The objectivity of the beam formulation is first investigated for static problems with large nodal rotations. It is found that errors associated with non-objectivity of the formulation are minimized to negligible levels using quadratic (3-noded) elements. In addition to this, two force calculation methods are presented and compared for the UVLM. They show subtle but important differences when applied to unsteady aerodynamic problems with large displacements. Nonlinear static aeroelastic analysis of a very flexible high-altitude long-endurance (HALE) wing is also carried out. and time-marching analysis is applied to the Goland wing in order to predict to the response at, and around, the flutter velocity. Conclusions drawn from the studies in this work work are directly applicable in the identification of appropriate modeling strategies in nonlinear flexible aircraft flight dynamics simulations. © 2013 by Robert J. S. Simpson and Rafael Palacios

Simplified buckling analysis of skeletal structures

Accepted versio

Stability and power optimality in time-periodic flapping wing structures

This paper investigates the nonlinear dynamics of a vehicle with two flexible flapping wings. The body dynamics and the wings\u27 deformation are monolithically grouped into a single system of equations, with aerodynamics accounted for by a quasi-steady blade element method. A periodic shooting method is then used to locate closed orbits of this non-autonomous system, and Floquet multipliers assess the linearized stability about the nonlinear orbit. This framework is then exposed to a gradient based optimizer, in order to quantify the role of wing planform variables, wing structure variables, and kinematic actuation variables in obtaining vehicles with superior open-loop stability characteristics, and/or low-power requirements

Nonlinear Aeroelastic Framework Based on Vortex-Lattice Method and Corotational Shell Finite Element

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97077/1/AIAA2012-1976.pd

Efficient and reliable nonlocal damage models

We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between nonadjacent finite elements associated to nonlocality––are addressed in detail. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. Efficiency is achieved by a proper combination of load-stepping control technique and iterative solver for the nonlinear equilibrium equations. A major issue is the computation of the consistent tangent matrix, which is nontrivial due to nonlocal interaction between Gauss points. With computational efficiency in mind, we also present a new nonlocal damage model based on the nonlocal average of displacements. For this new model, the consistent tangent matrix is considerably simpler to compute than for current models. The various ideas discussed in the paper are illustrated by means of three application examples: the uniaxial tension test, the three-point bending test and the single-edge notched beam test.Peer ReviewedPostprint (author’s final draft